In
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 ...
and
health
Health, according to the World Health Organization, is "a state of complete physical, mental and social well-being and not merely the absence of disease and infirmity".World Health Organization. (2006)''Constitution of the World Health Organiza ...
-related fields, a reference range or reference interval is the
range
Range may refer to:
Geography
* Range (geographic), a chain of hills or mountains; a somewhat linear, complex mountainous or hilly area (cordillera, sierra)
** Mountain range, a group of mountains bordered by lowlands
* Range, a term used to i ...
or the
interval of values that is deemed normal for a
physiological
Physiology (; ) is the scientific study of functions and mechanisms in a living system. As a sub-discipline of biology, physiology focuses on how organisms, organ systems, individual organs, cells, and biomolecules carry out the chemical ...
measurement in healthy persons (for example, the amount of
creatinine
Creatinine (; ) is a breakdown product of creatine phosphate from muscle and protein metabolism. It is released at a constant rate by the body (depending on muscle mass).
Biological relevance
Serum creatinine (a blood measurement) is an import ...
in the
blood
Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the c ...
, or the
partial pressure of oxygen
Blood gas tension refers to the partial pressure of gases in blood. There are several significant purposes for measuring gas tension. The most common gas tensions measured are oxygen tension (PxO2), carbon dioxide tension (PxCO2) and carbon monoxi ...
). It is a basis for comparison for a
physician
A physician (American English), medical practitioner (Commonwealth English), medical doctor, or simply doctor, is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through th ...
or other
health professional
A health professional, healthcare professional, or healthcare worker (sometimes abbreviated HCW) is a provider of health care treatment and advice based on formal training and experience. The field includes those who work as a nurse, physician (suc ...
to interpret a set of test results for a particular patient. Some important reference ranges in medicine are
reference ranges for blood tests
Reference ranges (reference intervals) for blood tests are sets of values used by a health professional to interpret a set of medical test results from blood samples. Reference ranges for blood tests are studied within the field of clinical chem ...
and
reference ranges for urine tests
Reference ranges for urine tests are described below:
See also
* Reference range
* Reference ranges for blood tests
References
{{Urine tests
Nephrology
...
.
The standard definition of a reference range (usually referred to if not otherwise specified) originates in what is most prevalent in a
reference group
In the social sciences, social groups can be categorized based on the various group dynamics that define social organization.Boundless team.Types of Social Groups" ''Social Groups and Organization'' Open_educational_resources">OER_course.html" ...
taken from the general (i.e. total) population. This is the general reference range. However, there are also ''optimal health ranges'' (ranges that appear to have the optimal health impact) and ranges for particular conditions or statuses (such as pregnancy reference ranges for hormone levels).
Values within the reference range (WRR) are those within normal limits (WNL). The limits are called the ''upper reference limit'' (URL) or ''upper limit of normal'' (ULN) and the ''lower reference limit'' (LRL) or ''lower limit of normal'' (LLN). In
health care
Health care or healthcare is the improvement of health via the prevention, diagnosis, treatment, amelioration or cure of disease, illness, injury, and other physical and mental impairments in people. Health care is delivered by health profe ...
–related publishing,
style sheets sometimes prefer the word ''reference'' over the word ''normal'' to prevent the nontechnical
senses
A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of stimuli. (For example, in the human body, the brain which is part of the central nervous system rec ...
of ''normal'' from being conflated with the statistical sense. Values outside a reference range are not
necessarily pathologic, and they are not necessarily abnormal in any sense other than statistically. Nonetheless, they are indicators of probable pathosis. Sometimes the underlying cause is obvious; in other cases, challenging
differential diagnosis
In healthcare, a differential diagnosis (abbreviated DDx) is a method of analysis of a patient's history and physical examination to arrive at the correct diagnosis. It involves distinguishing a particular disease or condition from others that p ...
is required to determine what is wrong and thus how to treat it.
