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Biostatistics (also known as biometry) are the development and application of
statistical Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industria ...
methods to a wide range of topics in
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
. It encompasses the design of biological
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...
s, the collection and analysis of data from those experiments and the interpretation of the results.


History


Biostatistics and genetics

Biostatistical modeling forms an important part of numerous modern biological theories.
Genetics Genetics is the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) It is an important branch in biology because heredity is vital to organisms' evolution. Gregor Mendel, a Moravian Augustinian friar wor ...
studies, since its beginning, used statistical concepts to understand observed experimental results. Some genetics scientists even contributed with statistical advances with the development of methods and tools.
Gregor Mendel Gregor Johann Mendel, Augustinians, OSA (; cs, Řehoř Jan Mendel; 20 July 1822 – 6 January 1884) was a biologist, meteorologist, mathematician, Augustinians, Augustinian friar and abbot of St Thomas's Abbey, Brno, St. Thomas' Abbey in Br ...
started the genetics studies investigating genetics segregation patterns in families of peas and used statistics to explain the collected data. In the early 1900s, after the rediscovery of Mendel's Mendelian inheritance work, there were gaps in understanding between genetics and evolutionary Darwinism.
Francis Galton Sir Francis Galton, FRS FRAI (; 16 February 1822 – 17 January 1911), was an English Victorian era polymath: a statistician, sociologist, psychologist, anthropologist, tropical explorer, geographer, inventor, meteorologist, proto- ...
tried to expand Mendel's discoveries with human data and proposed a different model with fractions of the heredity coming from each ancestral composing an infinite series. He called this the theory of " Law of Ancestral Heredity". His ideas were strongly disagreed by
William Bateson William Bateson (8 August 1861 – 8 February 1926) was an English biologist who was the first person to use the term genetics to describe the study of heredity, and the chief populariser of the ideas of Gregor Mendel following their rediscove ...
, who followed Mendel's conclusions, that genetic inheritance were exclusively from the parents, half from each of them. This led to a vigorous debate between the biometricians, who supported Galton's ideas, as
Raphael Weldon Walter Frank Raphael Weldon Fellow of the Royal Society, FRS (15 March 1860 – 13 April 1906), was an English evolutionary biologist and a founder of biometry. He was the joint founding editor of ''Biometrika'', with Francis Galton and Karl Pea ...
,
Arthur Dukinfield Darbishire Arthur Dukinfield Darbishire FRSE (14 February 1879 – 26 December 1915) was a short-lived but influential British zoologist and geneticist. He was the first person to lecture in Genetics in the UK. He caused a stir in the world of genetics ...
and
Karl Pearson Karl Pearson (; born Carl Pearson; 27 March 1857 – 27 April 1936) was an English mathematician and biostatistician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university st ...
, and Mendelians, who supported Bateson's (and Mendel's) ideas, such as
Charles Davenport Charles Benedict Davenport (June 1, 1866 – February 18, 1944) was a biologist and eugenics, eugenicist influential in the Eugenics in the United States, American eugenics movement. Early life and education Davenport was born in Stamford, Co ...
and
Wilhelm Johannsen Wilhelm Johannsen (3 February 1857 – 11 November 1927) was a Danish pharmacist, botanist, plant physiologist, and geneticist. He is best known for coining the terms gene, phenotype and genotype, and for his 1903 "pure line" experiments in g ...
. Later, biometricians could not reproduce Galton conclusions in different experiments, and Mendel's ideas prevailed. By the 1930s, models built on statistical reasoning had helped to resolve these differences and to produce the neo-Darwinian
modern evolutionary synthesis Modern synthesis or modern evolutionary synthesis refers to several perspectives on evolutionary biology, namely: * Modern synthesis (20th century), the term coined by Julian Huxley in 1942 to denote the synthesis between Mendelian genetics and s ...
. Solving these differences also allowed to define the concept of population genetics and brought together genetics and evolution. The three leading figures in the establishment of
population genetics Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and pop ...
and this synthesis all relied on statistics and developed its use in biology. *
Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who a ...
worked alongside statistician Betty Allan developing several basic statistical methods in support of his work studying the crop experiments at
Rothamsted Research Rothamsted Research, previously known as the Rothamsted Experimental Station and then the Institute of Arable Crops Research, is one of the oldest agricultural research institutions in the world, having been founded in 1843. It is located at Harp ...
, published in Fisher's books
Statistical Methods for Research Workers ''Statistical Methods for Research Workers'' is a classic book on statistics, written by the statistician R. A. Fisher. It is considered by some to be one of the 20th century's most influential books on statistical methods, together with his ''The ...
(1925) and
The Genetical Theory of Natural Selection ''The Genetical Theory of Natural Selection'' is a book by Ronald Fisher which combines Mendelian genetics with Charles Darwin's theory of natural selection, with Fisher being the first to argue that "Mendelism therefore validates Darwinism" and ...
(1930), as well as Allan's scientific papers. Fisher went on to give many contributions to genetics and statistics. Some of them include the
ANOVA Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician ...
,
p-value In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means ...
concepts,
Fisher's exact test Fisher's exact test is a statistical significance test used in the analysis of contingency tables. Although in practice it is employed when sample sizes are small, it is valid for all sample sizes. It is named after its inventor, Ronald Fisher, ...
and
Fisher's equation In mathematics, Fisher's equation (named after statistician and biologist Ronald Fisher) also known as the Kolmogorov–Petrovsky–Piskunov equation (named after Andrey Kolmogorov, Ivan Petrovsky, and Nikolai Piskunov), KPP equation or Fisher ...
for
population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has ...
. He is credited for the sentence "Natural selection is a mechanism for generating an exceedingly high degree of improbability". * Sewall G. Wright developed
F-statistics In population genetics, ''F''-statistics (also known as fixation indices) describe the statistically expected level of heterozygosity in a population; more specifically the expected degree of (usually) a reduction in heterozygosity when compared ...
and methods of computing them and defined
inbreeding coefficient The coefficient of inbreeding of an individual is the probability that two alleles at any locus in an individual are identical by descent from the common ancestor(s) of the two parents. The coefficient of inbreeding is: The probability that two ...
. *
J. B. S. Haldane John Burdon Sanderson Haldane (; 5 November 18921 December 1964), nicknamed "Jack" or "JBS", was a British-Indian scientist who worked in physiology, genetics, evolutionary biology, and mathematics. With innovative use of statistics in biolog ...
's book, ''The Causes of Evolution'', reestablished natural selection as the premier mechanism of evolution by explaining it in terms of the mathematical consequences of Mendelian genetics. He also developed the theory of
primordial soup Primordial soup, also known as, primordial goo, primordial ooze, prebiotic soup and prebiotic broth, is the hypothetical set of conditions present on the Earth around 3.7 to 4.0 billion years ago. It is an aspect of the heterotrophic theory (also k ...
. These and other biostatisticians, mathematical biologists, and statistically inclined geneticists helped bring together
evolutionary biology Evolutionary biology is the subfield of biology that studies the evolutionary processes (natural selection, common descent, speciation) that produced the diversity of life on Earth. It is also defined as the study of the history of life fo ...
and
genetics Genetics is the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) It is an important branch in biology because heredity is vital to organisms' evolution. Gregor Mendel, a Moravian Augustinian friar wor ...
into a consistent, coherent whole that could begin to be
quantitative Quantitative may refer to: * Quantitative research, scientific investigation of quantitative properties * Quantitative analysis (disambiguation) * Quantitative verse, a metrical system in poetry * Statistics, also known as quantitative analysis ...
ly modeled. In parallel to this overall development, the pioneering work of
D'Arcy Thompson Sir D'Arcy Wentworth Thompson CB FRS FRSE (2 May 1860 – 21 June 1948) was a Scottish biologist, mathematician and classics scholar. He was a pioneer of mathematical and theoretical biology, travelled on expeditions to the Bering Strait a ...
in ''On Growth and Form'' also helped to add quantitative discipline to biological study. Despite the fundamental importance and frequent necessity of statistical reasoning, there may nonetheless have been a tendency among biologists to distrust or deprecate results which are not qualitatively apparent. One anecdote describes
Thomas Hunt Morgan Thomas Hunt Morgan (September 25, 1866 – December 4, 1945) was an American evolutionary biologist, geneticist, embryologist, and science author who won the Nobel Prize in Physiology or Medicine in 1933 for discoveries elucidating the role tha ...
banning the Friden calculator from his department at
Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
, saying "Well, I am like a guy who is prospecting for gold along the banks of the Sacramento River in 1849. With a little intelligence, I can reach down and pick up big nuggets of gold. And as long as I can do that, I'm not going to let any people in my department waste scarce resources in
placer mining Placer mining () is the mining of stream bed (Alluvium, alluvial) deposits for minerals. This may be done by open-pit mining, open-pit (also called open-cast mining) or by various surface excavating equipment or tunneling equipment. Placer minin ...
."


