Establishing and using reference intervals

Selection of reference individuals

Health is a relative condition lacking a universal definition. The designation of good health and determination of normality for a candidate reference individual may involve a variety of examinations, such as a history and physical and/or certain clinical laboratory tests. The inclusion, exclusion and partitioning criteria can be implemented appropriately through a well-designed questionnaire [13]. Exclusion criteria are features which prevent the individual from being included in the reference sample. Although some criteria, such as alcohol, tobacco and some environmental factors, may be potential exclusion criteria, amounts of consumption of alcohol and tobacco can be recorded in detail on the sample questionnaire and the effects are evaluated statistically, primarily using multiple regression analysis [18]. Written informed consent from participants is needed from each reference individual who agrees to participate in the study. The consent form should state clearly that laboratory personnel is allowed to obtain specimens, and use the associated laboratory values and questionnaire information for the determination of RIs [13].

There are two main sampling approaches to include the reference individuals in the direct RI studies: (1) the priori approach. This refers to RI studies where the inclusion of reference individuals is determined before samples are collected. This is usually based on a questionnaire and/or clinical examination. Typically all results from these samples are included in the data with the exception of removing samples considered to be outliers based on a statistical procedure. (2) The posteriori approach. This refers to direct RI studies where the definition of reference individuals includes information applied after the samples have been collected or after the measurements have been performed.

Pre-analytical and analytical aspects

The pre-analytical considerations involve biological (i.e. sampling time in relation to biological rhythms, fasting or non-fasting and physical activity) and methodological factors (i.e. sample collection techniques, type of additives, with or without tourniquet and sampling equipment, specimen handling, transportation, time and speed of centrifugation, and storage conditions). For reproducibility and standardization, it is essential that the pre-analytical aspects are accurately defined and described as the preanalytical phase is known to have the highest errors in the total test process [22]. Some pre-analytical factors will affect results and so should be considered when performing RI studies, reviewing the literature, or when applying the intervals to patient results. Examples include serum versus heparin plasma when measuring potassium or total protein; time of day for collection for serum cortisol or testosterone; sample handling, such as the time until centrifugation for potassium measurement; and common interferences, such as hemolysis for potassium, CK, AST and LDH [23].

Analytical aspects include the analytical variability of the method used for the measurement, equipment/instrumentation, reagents, calibration standards, and calculation methods. Different commercial methods may be used in a trueness-based approach to the reference measurement system providing results traceable to the system and thus, comparable results can be produced in clinical laboratories. When performing a RI study, the reference measurement systems and standard reference materials are of great importance to ensure the traceability of the test results in comparisons [23].

Statistical evaluation to establish direct reference intervals

Calculation of RIs includes parametric and nonparametric calculation methods, detection of outliers, partitioning, and confidence intervals. In the parametric calculation method, the most suitable transformation method must be selected (e.g. logarithmic, Box-Cox power or some other function) and testing is then applied to establish whether the transformed reference values conform to Gaussian distribution [9]. Box-Cox power transformation often has been used to transform data to a Gaussian distribution for parametric computation of RIs [24]. However, this transformation occasionally fails. Therefore, the non-parametric method based on the determination of the 2.5 and 97.5 percentiles following sorting of the data, has been recommended for general use. Although the EP28-A3c recommends the non-parametric calculation method, the parametric calculation method may have an advantage over the non-parametric method in allowing identification and exclusion of extreme values during RI computation [25].

Whichever method is used in the calculation of the RIs, detection, and exclusion of the outliers are very important to obtain reliable RIs. A simple but effective method for the detection of outliers is a visual inspection of the data. The method proposed by Dixon (D: the absolute value of the difference between the suspected outlier and the next or proceeding value, R: the entire range of the observations) [26]. If the D/R ratio is more than 1/3, the outlier is discarded. However, this method is not very sensitive when there is more than one outlier. The Tukey method is a more sophisticated method, which includes Box-Cox transformation of the data to obtain Gaussian distribution followed by identification of the outliers in interquartile ranges (IQR: Q3–Q1; Q1: lower quartile, Q3: upper quartile). At levels of <Q1–1.5 IQR and/or >Q3+1.5 IQR, the outliers are discarded [27]. The latent abnormal value exclusion (LAVE) method proposed by Ichihara and Boyd [25] is a secondary exclusion method to exclude possibly abnormal results hidden within the reference values. This method is an iterative approach for the derivation of multiple reference RIs simultaneously when no exclusion of values has been made in the initial computation of the RIs. The algorithm then uses those initial values of RIs to judge the abnormality of each individual’s record by counting the number of abnormal results in tests other than the one for which the RI is being determined [28].