A cutoff or threshold is a limit used for
binary classification
Binary classification is the task of classifying the elements of a set into two groups (each called ''class'') on the basis of a classification rule. Typical binary classification problems include:
* Medical testing to determine if a patient has c ...
, mainly between normal versus pathological (or probably pathological). Establishment methods for cutoffs include using an upper or a lower limit of a reference range.
Standard definition
The standard definition of a reference range for a particular measurement is defined as the interval between which 95% of values of a reference population fall into, in such a way that 2.5% of the time a value will be less than the lower limit of this interval, and 2.5% of the time it will be larger than the upper limit of this interval, whatever the distribution of these values.
Reference ranges that are given by this definition are sometimes referred as ''standard ranges''.
Since a range is a defined statistical value (
Range (statistics)
In statistics, the range of a set of data is the difference between the largest and smallest values,
the result of subtracting the sample maximum and minimum. It is expressed in the same units as the data.
In descriptive statistics, range is ...
) that describes the interval between the smallest and largest values, many, including the International Federation of Clinical Chemistry prefer to use the expression reference interval rather than reference range.
Regarding the target population, if not otherwise specified, a standard reference range generally denotes the one in healthy individuals, or without any known condition that directly affects the ranges being established. These are likewise established using reference groups from the healthy population, and are sometimes termed ''normal ranges'' or ''normal values'' (and sometimes "usual" ranges/values). However, using the term ''normal'' may not be appropriate as not everyone outside the interval is abnormal, and people who have a particular condition may still fall within this interval.
However, reference ranges may also be established by taking samples from the whole population, with or without diseases and conditions. In some cases, diseased individuals are taken as the population, establishing reference ranges among those having a disease or condition. Preferably, there should be specific reference ranges for each subgroup of the population that has any factor that affects the measurement, such as, for example, specific ranges for each ''sex'', ''age group'', ''race'' or any other
general determinant
In epidemiology, a risk factor or determinant is a variable associated with an increased risk of disease or infection.
Due to a lack of harmonization across disciplines, determinant, in its more widely accepted scientific meaning, is often use ...
.
Establishment methods
Methods for establishing reference ranges can be based on assuming a
normal distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
:
f(x) = \frac e^
The parameter \mu ...
or a
log-normal distribution
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal ...
, or directly from percentages of interest, as detailed respectively in following sections. When establishing reference ranges from bilateral organs (e.g., vision or hearing), both results from the same individual can be used, although intra-subject correlation must be taken into account.
Normal distribution
![Standard deviation diagram](https://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg)
The 95% interval, is often estimated by assuming a
normal distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
:
f(x) = \frac e^
The parameter \mu ...
of the measured parameter, in which case it can be defined as the interval limited by 1.96
[Page 48 in: ] (often rounded up to 2) population
standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
s from either side of the population mean (also called the
expected value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a l ...
).
However, in the real world, neither the population mean nor the population standard deviation are known. They both need to be estimated from a sample, whose size can be designated ''n''. The population standard deviation is estimated by the sample standard deviation and the population mean is estimated by the sample mean (also called mean or
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 ...
). To account for these estimations, the 95%
prediction interval
In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are o ...
(95% PI) is calculated as:
: ,
where
is the 97.5% quantile of a
Student's t-distribution
In probability and statistics, Student's ''t''-distribution (or simply the ''t''-distribution) is any member of a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in sit ...
with ''n''−1
degrees of freedom
Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...
.
When the sample size is large (''n''≥30)
This method is often acceptably accurate if the standard deviation, as compared to the mean, is not very large. A more accurate method is to perform the calculations on logarithmized values, as described in separate section later.