Research planning

Any research in
life sciences This list of life sciences comprises the branches of science that involve the scientific study of life – such as microorganisms, plants, and animals including human beings. This science is one of the two major branches of natural science, the ...
is proposed to answer a scientific question we might have. To answer this question with a high certainty, we need
accurate Accuracy and precision are two measures of '' observational error''. ''Accuracy'' is how close a given set of measurements ( observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each ot ...
results. The correct definition of the main
hypothesis A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous obse ...
and the research plan will reduce errors while taking a decision in understanding a phenomenon. The research plan might include the research question, the hypothesis to be tested, the
experimental design The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...
,
data collection Data collection or data gathering is the process of gathering and measuring information on targeted variables in an established system, which then enables one to answer relevant questions and evaluate outcomes. Data collection is a research com ...
methods,
data analysis Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, enco ...
perspectives and costs involved. It is essential to carry the study based on the three basic principles of experimental statistics:
randomization Randomization is the process of making something random. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution d ...
, replication, and local control.


Research question

The research question will define the objective of a study. The research will be headed by the question, so it needs to be concise, at the same time it is focused on interesting and novel topics that may improve science and knowledge and that field. To define the way to ask the scientific question, an exhaustive
literature review A literature review is an overview of the previously published works on a topic. The term can refer to a full scholarly paper or a section of a scholarly work such as a book, or an article. Either way, a literature review is supposed to provid ...
might be necessary. So the research can be useful to add value to the
scientific community The scientific community is a diverse network of interacting scientists. It includes many " sub-communities" working on particular scientific fields, and within particular institutions; interdisciplinary and cross-institutional activities are als ...
.


Hypothesis definition

Once the aim of the study is defined, the possible answers to the research question can be proposed, transforming this question into a
hypothesis A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous obse ...
. The main propose is called
null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...
(H0) and is usually based on a permanent knowledge about the topic or an obvious occurrence of the phenomena, sustained by a deep literature review. We can say it is the standard expected answer for the data under the situation in
test Test(s), testing, or TEST may refer to: * Test (assessment), an educational assessment intended to measure the respondents' knowledge or other abilities Arts and entertainment * ''Test'' (2013 film), an American film * ''Test'' (2014 film), ...
. In general, HO assumes no association between treatments. On the other hand, the alternative hypothesis is the denial of HO. It assumes some degree of association between the treatment and the outcome. Although, the hypothesis is sustained by question research and its expected and unexpected answers. As an example, consider groups of similar animals (mice, for example) under two different diet systems. The research question would be: what is the best diet? In this case, H0 would be that there is no difference between the two diets in mice
metabolism Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run cell ...
(H0: μ1 = μ2) and the alternative hypothesis would be that the diets have different effects over animals metabolism (H1: μ1 ≠ μ2). The
hypothesis A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous obse ...
is defined by the researcher, according to his/her interests in answering the main question. Besides that, the alternative hypothesis can be more than one hypothesis. It can assume not only differences across observed parameters, but their degree of differences (''i.e.'' higher or shorter).


Sampling

Usually, a study aims to understand an effect of a phenomenon over a
population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
. In
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
, a
population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
is defined as all the
individuals An individual is that which exists as a distinct entity. Individuality (or self-hood) is the state or quality of being an individual; particularly (in the case of humans) of being a person unique from other people and possessing one's own need ...
of a given
species In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate s ...
, in a specific area at a given time. In biostatistics, this concept is extended to a variety of collections possible of study. Although, in biostatistics, a
population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
is not only the
individuals An individual is that which exists as a distinct entity. Individuality (or self-hood) is the state or quality of being an individual; particularly (in the case of humans) of being a person unique from other people and possessing one's own need ...
, but the total of one specific component of their
organisms In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells (cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and fungi; ...
, as the whole
genome In the fields of molecular biology and genetics, a genome is all the genetic information of an organism. It consists of nucleotide sequences of DNA (or RNA in RNA viruses). The nuclear genome includes protein-coding genes and non-coding ge ...
, or all the sperm cells, for animals, or the total leaf area, for a plant, for example. It is not possible to take the
measures Measure may refer to: * Measurement, the assignment of a number to a characteristic of an object or event Law * Ballot measure, proposed legislation in the United States * Church of England Measure, legislation of the Church of England * Measu ...
from all the elements of a
population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
. Because of that, the sampling process is very important for
statistical inference Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution, distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical ...
. Sampling is defined as to randomly get a representative part of the entire population, to make posterior inferences about the population. So, the
sample Sample or samples may refer to: Base meaning * Sample (statistics), a subset of a population – complete data set * Sample (signal), a digital discrete sample of a continuous analog signal * Sample (material), a specimen or small quantity of s ...
might catch the most variability across a population. The
sample size Sample size determination is the act of choosing the number of observations or Replication (statistics), replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make stat ...
is determined by several things, since the scope of the research to the resources available. In
clinical research Clinical research is a branch of healthcare science that determines the safety and effectiveness ( efficacy) of medications, devices, diagnostic products and treatment regimens intended for human use. These may be used for prevention, treatm ...
, the trial type, as
inferiority In psychology, an inferiority complex is an intense personal feeling of inadequacy, often resulting in the belief that one is in some way deficient, or inferior, to others. According to Alfred Adler, a feeling of inferiority may be brought ab ...
, equivalence, and superiority is a key in determining sample
size Size in general is the Magnitude (mathematics), magnitude or dimensions of a thing. More specifically, ''geometrical size'' (or ''spatial size'') can refer to linear dimensions (length, width, height, diameter, perimeter), area, or volume ...
.


