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)) 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.Establishment methods
Methods for establishing reference ranges can be based on assuming aNormal distribution
The 95% interval, is often estimated by assuming a=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, but do not compensate for systematic error, 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 3.8Last 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=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 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 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=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 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 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 theDirectly 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 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 (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.Interpretation of standard ranges in medical tests
In case of medical tests 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 tests and screening 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, if not given already, can be inversely calculated by the fact that the absolute value 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 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 111Example
Let's say, for example, that an individual takes a test that measures the ionized calcium 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 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 (usually defined as a calcium level above the reference range) is mostly caused by either primary hyperparathyroidism 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, if not given already, can be inversely calculated by knowing that the absolute value 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 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 theOptimal health range
''Optimal (health) range'' or ''therapeutic target'' (not to be confused with biological target) 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, since approximately 90 percent of North Americans may actually suffer more or less from folate deficiency, 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 has a similar tendency. In contrast, for e.g.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, forGeneral 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 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 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 for urine testsSee also
* Clinical pathology * Joint Committee for Traceability in Laboratory Medicine * Medical technologist * Reference ranges for blood testsReferences
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