The following example of this (''not'' logarithmized) method is based on values of
fasting plasma glucose
Many types of glucose tests exist and they can be used to estimate blood sugar levels at a given time or, over a longer period of time, to obtain average levels or to see how fast body is able to normalize changed glucose levels. Eating food for e ...
taken from a reference group of 12 subjects:
[Table 1. Subject characteristics]
in:
As can be given from, for example, a
table of selected values of Student's t-distribution, the 97.5% percentile with (12-1) degrees of freedom corresponds to
Subsequently, the lower and upper limits of the standard reference range are calculated as:
:
:
Thus, the standard reference range for this example is estimated to be 4.4 to 6.3 mmol/L.
=Confidence interval of limit
=
The 90% ''confidence interval of a standard reference range limit'' as estimated assuming a normal distribution can be calculated by:
: Lower limit of the confidence interval = percentile limit - 2.81 ×
: Upper limit of the confidence interval = percentile limit + 2.81 × ,
where SD is the standard deviation, and n is the number of samples.
Taking the example from the previous section, the number of samples is 12 and the standard deviation is 0.42 mmol/L, resulting in:
:''Lower limit of the confidence interval'' of the ''lower limit of the standard reference range'' = 4.4 - 2.81 × ≈ 4.1
:''Upper limit of the confidence interval'' of the ''lower limit of the standard reference range'' = 4.4 + 2.81 × ≈ 4.7
Thus, the lower limit of the reference range can be written as 4.4 (90% CI 4.1–4.7) mmol/L.
Likewise, with similar calculations, the upper limit of the reference range can be written as 6.3 (90% CI 6.0–6.6) mmol/L.
These confidence intervals reflect
random error
Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a " mistake ...
, but do not compensate for
systematic error
Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a " mistak ...
, which in this case can arise from, for example, the reference group not having fasted long enough before blood sampling.
As a comparison, actual reference ranges used clinically for fasting plasma glucose are estimated to have a lower limit of approximately 3.8
[Last page of ] to 4.0,
[Reference range list from Uppsala University Hospital ("Laborationslista"). Artnr 40284 Sj74a. Issued on April 22, 2008] and an upper limit of approximately 6.0
[ to 6.1.]
Log-normal distribution
In reality, biological parameters tend to have a log-normal distribution
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal ...
, rather than the arithmetical normal distribution (which is generally referred to as normal distribution without any further specification).
An explanation for this log-normal distribution for biological parameters is: The event where a sample has half the value of the mean or median tends to have almost equal probability to occur as the event where a sample has twice the value of the mean or median. Also, only a log-normal distribution can compensate for the inability of almost all biological parameters to be of negative number
In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed m ...
s (at least when measured on absolute scale
There is no single definition of an absolute scale. In statistics and measurement theory, it is simply a ratio scale in which the unit of measurement is fixed, and values are obtained by counting. According to another definition it is a system of ...
s), with the consequence that there is no definite limit to the size of outliers (extreme values) on the high side, but, on the other hand, they can never be less than zero, resulting in a positive skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined.
For a unimodal d ...
.
As shown in diagram at right, this phenomenon has relatively small effect if the standard deviation (as compared to the mean) is relatively small, as it makes the log-normal distribution appear similar to an arithmetical normal distribution. Thus, the arithmetical normal distribution may be more appropriate to use with small standard deviations for convenience, and the log-normal distribution with large standard deviations.
In a log-normal distribution, the geometric standard deviation
In probability theory and statistics, the geometric standard deviation (GSD) describes how spread out are a set of numbers whose preferred average is the geometric mean. For such data, it may be preferred to the more usual standard deviation. Note ...
s and geometric mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the ...
more accurately estimate the 95% prediction interval than their arithmetic counterparts.
=Necessity
=
Reference ranges for substances that are usually within relatively narrow limits (coefficient of variation less than 0.213, as detailed below) such as electrolytes
An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon di ...
can be estimated by assuming arithmetically normal distribution, whereas reference ranges for those that vary significantly (coefficient of variation generally over 0.213) such as most hormones
A hormone (from the Ancient Greek, Greek participle , "setting in motion") is a class of cell signaling, signaling molecules in multicellular organisms that are sent to distant organs by complex biological processes to regulate physiology and beh ...