Experimental design

Experimental designs sustain those basic principles of experimental statistics. There are three basic experimental designs to randomly allocate treatments in all plots of the
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...
. They are
completely randomized design In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take other nuisance variables into account. This article describes completely randomized designs that have one primar ...
,
randomized block design In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another. Blocking can be used to tackle the problem of pseudoreplication. Use Blocking reduces un ...
, and factorial designs. Treatments can be arranged in many ways inside the experiment. In
agriculture Agriculture or farming is the practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that enabled people to ...
, the correct
experimental design The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...
is the root of a good study and the arrangement of treatments within the study is essential because
environment Environment most often refers to: __NOTOC__ * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...
largely affects the plots (
plants Plants are predominantly Photosynthesis, photosynthetic eukaryotes of the Kingdom (biology), kingdom Plantae. Historically, the plant kingdom encompassed all living things that were not animals, and included algae and fungi; however, all curr ...
,
livestock Livestock are the domesticated animals raised in an agricultural setting to provide labor and produce diversified products for consumption such as meat, eggs, milk, fur, leather, and wool. The term is sometimes used to refer solely to animals ...
,
microorganisms A microorganism, or microbe,, ''mikros'', "small") and ''organism'' from the el, ὀργανισμός, ''organismós'', "organism"). It is usually written as a single word but is sometimes hyphenated (''micro-organism''), especially in olde ...
). These main arrangements can be found in the literature under the names of " lattices", "incomplete blocks", " split plot", "augmented blocks", and many others. All of the designs might include control plots, determined by the researcher, to provide an error estimation during
inference Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...
. In
clinical studies Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dietar ...
, the
sample Sample or samples may refer to: Base meaning * Sample (statistics), a subset of a population – complete data set * Sample (signal), a digital discrete sample of a continuous analog signal * Sample (material), a specimen or small quantity of s ...
s are usually smaller than in other biological studies, and in most cases, the
environment Environment most often refers to: __NOTOC__ * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...
effect can be controlled or measured. It is common to use randomized controlled clinical trials, where results are usually compared with
observational study In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws inferences from a sample (statistics), sample to a statistical population, population where the dependent and independent variables, independ ...
designs such as case–control or
cohort Cohort or cohortes may refer to: * Cohort (educational group), a group of students working together through the same academic curriculum * Cohort (floating point), a set of different encodings of the same numerical value * Cohort (military unit ...
.


Data collection

Data collection methods must be considered in research planning, because it highly influences the sample size and experimental design. Data collection varies according to type of data. For
qualitative data Qualitative properties are properties that are observed and can generally not be measured with a numerical result. They are contrasted to quantitative properties which have numerical characteristics. Some engineering and scientific properties are ...
, collection can be done with structured questionnaires or by observation, considering presence or intensity of disease, using score criterion to categorize levels of occurrence. For
quantitative data Quantitative research is a research strategy that focuses on quantifying the collection and analysis of data. It is formed from a deductive approach where emphasis is placed on the testing of theory, shaped by empiricist and positivist philoso ...
, collection is done by measuring numerical information using instruments. In agriculture and biology studies, yield data and its components can be obtained by metric measures. However, pest and disease injuries in plats are obtained by observation, considering score scales for levels of damage. Especially, in genetic studies, modern methods for data collection in field and laboratory should be considered, as high-throughput platforms for phenotyping and genotyping. These tools allow bigger experiments, while turn possible evaluate many plots in lower time than a human-based only method for data collection. Finally, all data collected of interest must be stored in an organized data frame for further analysis.


Analysis and data interpretation


Descriptive tools

Data can be represented through
tables Table may refer to: * Table (furniture), a piece of furniture with a flat surface and one or more legs * Table (landform), a flat area of land * Table (information), a data arrangement with rows and columns * Table (database), how the table data ...
or
graphical Graphics () are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain. In contemporary usage, it includes a pictorial representation of data, as in design and manufacture ...
representation, such as line charts, bar charts, histograms, scatter plot. Also, measures of central tendency and variability can be very useful to describe an overview of the data. Follow some examples:


Frequency tables

One type of tables are the
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
table, which consists of data arranged in rows and columns, where the frequency is the number of occurrences or repetitions of data. Frequency can be: Absolute: represents the number of times that a determined value appear; N = f_1 + f_2 + f_3 + ... + f_n Relative: obtained by the division of the absolute frequency by the total number; n_i = \frac In the next example, we have the number of genes in ten
operon In genetics, an operon is a functioning unit of DNA containing a cluster of genes under the control of a single promoter. The genes are transcribed together into an mRNA strand and either translated together in the cytoplasm, or undergo splic ...
s of the same organism. :


Line graph

Line graph In the mathematical discipline of graph theory, the line graph of an undirected graph is another graph that represents the adjacencies between edges of . is constructed in the following way: for each edge in , make a vertex in ; for every ...
s represent the variation of a value over another metric, such as time. In general, values are represented in the vertical axis, while the time variation is represented in the horizontal axis.


Bar chart

A
bar chart A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is ...
is a graph that shows categorical data as bars presenting heights (vertical bar) or widths (horizontal bar) proportional to represent values. Bar charts provide an image that could also be represented in a tabular format. In the bar chart example, we have the birth rate in Brazil for the December months from 2010 to 2016. The sharp fall in December 2016 reflects the outbreak of
Zika virus ''Zika virus'' (ZIKV; pronounced or ) is a member of the virus family ''Flaviviridae''. It is spread by daytime-active ''Aedes'' mosquitoes, such as '' A. aegypti'' and '' A. albopictus''. Its name comes from the Ziika Forest of Uganda, whe ...
in the birth rate in Brazil.


Histograms

The
histogram A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to " bin" (or "bucket") the range of values—that is, divide the ent ...
(or frequency distribution) is a graphical representation of a dataset tabulated and divided into uniform or non-uniform classes. It was first introduced by
Karl Pearson Karl Pearson (; born Carl Pearson; 27 March 1857 – 27 April 1936) was an English mathematician and biostatistician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university st ...
.


