Reference range

In health-related fields, a reference range or reference interval usually describes the variations of a measurement or value in healthy individuals. It is a basis for a physician or other health professional to interpret a set of results for a particular patient.

The standard definition of a reference range (usually referred to if not otherwise specified) basically originates in what is most prevalent in a control group taken from the population. However, there are also optimal health ranges that are those that appear to have the optimal health impact on people.

Standard definition
The standard definition of a reference range for a particular measurement is defined as the prediction interval between which 95% of values of a control group fall into, in such a way that 2.5% of the time a sample 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.

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 control 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.

Normal distribution


The 95% prediction interval, is often estimated by assuming a normal distribution of the measured parameter, in which case it can alternatively be defined as the interval limited by 1.96 (often rounded up to 2) standard deviations from either side of the arithmetic mean (usually simply called the "mean").

This method is often acceptably accurate if the standard deviation, as compared to the mean, is not very large.

In case of a bimodal distribution (seen below), 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.



Log-normal distribution
In reality, biological parameters tend to have a log-normal distributions, rather than the arithmetical normal distribution (which is generally referred to as normal distribution without any further specification).

An explanation for this distribution is the inability of almost all biological parameters to be of negative numbers (at least when measured on absolute scales), and therefore, 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.

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 deviations and geometric mean more accurately estimate the 95% prediction interval than their arithmetic counterparts. The method 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 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.

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 control group. For example, if the control 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 control group rather than just the measurements at the 2.5th and 97.5th percentiles.

Optimal 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. uric acid, having a level not exceeding the standard reference range still does not exclude the risk of getting gout or kidney stones.

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 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 more preferable than 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, a lower cut-off value is used in distinguishing healthy babies from those with acyanotic heart disease, compared to the cut-off value used in distinguishing healthy babies from those with congenital nonspherocytic anemia.

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 such as age, diet, etc. that are not compensated for. Optimally, there should be reference ranges from a control 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.

Examples

 * Reference ranges for blood tests
 * Reference ranges for urine tests