[ ] are more accurately established by log-normal distribution.
The necessity to establish a reference range by log-normal distribution rather than arithmetic normal distribution can be regarded as depending on how much difference it would make to ''not'' do so, which can be described as the ratio:
:
where:
* ''Limitlog-normal'' is the (lower or upper) limit as estimated by assuming log-normal distribution
* ''Limitnormal'' is the (lower or upper) limit as estimated by assuming arithmetically normal distribution.
This difference can be put solely in relation to the coefficient of variation
In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as ...
, as in the diagram at right, where:
:
where:
* ''s.d.'' is the arithmetic standard deviation
* ''m'' is the arithmetic mean
In practice, it can be regarded as necessary to use the establishment methods of a log-normal distribution if the difference ratio becomes more than 0.1, meaning that a (lower or upper) limit estimated from an assumed arithmetically normal distribution would be more than 10% different from the corresponding limit as estimated from a (more accurate) log-normal distribution. As seen in the diagram, a difference ratio of 0.1 is reached for the lower limit at a coefficient of variation of 0.213 (or 21.3%), and for the upper limit at a coefficient of variation at 0.413 (41.3%). The lower limit is more affected by increasing coefficient of variation, and its "critical" coefficient of variation of 0.213 corresponds to a ratio of (upper limit)/(lower limit) of 2.43, so as a rule of thumb, if the upper limit is more than 2.4 times the lower limit when estimated by assuming arithmetically normal distribution, then it should be considered to do the calculations again by log-normal distribution.
Taking the example from previous section, the arithmetic standard deviation (s.d.) is estimated at 0.42 and the arithmetic mean (m) is estimated at 5.33. Thus the coefficient of variation is 0.079. This is less than both 0.213 and 0.413, and thus both the lower and upper limit of fasting blood glucose can most likely be estimated by assuming arithmetically normal distribution. More specifically, the coefficient of variation of 0.079 corresponds to a difference ratio of 0.01 (1%) for the lower limit and 0.007 (0.7%) for the upper limit.
=From logarithmized sample values
=
A method to estimate the reference range for a parameter with log-normal distribution is to logarithmize all the measurements with an arbitrary base (for example ''e''), derive the mean and standard deviation of these logarithms, determine the logarithms located (for a 95% prediction interval) 1.96 standard deviations below and above that mean, and subsequently exponentiate
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...
using those two logarithms as exponents and using the same base as was used in logarithmizing, with the two resultant values being the lower and upper limit of the 95% prediction interval.
The following example of this method is based on the same values of fasting plasma glucose
Many types of glucose tests exist and they can be used to estimate blood sugar levels at a given time or, over a longer period of time, to obtain average levels or to see how fast body is able to normalize changed glucose levels. Eating food for e ...
as used in the previous section, using ''e'' as a base:[
Subsequently, the still logarithmized lower limit of the reference range is calculated as:
:
and the upper limit of the reference range as:
:
Conversion back to non-logarithmized values are subsequently performed as:
:
:
Thus, the standard reference range for this example is estimated to be 4.4 to 6.4.
]
=From arithmetic mean and variance
=
An alternative method of establishing a reference range with the assumption of log-normal distribution is to use the arithmetic mean and arithmetic value of standard deviation. This is somewhat more tedious to perform, but may be useful in cases where a study presents only the arithmetic mean and standard deviation, while leaving out the source data. If the original assumption of arithmetically normal distribution is less appropriate than the log-normal one, then, using the arithmetic mean and standard deviation may be the only available parameters to determine the reference range.
By assuming that the expected value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a l ...
can represent the arithmetic mean in this case, the parameters ''μlog'' and ''σlog'' can be estimated from the arithmetic mean (''m'') and standard deviation (''s.d.'') as:
:
:
Following the exampled reference group from the previous section:
:
:
Subsequently, the logarithmized, and later non-logarithmized, lower and upper limit are calculated just as by logarithmized sample values.