Scatter plot

A
scatter plot A scatter plot (also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram) is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. ...
is a mathematical diagram that uses Cartesian coordinates to display values of a dataset. A scatter plot shows the data as a set of points, each one presenting the value of one variable determining the position on the horizontal axis and another variable on the vertical axis. They are also called scatter graph, scatter chart, scattergram, or scatter diagram.


Mean

The
arithmetic mean In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The colle ...
is the sum of a collection of values () divided by the number of items of this collection (). : \bar = \frac\left (\sum_^n\right ) = \frac


Median

The
median In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic fe ...
is the value in the middle of a dataset.


Mode

The
mode Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...
is the value of a set of data that appears most often.


Box plot

Box plot In descriptive statistics, a box plot or boxplot is a method for graphically demonstrating the locality, spread and skewness groups of numerical data through their quartiles. In addition to the box on a box plot, there can be lines (which are ca ...
is a method for graphically depicting groups of numerical data. The maximum and minimum values are represented by the lines, and the interquartile range (IQR) represent 25–75% of the data.
Outlier In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are ...
s may be plotted as circles.


Correlation coefficients

Although correlations between two different kinds of data could be inferred by graphs, such as scatter plot, it is necessary validate this though numerical information. For this reason,
correlation coefficient A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components ...
s are required. They provide a numerical value that reflects the strength of an association.


Pearson correlation coefficient

Pearson correlation coefficient In statistics, the Pearson correlation coefficient (PCC, pronounced ) ― also known as Pearson's ''r'', the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ...
is a measure of association between two variables, X and Y. This coefficient, usually represented by ''ρ'' (rho) for the population and ''r'' for the sample, assumes values between −1 and 1, where ''ρ'' = 1 represents a perfect positive correlation, ''ρ'' = −1 represents a perfect negative correlation, and ''ρ'' = 0 is no linear correlation.


Inferential statistics

It is used to make
inference Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...
s about an unknown population, by estimation and/or hypothesis testing. In other words, it is desirable to obtain parameters to describe the population of interest, but since the data is limited, it is necessary to make use of a representative sample in order to estimate them. With that, it is possible to test previously defined hypotheses and apply the conclusions to the entire population. The standard error of the mean is a measure of variability that is crucial to do inferences. *
Hypothesis testing A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...
Hypothesis testing is essential to make inferences about populations aiming to answer research questions, as settled in "Research planning" section. Authors defined four steps to be set: # ''The hypothesis to be tested'': as stated earlier, we have to work with the definition of a
null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...
(H0), that is going to be tested, and an alternative hypothesis. But they must be defined before the experiment implementation. # ''Significance level and decision rule'': A decision rule depends on the
level of significance In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the fa ...
, or in other words, the acceptable error rate (α). It is easier to think that we define a ''critical value'' that determines the statistical significance when a
test statistic A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.Berger, R. L.; Casella, G. (2001). ''Statistical Inference'', Duxbury Press, Second Edition (p.374) A hypothesis test is typically specifi ...
is compared with it. So, α also has to be predefined before the experiment. # ''Experiment and statistical analysis'': This is when the experiment is really implemented following the appropriate
experimental design The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...
, data is collected and the more suitable statistical tests are evaluated. # ''Inference'': Is made when the
null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...
is rejected or not rejected, based on the evidence that the comparison of
p-value In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means ...
s and α brings. It is pointed that the failure to reject H0 just means that there is not enough evidence to support its rejection, but not that this hypothesis is true. *
Confidence intervals In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as 9 ...
A confidence interval is a range of values that can contain the true real parameter value in given a certain level of confidence. The first step is to estimate the best-unbiased estimate of the population parameter. The upper value of the interval is obtained by the sum of this estimate with the multiplication between the standard error of the mean and the confidence level. The calculation of lower value is similar, but instead of a sum, a subtraction must be applied.


Statistical considerations


Power and statistical error

When testing a hypothesis, there are two types of statistic errors possible:
Type I error In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the fa ...
and
Type II error In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the f ...
. The type I error or
false positive A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present), while a false negative is the opposite error, where the test result ...
is the incorrect rejection of a true null hypothesis and the type II error or
false negative A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present), while a false negative is the opposite error, where the test result ...
is the failure to reject a false
null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...
. The
significance level In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis (simply by chance alone). More precisely, a study's defined significance level, denoted by \alpha, is the ...
denoted by α is the type I error rate and should be chosen before performing the test. The type II error rate is denoted by β and statistical power of the test is 1 − β.


p-value

The
p-value In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means ...
is the probability of obtaining results as extreme as or more extreme than those observed, assuming the
null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...
(H0) is true. It is also called the calculated probability. It is common to confuse the p-value with the significance level (α), but, the α is a predefined threshold for calling significant results. If p is less than α, the null hypothesis (H0) is rejected.


Multiple testing

In multiple tests of the same hypothesis, the probability of the occurrence of falses positives (familywise error rate) increase and some strategy are used to control this occurrence. This is commonly achieved by using a more stringent threshold to reject null hypotheses. The
Bonferroni correction In statistics, the Bonferroni correction is a method to counteract the multiple comparisons problem. Background The method is named for its use of the Bonferroni inequalities. An extension of the method to confidence intervals was proposed by Oliv ...
defines an acceptable global significance level, denoted by α* and each test is individually compared with a value of α = α*/m. This ensures that the familywise error rate in all m tests, is less than or equal to α*. When m is large, the Bonferroni correction may be overly conservative. An alternative to the Bonferroni correction is to control the false discovery rate (FDR). The FDR controls the expected proportion of the rejected
null hypotheses In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...
(the so-called discoveries) that are false (incorrect rejections). This procedure ensures that, for independent tests, the false discovery rate is at most q*. Thus, the FDR is less conservative than the Bonferroni correction and have more power, at the cost of more false positives.


Mis-specification and robustness checks

The main hypothesis being tested (e.g., no association between treatments and outcomes) is often accompanied by other technical assumptions (e.g., about the form of the probability distribution of the outcomes) that are also part of the null hypothesis. When the technical assumptions are violated in practice, then the null may be frequently rejected even if the main hypothesis is true. Such rejections are said to be due to model mis-specification. Verifying whether the outcome of a statistical test does not change when the technical assumptions are slightly altered (so-called robustness checks) is the main way of combating mis-specification.


Model selection criteria

Model criteria selection will select or model that more approximate true model. The Akaike's Information Criterion (AIC) and The Bayesian Information Criterion (BIC) are examples of asymptotically efficient criteria.