Directly from percentages of interest
Reference ranges can also be established directly from the 2.5th and 97.5th percentile of the measurements in the reference group. For example, if the reference group consists of 200 people, and counting from the measurement with lowest value to highest, the lower limit of the reference range would correspond to the 5th measurement and the upper limit would correspond to the 195th measurement.
This method can be used even when measurement values do not appear to conform conveniently to any form of normal distribution or other function.
However, the reference range limits as estimated in this way have higher variance, and therefore less reliability, than those estimated by an arithmetic or log-normal distribution (when such is applicable), because the latter ones acquire statistical power
In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis (H_0) when a specific alternative hypothesis (H_1) is true. It is commonly denoted by 1-\beta, and represents the chances ...
from the measurements of the whole reference group rather than just the measurements at the 2.5th and 97.5th percentiles. Still, this variance decreases with increasing size of the reference group, and therefore, this method may be optimal where a large reference group easily can be gathered, and the distribution mode of the measurements is uncertain.
Bimodal distribution
In case of a bimodal distribution
In statistics, a multimodal distribution is a probability distribution with more than one mode. These appear as distinct peaks (local maxima) in the probability density function, as shown in Figures 1 and 2. Categorical, continuous, and dis ...
(seen at right), it is useful to find out why this is the case. Two reference ranges can be established for the two different groups of people, making it possible to assume a normal distribution for each group. This bimodal pattern is commonly seen in tests that differ between men and women, such as prostate specific antigen
Prostate-specific antigen (PSA), also known as gamma-seminoprotein or kallikrein-3 (KLK3), P-30 antigen, is a glycoprotein enzyme encoded in humans by the ''KLK3'' gene. PSA is a member of the kallikrein-related peptidase family and is secreted b ...
.
Interpretation of standard ranges in medical tests
In case of medical test
A medical test is a medical procedure performed to detect, diagnose, or monitor diseases, disease processes, susceptibility, or to determine a course of treatment. Medical tests such as, physical and visual exams, diagnostic imaging, genetic te ...
s whose results are of continuous values, reference ranges can be used in the interpretation of an individual test result. This is primarily used for diagnostic test
A medical test is a medical procedure performed to detect, diagnose, or monitor diseases, disease processes, susceptibility, or to determine a course of treatment. Medical tests such as, physical and visual exams, diagnostic imaging, genetic ...
s and screening
Screening may refer to:
* Screening cultures, a type a medical test that is done to find an infection
* Screening (economics), a strategy of combating adverse selection (includes sorting resumes to select employees)
* Screening (environmental), a ...
tests, while monitoring tests may optimally be interpreted from previous tests of the same individual instead.
Probability of random variability
Reference ranges aid in the evaluation of whether a test result's deviation from the mean is a result of random variability or a result of an underlying disease or condition. If the reference group used to establish the reference range can be assumed to be representative of the individual person in a healthy state, then a test result from that individual that turns out to be lower or higher than the reference range can be interpreted as that there is less than 2.5% probability that this would have occurred by random variability in the absence of disease or other condition, which, in turn, is strongly indicative for considering an underlying disease or condition as a cause.
Such further consideration can be performed, for example, by an epidemiology-based differential diagnostic procedure, where potential candidate conditions are listed that may explain the finding, followed by calculations of how probable they are to have occurred in the first place, in turn followed by a comparison with the probability that the result would have occurred by random variability.
If the establishment of the reference range could have been made assuming a normal distribution, then the probability that the result would be an effect of random variability can be further specified as follows:
The standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
, if not given already, can be inversely calculated by the fact that the absolute value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), an ...
of the difference between the mean and either the upper or lower limit of the reference range is approximately 2 standard deviations (more accurately 1.96), and thus:
:.
The standard score
In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mean ...
for the individual's test can subsequently be calculated as:
:.
The probability that a value is of a certain distance from the mean can subsequently be calculated from the relation between standard score and prediction intervals. For example, a standard score of 2.58 corresponds to a prediction interval of 99%,[Page 111]
in: corresponding to a probability of 0.5% that a result is at least such far from the mean in the absence of disease.
Example
Let's say, for example, that an individual takes a test that measures the ionized calcium
Calcium ions (Ca2+) contribute to the physiology and biochemistry of organisms' cells. They play an important role in signal transduction pathways, where they act as a second messenger, in neurotransmitter release from neurons, in contractio ...
in the blood, resulting in a value of 1.30 mmol/L, and a reference group that appropriately represents the individual has established a reference range of 1.05 to 1.25 mmol/L. The individual's value is higher than the upper limit of the reference range, and therefore has less than 2.5% probability of being a result of random variability, constituting a strong indication to make a differential diagnosis
In healthcare, a differential diagnosis (abbreviated DDx) is a method of analysis of a patient's history and physical examination to arrive at the correct diagnosis. It involves distinguishing a particular disease or condition from others that p ...
of possible causative conditions.
In this case, an epidemiology-based differential diagnostic procedure is used, and its first step is to find candidate conditions that can explain the finding.
Hypercalcemia
Hypercalcemia, also spelled hypercalcaemia, is a high calcium (Ca2+) level in the blood serum. The normal range is 2.1–2.6 mmol/L (8.8–10.7 mg/dL, 4.3–5.2 mEq/L), with levels greater than 2.6 mmol/L defined as hypercalcemi ...
(usually defined as a calcium level above the reference range) is mostly caused by either primary hyperparathyroidism
Primary hyperparathyroidism (or PHPT) is a medical condition where the parathyroid gland (or a benign tumor within it) produce excess amounts of parathyroid hormone (PTH). The symptoms of the condition relate to the resulting elevated serum calcium ...
or malignancy,[Table 20-4 in: 8th edition.] and therefore, it is reasonable to include these in the differential diagnosis.
Using for example epidemiology and the individual's risk factors, let's say that the probability that the hypercalcemia would have been caused by primary hyperparathyroidism in the first place is estimated to be 0.00125 (or 0.125%), the equivalent probability for cancer is 0.0002, and 0.0005 for other conditions. With a probability given as less than 0.025 of no disease, this corresponds to a probability that the hypercalcemia would have occurred in the first place of up to 0.02695. However, the hypercalcemia ''has occurred'' with a probability of 100%, resulting adjusted probabilities of at least 4.6% that primary hyperparathyroidism has caused the hypercalcemia, at least 0.7% for cancer, at least 1.9% for other conditions and up to 92.8% for that there is no disease and the hypercalcemia is caused by random variability.
In this case, further processing benefits from specification of the probability of random variability:
The value is assumed to conform acceptably to a normal distribution, so the mean can be assumed to be 1.15 in the reference group. The standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
, if not given already, can be inversely calculated by knowing that the absolute value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), an ...
of the difference between the mean and, for example, the upper limit of the reference range, is approximately 2 standard deviations (more accurately 1.96), and thus:
:.
The standard score
In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mean ...
for the individual's test is subsequently calculated as:
:.
The probability that a value is of so much larger value than the mean as having a standard score of 3 corresponds to a probability of approximately 0.14% (given by , with 99.7% here being given from the 68–95–99.7 rule
In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within
an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, ...
).
Using the same probabilities that the hypercalcemia would have occurred in the first place by the other candidate conditions, the probability that hypercalcemia would have occurred in the first place is 0.00335, and given the fact that hypercalcemia ''has occurred'' gives adjusted probabilities of 37.3%, 6.0%, 14.9% and 41.8%, respectively, for primary hyperparathyroidism, cancer, other conditions and no disease.