Developments and big data

Recent developments have made a large impact on biostatistics. Two important changes have been the ability to collect data on a high-throughput scale, and the ability to perform much more complex analysis using computational techniques. This comes from the development in areas as
sequencing In genetics and biochemistry, sequencing means to determine the primary structure (sometimes incorrectly called the primary sequence) of an unbranched biopolymer. Sequencing results in a symbolic linear depiction known as a sequence which succ ...
technologies,
Bioinformatics Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combi ...
and
Machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
(
Machine learning in bioinformatics Machine learning in bioinformatics is the application of machine learning algorithms to bioinformatics, including genomics, proteomics, microarrays, systems biology, evolution, and text mining. Prior to the emergence of machine learning, bioinform ...
).


Use in high-throughput data

New biomedical technologies like
microarrays A microarray is a multiplex lab-on-a-chip. Its purpose is to simultaneously detect the expression of thousands of genes from a sample (e.g. from a tissue). It is a two-dimensional array on a solid substrate—usually a glass slide or silicon t ...
, next-generation sequencers (for genomics) and
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is use ...
(for proteomics) generate enormous amounts of data, allowing many tests to be performed simultaneously. Careful analysis with biostatistical methods is required to separate the signal from the noise. For example, a microarray could be used to measure many thousands of genes simultaneously, determining which of them have different expression in diseased cells compared to normal cells. However, only a fraction of genes will be differentially expressed.
Multicollinearity In statistics, multicollinearity (also collinearity) is a phenomenon in which one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy. In this situation, the coeffic ...
often occurs in high-throughput biostatistical settings. Due to high intercorrelation between the predictors (such as
gene expression Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, protein or non-coding RNA, and ultimately affect a phenotype, as the final effect. The ...
levels), the information of one predictor might be contained in another one. It could be that only 5% of the predictors are responsible for 90% of the variability of the response. In such a case, one could apply the biostatistical technique of dimension reduction (for example via principal component analysis). Classical statistical techniques like linear or
logistic regression In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear function (calculus), linear combination of one or more independent var ...
and
linear discriminant analysis Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features ...
do not work well for high dimensional data (i.e. when the number of observations n is smaller than the number of features or predictors p: n < p). As a matter of fact, one can get quite high R2-values despite very low predictive power of the statistical model. These classical statistical techniques (esp.
least squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...
linear regression) were developed for low dimensional data (i.e. where the number of observations n is much larger than the number of predictors p: n >> p). In cases of high dimensionality, one should always consider an independent validation test set and the corresponding residual sum of squares (RSS) and R2 of the validation test set, not those of the training set. Often, it is useful to pool information from multiple predictors together. For example, Gene Set Enrichment Analysis (GSEA) considers the perturbation of whole (functionally related) gene sets rather than of single genes. These gene sets might be known biochemical pathways or otherwise functionally related genes. The advantage of this approach is that it is more robust: It is more likely that a single gene is found to be falsely perturbed than it is that a whole pathway is falsely perturbed. Furthermore, one can integrate the accumulated knowledge about biochemical pathways (like the
JAK-STAT signaling pathway The JAK-STAT signaling pathway is a chain of interactions between proteins in a cell, and is involved in processes such as immunity, cell division, cell death, and tumour formation. The pathway communicates information from chemical signals out ...
) using this approach.


Bioinformatics advances in databases, data mining, and biological interpretation

The development of
biological database Biological databases are libraries of biological sciences, collected from scientific experiments, published literature, high-throughput experiment technology, and computational analysis. They contain information from research areas including genom ...
s enables storage and management of biological data with the possibility of ensuring access for users around the world. They are useful for researchers depositing data, retrieve information and files (raw or processed) originated from other experiments or indexing scientific articles, as
PubMed PubMed is a free search engine accessing primarily the MEDLINE database of references and abstracts on life sciences and biomedical topics. The United States National Library of Medicine (NLM) at the National Institutes of Health maintain the ...
. Another possibility is search for the desired term (a gene, a protein, a disease, an organism, and so on) and check all results related to this search. There are databases dedicated to
SNPs In genetics, a single-nucleotide polymorphism (SNP ; plural SNPs ) is a germline substitution of a single nucleotide at a specific position in the genome. Although certain definitions require the substitution to be present in a sufficiently larg ...
(
dbSNP The Single Nucleotide Polymorphism Database (dbSNP) is a free public archive for genetic variation within and across different species developed and hosted by the National Center for Biotechnology Information (NCBI) in collaboration with the Natio ...
), the knowledge on genes characterization and their pathways (
KEGG KEGG (Kyoto Encyclopedia of Genes and Genomes) is a collection of databases dealing with genomes, biological pathways, diseases, drugs, and chemical substances. KEGG is utilized for bioinformatics research and education, including data analysis i ...
) and the description of gene function classifying it by cellular component, molecular function and biological process (
Gene Ontology The Gene Ontology (GO) is a major bioinformatics initiative to unify the representation of gene and gene product attributes across all species. More specifically, the project aims to: 1) maintain and develop its controlled vocabulary of gene and g ...
). In addition to databases that contain specific molecular information, there are others that are ample in the sense that they store information about an organism or group of organisms. As an example of a database directed towards just one organism, but that contains much data about it, is the ''
Arabidopsis thaliana ''Arabidopsis thaliana'', the thale cress, mouse-ear cress or arabidopsis, is a small flowering plant native to Eurasia and Africa. ''A. thaliana'' is considered a weed; it is found along the shoulders of roads and in disturbed land. A winter a ...
'' genetic and molecular database – TAIR. Phytozome, in turn, stores the assemblies and annotation files of dozen of plant genomes, also containing visualization and analysis tools. Moreover, there is an interconnection between some databases in the information exchange/sharing and a major initiative was the
International Nucleotide Sequence Database Collaboration The International Nucleotide Sequence Database Collaboration (INSDC) consists of a joint effort to collect and disseminate databases containing DNA and RNA sequences. It involves the following computerized databases: DNA Data Bank of Japan (Japan ...
(INSDC) which relates data from DDBJ, EMBL-EBI, and NCBI. Nowadays, increase in size and complexity of molecular datasets leads to use of powerful statistical methods provided by computer science algorithms which are developed by
machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
area. Therefore, data mining and machine learning allow detection of patterns in data with a complex structure, as biological ones, by using methods of supervised and
unsupervised learning Unsupervised learning is a type of algorithm that learns patterns from untagged data. The hope is that through mimicry, which is an important mode of learning in people, the machine is forced to build a concise representation of its world and t ...
, regression, detection of clusters and association rule mining, among others. To indicate some of them,
self-organizing map A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning technique used to produce a low-dimensional (typically two-dimensional) representation of a higher dimensional data set while preserving the to ...
s and ''k''-means are examples of cluster algorithms;
neural networks A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological ...
implementation and
support vector machine In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. Developed at AT&T Bell Laboratorie ...
s models are examples of common machine learning algorithms. Collaborative work among molecular biologists, bioinformaticians, statisticians and computer scientists is important to perform an experiment correctly, going from planning, passing through data generation and analysis, and ending with biological interpretation of the results.