Optimal health range
''Optimal (health) range'' or ''therapeutic target'' (not to be confused with biological target
A biological target is anything within a living organism to which some other entity (like an endogenous ligand or a drug) is directed and/or binds, resulting in a change in its behavior or function. Examples of common classes of biological targets ...
) is a reference range or limit that is based on concentrations or levels that are associated with optimal health or minimal risk of related complications and diseases, rather than the standard range based on normal distribution in the population.
It may be more appropriate to use for e.g. folate
Folate, also known as vitamin B9 and folacin, is one of the B vitamins. Manufactured folic acid, which is converted into folate by the body, is used as a dietary supplement and in food fortification as it is more stable during processing and ...
, since approximately 90 percent of North Americans may actually suffer more or less from folate deficiency
Folate deficiency, also known as vitamin B9 deficiency, is a low level of folate and derivatives in the body. Signs of folate deficiency are often subtle. A low number of red blood cells (anemia) is a late finding in folate deficiency and folate ...
, but only the 2.5 percent that have the lowest levels will fall below the standard reference range. In this case, the actual folate ranges for optimal health are substantially higher than the standard reference ranges. Vitamin D
Vitamin D is a group of fat-soluble secosteroids responsible for increasing intestinal absorption of calcium, magnesium, and phosphate, and many other biological effects. In humans, the most important compounds in this group are vitamin D3 (c ...
has a similar tendency. In contrast, for e.g. uric acid
Uric acid is a heterocyclic compound of carbon, nitrogen, oxygen, and hydrogen with the formula C5H4N4O3. It forms ions and salts known as urates and acid urates, such as ammonium acid urate. Uric acid is a product of the metabolic breakdown of ...
, having a level not exceeding the standard reference range still does not exclude the risk of getting gout or kidney stones. Furthermore, for most toxin
A toxin is a naturally occurring organic poison produced by metabolic activities of living cells or organisms. Toxins occur especially as a protein or conjugated protein. The term toxin was first used by organic chemist Ludwig Brieger (1849– ...
s, the standard reference range is generally lower than the level of toxic effect.
A problem with optimal health range is a lack of a standard method of estimating the ranges. The limits may be defined as those where the health risks exceed a certain threshold, but with various risk profiles between different measurements (such as folate and vitamin D), and even different risk aspects for one and the same measurement (such as both deficiency
A deficiency is generally a lack of something. It may also refer to:
*A deficient number, in mathematics, a number ''n'' for which ''σ''(''n'') < 2''n''
* and toxicity of vitamin A) it is difficult to standardize. Subsequently, optimal health ranges, when given by various sources, have an additional variability caused by various definitions of the parameter. Also, as with standard reference ranges, there should be specific ranges for different determinants that affects the values, such as sex, age etc. Ideally, there should rather be an estimation of what is the optimal value for every individual, when taking all significant factors of that individual into account - a task that may be hard to achieve by studies, but long clinical experience by a physician may make this method preferable to using reference ranges.
One-sided cut-off values
In many cases, only one side of the range is usually of interest, such as with markers of pathology including cancer antigen 19-9, where it is generally without any clinical significance to have a value below what is usual in the population. Therefore, such targets are often given with only one limit of the reference range given, and, strictly, such values are rather ''cut-off values'' or ''threshold values''.
They may represent both standard ranges and optimal health ranges. Also, they may represent an appropriate value to distinguish healthy person from a specific disease, although this gives additional variability by different diseases being distinguished. For example, for NT-proBNP
The N-terminal prohormone of brain natriuretic peptide (NT-proBNP or BNPT) is a prohormone with a 76 amino acid N-terminal inactive protein that is cleaved from the molecule to release brain natriuretic peptide.
Both BNP and NT-proBNP levels in ...
, a lower cut-off value is used in distinguishing healthy babies from those with acyanotic heart disease
A cyanotic heart defect is any congenital heart defect (CHD) that occurs due to deoxygenated blood bypassing the lungs and entering the systemic circulation, or a mixture of oxygenated and unoxygenated blood entering the systemic circulation. It is ...
, compared to the cut-off value used in distinguishing healthy babies from those with congenital nonspherocytic anemia.[Screening for Congenital Heart Disease with NT-proBNP: Results]
By Emmanuel Jairaj Moses, Sharifah A.I. Mokhtar, Amir Hamzah, Basir Selvam Abdullah, and Narazah Mohd Yusoff. Laboratory Medicine. 2011;42(2):75–80. American Society for Clinical Pathology
General drawbacks
For standard as well as optimal health ranges, and cut-offs, sources of inaccuracy and imprecision include:
* Instruments and lab techniques used, or how the measurements are interpreted by observers. These may apply both to the instruments etc. used to establish the reference ranges and the instruments, etc. used to acquire the value for the individual to whom these ranges is applied. To compensate, individual laboratories should have their own lab ranges to account for the instruments used in the laboratory.
* Determinants
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and ...
such as age, diet, etc. that are not compensated for. Optimally, there should be reference ranges from a reference group that is as similar as possible to each individual they are applied to, but it's practically impossible to compensate for every single determinant, often not even when the reference ranges are established from multiple measurements of the same individual they are applied to, because of test-retest variability.
Also, reference ranges tend to give the impression of definite thresholds that clearly separate "good" or "bad" values, while in reality there are generally continuously increasing risks with increased distance from usual or optimal values.
With this and uncompensated factors in mind, the ideal interpretation method of a test result would rather consist of a comparison of what would be expected or optimal in the individual when taking all factors and conditions of that individual into account, rather than strictly classifying the values as "good" or "bad" by using reference ranges from other people.
In a recent paper, Rappoport et al. described a novel way to redefine reference range from an electronic health record
An electronic health record (EHR) is the systematized collection of patient and population electronically stored health information in a digital format. These records can be shared across different health care settings. Records are shared throu ...
system. In such a system, a higher population resolution can be achieved (e.g., age, sex, race and ethnicity-specific).
Examples
* Reference ranges for blood tests
Reference ranges (reference intervals) for blood tests are sets of values used by a health professional to interpret a set of medical test results from blood samples. Reference ranges for blood tests are studied within the field of clinical chem ...
* Reference ranges for urine tests
Reference ranges for urine tests are described below:
See also
* Reference range
* Reference ranges for blood tests
References
{{Urine tests
Nephrology
...
See also
* Clinical pathology
Clinical pathology is a medical specialty that is concerned with the diagnosis of disease based on the laboratory analysis of bodily fluids, such as blood, urine, and tissue homogenates or extracts using the tools of chemistry, microbiology, ...
* Joint Committee for Traceability in Laboratory Medicine
The Joint Committee for Traceability in Laboratory Medicine or JCTLM is collaboration between the International Committee for Weights and Measures (CIPM), the International Federation for Clinical Chemistry and Laboratory Medicine (IFCC), and the ...
* Medical technologist
A medical laboratory scientist (MLS) or clinical laboratory scientist (CLS) or medical technologist (MT) performs diagnostic testing of blood and body fluids in clinical laboratories. The scope of a medical laboratory scientist's work begins wit ...
* Reference ranges for blood tests
Reference ranges (reference intervals) for blood tests are sets of values used by a health professional to interpret a set of medical test results from blood samples. Reference ranges for blood tests are studied within the field of clinical chem ...
References
Further reading
* The procedures and vocabulary referring to reference intervals: CLSI (Committee for Laboratory Standards Institute) and IFCC (International Federation of Clinical Chemistry) ''CLSI - Defining, Establishing, and Verifying Reference Intervals in the Laboratory; Approved guideline'' - Third Edition. Document C28-A3 ()Wayne, PA, USA, 2008
Reference Value Advisor
: A free set of Excel macros allowing the determination of reference intervals in accordance with the CLSI procedures. Based on:
{{Authority control
Research
Clinical pathology