Use of computationally intensive methods

On the other hand, the advent of modern computer technology and relatively cheap computing resources have enabled computer-intensive biostatistical methods like
bootstrapping In general, bootstrapping usually refers to a self-starting process that is supposed to continue or grow without external input. Etymology Tall boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers ...
and re-sampling methods. In recent times,
random forests Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that operates by constructing a multitude of decision trees at training time. For classification tasks, the output of t ...
have gained popularity as a method for performing
statistical classification In statistics, classification is the problem of identifying which of a set of categories (sub-populations) an observation (or observations) belongs to. Examples are assigning a given email to the "spam" or "non-spam" class, and assigning a diagno ...
. Random forest techniques generate a panel of decision trees. Decision trees have the advantage that you can draw them and interpret them (even with a basic understanding of mathematics and statistics). Random Forests have thus been used for clinical decision support systems.


Applications


Public health

Public health Public health is "the science and art of preventing disease, prolonging life and promoting health through the organized efforts and informed choices of society, organizations, public and private, communities and individuals". Analyzing the det ...
, including
epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decisions and evidenc ...
,
health services research Health services research (HSR) became a burgeoning field in North America in the 1960s, when scientific information and policy deliberation began to coalesce. Sometimes also referred to as health systems research or health policy and systems resear ...
,
nutrition Nutrition is the biochemical and physiological process by which an organism uses food to support its life. It provides organisms with nutrients, which can be metabolized to create energy and chemical structures. Failure to obtain sufficient n ...
,
environmental health Environmental health is the branch of public health concerned with all aspects of the natural and built environment affecting human health. In order to effectively control factors that may affect health, the requirements that must be met in ...
and health care policy & management. In these
medicine Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pract ...
contents, it's important to consider the design and analysis of the
clinical trial Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dietar ...
s. As one example, there is the assessment of severity state of a patient with a prognosis of an outcome of a disease. With new technologies and genetics knowledge, biostatistics are now also used for
Systems medicine Systems medicine is an interdisciplinary field of study that looks at the systems of the human body as part of an integrated whole, incorporating biochemical, physiological, and environment interactions. Systems medicine draws on systems science an ...
, which consists in a more personalized medicine. For this, is made an integration of data from different sources, including conventional patient data, clinico-pathological parameters, molecular and genetic data as well as data generated by additional new-omics technologies.


Quantitative genetics

The study of
Population genetics Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and pop ...
and
Statistical genetics Statistical genetics is a scientific field concerned with the development and application of statistical methods for drawing inferences from genetic data. The term is most commonly used in the context of human genetics. Research in statistical gen ...
in order to link variation in
genotype The genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the alleles or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a ...
with a variation in
phenotype In genetics, the phenotype () is the set of observable characteristics or traits of an organism. The term covers the organism's morphology or physical form and structure, its developmental processes, its biochemical and physiological proper ...
. In other words, it is desirable to discover the genetic basis of a measurable trait, a quantitative trait, that is under polygenic control. A genome region that is responsible for a continuous trait is called
Quantitative trait locus A quantitative trait locus (QTL) is a locus (section of DNA) that correlates with variation of a quantitative trait in the phenotype of a population of organisms. QTLs are mapped by identifying which molecular markers (such as SNPs or AFLPs) c ...
(QTL). The study of QTLs become feasible by using
molecular marker A molecular marker is a molecule, sampled from some source, that gives information about its source. For example, DNA is a molecular marker that gives information about the organism from which it was taken. For another example, some proteins can be ...
s and measuring traits in populations, but their mapping needs the obtaining of a population from an experimental crossing, like an F2 or
Recombinant inbred strain A recombinant inbred strain or recombinant inbred line (RIL) is an organism with chromosomes that incorporate an essentially permanent set of recombination events between chromosomes inherited from two or more inbred strains. F1 and F2 generations ...
s/lines (RILs). To scan for QTLs regions in a genome, a
gene map Gene maps help describe the spatial arrangement of genes on a chromosome. Genes are designated to a specific location on a chromosome known as the locus and can be used as molecular markers to find the distance between other genes on a chromosom ...
based on linkage have to be built. Some of the best-known QTL mapping algorithms are Interval Mapping, Composite Interval Mapping, and Multiple Interval Mapping. However, QTL mapping resolution is impaired by the amount of recombination assayed, a problem for species in which it is difficult to obtain large offspring. Furthermore, allele diversity is restricted to individuals originated from contrasting parents, which limit studies of allele diversity when we have a panel of individuals representing a natural population. For this reason, the
Genome-wide association study In genomics, a genome-wide association study (GWA study, or GWAS), also known as whole genome association study (WGA study, or WGAS), is an observational study of a genome-wide set of Single-nucleotide polymorphism, genetic variants in different i ...
was proposed in order to identify QTLs based on
linkage disequilibrium In population genetics, linkage disequilibrium (LD) is the non-random association of alleles at different loci in a given population. Loci are said to be in linkage disequilibrium when the frequency of association of their different alleles is h ...
, that is the non-random association between traits and molecular markers. It was leveraged by the development of high-throughput
SNP genotyping SNP genotyping is the measurement of genetic variations of single nucleotide polymorphisms (SNPs) between members of a species. It is a form of genotyping, which is the measurement of more general genetic variation. SNPs are one of the most common ...
. In
animal Animals are multicellular, eukaryotic organisms in the Kingdom (biology), biological kingdom Animalia. With few exceptions, animals Heterotroph, consume organic material, Cellular respiration#Aerobic respiration, breathe oxygen, are Motilit ...
and
plant breeding Plant breeding is the science of changing the traits of plants in order to produce desired characteristics. It has been used to improve the quality of nutrition in products for humans and animals. The goals of plant breeding are to produce cro ...
, the use of markers in
selection Selection may refer to: Science * Selection (biology), also called natural selection, selection in evolution ** Sex selection, in genetics ** Mate selection, in mating ** Sexual selection in humans, in human sexuality ** Human mating strategie ...
aiming for breeding, mainly the molecular ones, collaborated to the development of
marker-assisted selection Marker assisted selection or marker aided selection (MAS) is an indirect selection process where a trait of interest is selected based on a marker ( morphological, biochemical or DNA/ RNA variation) linked to a trait of interest (e.g. producti ...
. While QTL mapping is limited due resolution, GWAS does not have enough power when rare variants of small effect that are also influenced by environment. So, the concept of Genomic Selection (GS) arises in order to use all molecular markers in the selection and allow the prediction of the performance of candidates in this selection. The proposal is to genotype and phenotype a training population, develop a model that can obtain the genomic estimated breeding values (GEBVs) of individuals belonging to a genotype and but not phenotype population, called testing population. This kind of study could also include a validation population, thinking in the concept of cross-validation, in which the real phenotype results measured in this population are compared with the phenotype results based on the prediction, what used to check the accuracy of the model. As a summary, some points about the application of quantitative genetics are: * This has been used in agriculture to improve crops (
Plant breeding Plant breeding is the science of changing the traits of plants in order to produce desired characteristics. It has been used to improve the quality of nutrition in products for humans and animals. The goals of plant breeding are to produce cro ...
) and
livestock Livestock are the domesticated animals raised in an agricultural setting to provide labor and produce diversified products for consumption such as meat, eggs, milk, fur, leather, and wool. The term is sometimes used to refer solely to animals ...
(
Animal breeding Animal breeding is a branch of animal science that addresses the evaluation (using best linear unbiased prediction and other methods) of the genetic value (estimated breeding value, EBV) of livestock. Selecting for breeding animals with superior EB ...
). * In biomedical research, this work can assist in finding candidates
gene In biology, the word gene (from , ; "...Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a ba ...
allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is a variation of the same sequence of nucleotides at the same place on a long DNA molecule, as described in leading textbooks on genetics and evolution. ::"The chro ...
s that can cause or influence predisposition to diseases in
human genetics Human genetics is the study of inheritance as it occurs in human beings. Human genetics encompasses a variety of overlapping fields including: classical genetics, cytogenetics, molecular genetics, biochemical genetics, genomics, population gene ...


Expression data

Studies for differential expression of genes from
RNA-Seq RNA-Seq (named as an abbreviation of RNA sequencing) is a sequencing technique which uses next-generation sequencing (NGS) to reveal the presence and quantity of RNA in a biological sample at a given moment, analyzing the continuously changing c ...
data, as for
RT-qPCR A real-time polymerase chain reaction (real-time PCR, or qPCR) is a laboratory technique of molecular biology based on the polymerase chain reaction (PCR). It monitors the amplification of a targeted DNA molecule during the PCR (i.e., in real ...
and
microarrays A microarray is a multiplex lab-on-a-chip. Its purpose is to simultaneously detect the expression of thousands of genes from a sample (e.g. from a tissue). It is a two-dimensional array on a solid substrate—usually a glass slide or silicon t ...
, demands comparison of conditions. The goal is to identify genes which have a significant change in abundance between different conditions. Then, experiments are designed appropriately, with replicates for each condition/treatment, randomization and blocking, when necessary. In RNA-Seq, the quantification of expression uses the information of mapped reads that are summarized in some genetic unit, as
exon An exon is any part of a gene that will form a part of the final mature RNA produced by that gene after introns have been removed by RNA splicing. The term ''exon'' refers to both the DNA sequence within a gene and to the corresponding sequen ...
s that are part of a gene sequence. As
microarray A microarray is a multiplex lab-on-a-chip. Its purpose is to simultaneously detect the expression of thousands of genes from a sample (e.g. from a tissue). It is a two-dimensional array on a solid substrate—usually a glass slide or silicon t ...
results can be approximated by a normal distribution, RNA-Seq counts data are better explained by other distributions. The first used distribution was the Poisson one, but it underestimate the sample error, leading to false positives. Currently, biological variation is considered by methods that estimate a dispersion parameter of a
negative binomial distribution In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-r ...
.
Generalized linear model In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and b ...
s are used to perform the tests for statistical significance and as the number of genes is high, multiple tests correction have to be considered. Some examples of other analysis on
genomics Genomics is an interdisciplinary field of biology focusing on the structure, function, evolution, mapping, and editing of genomes. A genome is an organism's complete set of DNA, including all of its genes as well as its hierarchical, three-dim ...
data comes from microarray or
proteomics Proteomics is the large-scale study of proteins. Proteins are vital parts of living organisms, with many functions such as the formation of structural fibers of muscle tissue, enzymatic digestion of food, or synthesis and replication of DNA. In ...
experiments. Often concerning diseases or disease stages.


Other studies

*
Ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps wi ...
,
ecological forecasting Ecological forecasting uses knowledge of physics, ecology and physiology to predict how ecological populations, communities, or ecosystems will change in the future in response to environmental factors such as climate change. The goal of the approac ...
* Biological
sequence analysis In bioinformatics, sequence analysis is the process of subjecting a DNA, RNA or peptide sequence to any of a wide range of analytical methods to understand its features, function, structure, or evolution. Methodologies used include sequence alignm ...
*
Systems biology Systems biology is the computational modeling, computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological syst ...
for gene network inference or pathways analysis. *
Clinical research Clinical research is a branch of healthcare science that determines the safety and effectiveness ( efficacy) of medications, devices, diagnostic products and treatment regimens intended for human use. These may be used for prevention, treatm ...
and pharmaceutical development *
Population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has ...
, especially in regards to
fisheries science Fisheries science is the academic discipline of managing and understanding fisheries. It is a multidisciplinary science, which draws on the disciplines of limnology, oceanography, freshwater biology, marine biology, meteorology, conservation, eco ...
. *
Phylogenetics In biology, phylogenetics (; from Greek language, Greek wikt:φυλή, φυλή/wikt:φῦλον, φῦλον [] "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary his ...
and evolution * Pharmacodynamics *
Pharmacokinetics Pharmacokinetics (from Ancient Greek ''pharmakon'' "drug" and ''kinetikos'' "moving, putting in motion"; see chemical kinetics), sometimes abbreviated as PK, is a branch of pharmacology dedicated to determining the fate of substances administered ...
*
Neuroimaging Neuroimaging is the use of quantitative (computational) techniques to study the structure and function of the central nervous system, developed as an objective way of scientifically studying the healthy human brain in a non-invasive manner. Incre ...


Tools

There are a lot of tools that can be used to do statistical analysis in biological data. Most of them are useful in other areas of knowledge, covering a large number of applications (alphabetical). Here are brief descriptions of some of them: * ASReml: Another software developed by VSNi that can be used also in R environment as a package. It is developed to estimate variance components under a general linear mixed model using
restricted maximum likelihood In statistics, the restricted (or residual, or reduced) maximum likelihood (REML) approach is a particular form of maximum likelihood estimation that does not base estimates on a maximum likelihood fit of all the information, but instead uses a like ...
(REML). Models with fixed effects and random effects and nested or crossed ones are allowed. Gives the possibility to investigate different variance-covariance matrix structures. *CycDesigN: A computer package developed by VSNi that helps the researchers create experimental designs and analyze data coming from a design present in one of three classes handled by CycDesigN. These classes are resolvable, non-resolvable, partially replicated and crossover designs. It includes less used designs the Latinized ones, as t-Latinized design. *
Orange Orange most often refers to: *Orange (fruit), the fruit of the tree species '' Citrus'' × ''sinensis'' ** Orange blossom, its fragrant flower *Orange (colour), from the color of an orange, occurs between red and yellow in the visible spectrum * ...
: A programming interface for high-level data processing, data mining and data visualization. Include tools for gene expression and genomics. * R: An
open source Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use the source code, design documents, or content of the product. The open-source model is a decentralized sof ...
environment and programming language dedicated to statistical computing and graphics. It is an implementation of S language maintained by CRAN. In addition to its functions to read data tables, take descriptive statistics, develop and evaluate models, its repository contains packages developed by researchers around the world. This allows the development of functions written to deal with the statistical analysis of data that comes from specific applications. In the case of Bioinformatics, for example, there are packages located in the main repository (CRAN) and in others, as
Bioconductor Bioconductor is a Free software, free, Open-source software, open source and Open source software development, open development software project for the analysis and comprehension of Genome, genomic data generated by Wet laboratory, wet lab experi ...
. It is also possible to use packages under development that are shared in hosting-services as
GitHub GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, continuous ...
. * SAS: A data analysis software widely used, going through universities, services and industry. Developed by a company with the same name (
SAS Institute SAS Institute (or SAS, pronounced "sass") is an American multinational developer of analytics software based in Cary, North Carolina. SAS develops and markets a suite of analytics software ( also called SAS), which helps access, manage, analy ...
), it uses
SAS language The SAS language is a computer programming language used for statistical analysis, created by Anthony James Barr at North Carolina State University.Barr & Goodnight, et al. 1976:"The SAS Staff". Attribution of contributions to SAS 72 and SAS 76. It ...
for programming. * PLA 3.0: Is a biostatistical analysis software for regulated environments (e.g. drug testing) which supports Quantitative Response Assays (Parallel-Line, Parallel-Logistics, Slope-Ratio) and Dichotomous Assays (Quantal Response, Binary Assays). It also supports weighting methods for combination calculations and the automatic data aggregation of independent assay data. *
Weka The weka, also known as the Māori hen or woodhen (''Gallirallus australis'') is a flightless bird species of the rail family. It is endemic to New Zealand. It is the only extant member of the genus ''Gallirallus''. Four subspecies are recognize ...
: A
Java Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's List ...
software for
machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
and data mining, including tools and methods for visualization, clustering, regression, association rule, and classification. There are tools for cross-validation, bootstrapping and a module of algorithm comparison. Weka also can be run in other programming languages as Perl or R. *
Python (programming language) Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically-typed and garbage-collected. It supports multiple programming para ...
image analysis, deep-learning, machine-learning * SQL databases *
NoSQL A NoSQL (originally referring to "non- SQL" or "non-relational") database provides a mechanism for storage and retrieval of data that is modeled in means other than the tabular relations used in relational databases. Such databases have existed ...
* NumPy numerical python *
SciPy SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing. SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal ...
*
SageMath SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, numbe ...
*
LAPACK LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also ...
linear algebra *
MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...
*
Apache Hadoop Apache Hadoop () is a collection of open-source software utilities that facilitates using a network of many computers to solve problems involving massive amounts of data and computation. It provides a software framework for distributed storage ...
*
Apache Spark Apache Spark is an open-source unified analytics engine for large-scale data processing. Spark provides an interface for programming clusters with implicit data parallelism and fault tolerance. Originally developed at the University of Californi ...
*
Amazon Web Services Amazon Web Services, Inc. (AWS) is a subsidiary of Amazon.com, Amazon that provides Software as a service, on-demand cloud computing computing platform, platforms and Application programming interface, APIs to individuals, companies, and gover ...


Scope and training programs

Almost all educational programmes in biostatistics are at
postgraduate Postgraduate or graduate education refers to academic or professional degrees, certificates, diplomas, or other qualifications pursued by post-secondary students who have earned an undergraduate ( bachelor's) degree. The organization and stru ...
level. They are most often found in schools of public health, affiliated with schools of medicine, forestry, or agriculture, or as a focus of application in departments of statistics. In the United States, where several universities have dedicated biostatistics departments, many other top-tier universities integrate biostatistics faculty into statistics or other departments, such as
epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decisions and evidenc ...
. Thus, departments carrying the name "biostatistics" may exist under quite different structures. For instance, relatively new biostatistics departments have been founded with a focus on
bioinformatics Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combi ...
and
computational biology Computational biology refers to the use of data analysis, mathematical modeling and computational simulations to understand biological systems and relationships. An intersection of computer science, biology, and big data, the field also has fo ...
, whereas older departments, typically affiliated with schools of
public health Public health is "the science and art of preventing disease, prolonging life and promoting health through the organized efforts and informed choices of society, organizations, public and private, communities and individuals". Analyzing the det ...
, will have more traditional lines of research involving epidemiological studies and
clinical trial Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dietar ...
s as well as bioinformatics. In larger universities around the world, where both a statistics and a biostatistics department exist, the degree of integration between the two departments may range from the bare minimum to very close collaboration. In general, the difference between a statistics program and a biostatistics program is twofold: (i) statistics departments will often host theoretical/methodological research which are less common in biostatistics programs and (ii) statistics departments have lines of research that may include biomedical applications but also other areas such as industry (
quality control Quality control (QC) is a process by which entities review the quality of all factors involved in production. ISO 9000 defines quality control as "a part of quality management focused on fulfilling quality requirements". This approach places ...
), business and
economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...
and biological areas other than medicine.


Specialized journals

* Biostatistics * International Journal of Biostatistics * Journal of Epidemiology and Biostatistics * Biostatistics and Public Health * Biometrics * Biometrika * Biometrical Journal * Communications in Biometry and Crop Science * Statistical Applications in Genetics and Molecular Biology * Statistical Methods in Medical Research * Pharmaceutical Statistics * Statistics in Medicine


See also

*
Bioinformatics Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combi ...
*
Epidemiological method The science of epidemiology has matured significantly from the times of Hippocrates, Semmelweis and John Snow. The techniques for gathering and analyzing epidemiological data vary depending on the type of disease being monitored but each study will ...
*
Epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decisions and evidenc ...
*
Group size measures Many animals, including humans, tend to live in groups, herds, flocks, bands, packs, shoals, or colonies (hereafter: groups) of conspecific individuals. The size of these groups, as expressed by the number of people/etc in a group such as eight gr ...
*
Health indicator Health indicators are quantifiable characteristics of a population which researchers use as supporting evidence for describing the health of a population. Typically, researchers will use a survey methodology to gather information about a populatio ...
*
Mathematical and theoretical biology Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development a ...


References


External links


The International Biometric Society

The Collection of Biostatistics Research Archive

Guide to Biostatistics (MedPageToday.com)

Biomedical Statistics
{{Authority control Bioinformatics