Stratification of RIs by age and gender is the minimum pre-requisite and other means include race, ethnicity, body mass index or nutritional habits. The most widely-used partitioning method is that of Harris and Boyd, in which the means and standard deviations of the subgroups are considered as a separate different standard deviation that may produce different limits [29]. However, this method is only appropriate for analytes with a Gaussian distribution with subclasses, where the values are of similar size and standard deviation. A similar method was proposed by Lahti et al. allowing the estimation specifically of the percentage of subjects in a subclass outside the RIs of the entire population in any situation [30]. More recently, Ichihara and Boyd recommended a partitioning method on the basis of the magnitude of the standard deviations of test results named standard deviation ratio (SDR) [25]. An SDR greater than 0.3 can be regarded as a guide for the consideration of partitioning reference values. This method is based on two or three-level nested analysis of variance.

It is clearly recommended that at least 120 subjects are required to calculate the confidence intervals (CIs) of the lower and upper RIs in the guideline [13]. The CI is a range of values including the true percentile (e.g. the 2.5th percentile of the population) with a specified probability, usually of 90% or 95%, as the “confidence level” of the interval. Horn and Pesce proposed a “robust method” that based on the transformation of the original data according to Box and Cox followed by a “robust” algorithm giving different weights to the data, depending upon their distance from the mean [31]. However, a robust method with such a small number of reference subjects (e.g. n=20) can lead to uncertainty of calculated reference limits revealed by the width of its CIs. In the EP28-A3c guideline, non-parametric CIs are given from the observed values corresponding to certain rank numbers from Reed et al. [32]. When there is a small n, to calculate the 90% CIs around the limits, it is recommended to use “the bootstrap method” which is a “resampling” method and creates a “pseudosample” from the data. The RI is derived from each pseudosample and the process is repeated many times (100–2000) yielding a distribution of lower and upper RIs [33]. From this distribution, 5^th and the 95^th quantiles may be used to determine the 90% CI for each limit.

Source of the data

As the aim is to produce “health-associated” RIs, then results from outpatients are clearly preferred, particularly from those in a primary care setting. The high frequency of inflammation, recumbency, intravenous fluids, medications, and dietary changes, in addition to the disease(s) leading to the admission, makes inpatient samples less desirable.

Number of subjects

There is no prescription for the number of samples required; however, “more is better” to produce robust results. However, to provide a starting point for further work in this area, 1000 subjects may be considered a small number and above 10,000 as a large number, and in populations that are poorly represented in a database (e.g. extremes of age), smaller numbers may still provide useful information. It is recommended to use a minimum of 400 reference subjects for each partition for a statistically reliable reference interval calculation [25].

Stability over time

Before using any data set, it is important to ensure that the analytical method and the population have been stable over the period of data collection [41]. The first assessment is a historical review, i.e. has the method been changed or the population serviced changed during the period of data collection. This can be further assessed by reviewing medians and other percentiles over the time period of data collection, together with the assessment of QC and EQA results.

Partitioning

Partitioning can be performed by plotting medians and selected centiles (e.g. 10^th and 90^th) for males and females against patient age. The need for partitioning can be assessed by several objective criteria. Harris and Boyd [29] recommend a separate Rl when the ratio of standard deviation (larger over smaller) between the subgroups exceed 1.5, or when the Z-statistics between the two subgroup distribution exceeds 3.

Exclusions

Data sets can be “biochemically filtered” to reduce the frequency of results from subjects where there is a higher likelihood of disease affecting the result. A recommended approach is to exclude specific subgroups (e.g. emergency departments or intensive care units). An additional recommended approach is to limit results to a single result per patient. As a diseased patient is more likely to be retested than a non-diseased patient, failure to do this is likely to lead to overrepresentation of results from unwell subjects. When selecting a single result, the last result of a patient during a “healthcare episode” is preferred as it is most likely to represent a return towards health [14].

Statistical techniques

The Bhattacharya method is a graphical method for identifying a Gaussian distribution in the midst of other data [42]. It was originally developed in the precomputer era using manual paper-based systems. Computer-based versions have been developed in Java and Microsoft Excel. The Bhattacharya method is user-dependent, requiring selection of bin size for the data, the bin location and the number of bins included in the analysis. The Hoffmann technique also identifies a homeostatically regulated population subset of test results in a data set that is assumed to follow Gaussian or near-Gaussian distribution [43]. Like the Bhattacharya method, it was developed in the precomputer era for paper-based systems. More recently, this method has been used in a computerized form [44], [45]. A limitation of the Hoffmann procedure is that it is influenced by the presence of a secondary population of significant size [46] although filtering of the data can reduce this effect. A more sophisticated procedure than those of Hoffmann and Bhattacharya was developed by Arzideh et al. [41]. In this process, a smoothed kernel density function was estimated for the distribution of the total mixed data of the sample group (combined data of non-diseased and diseased subjects). It was assumed that the “central” part of the distribution of all data represents the non-diseased population. Standard parametric (mean and standard deviation) or non-parametric statistics (percentiles), such as those used in direct RI studies, can also be used for indirect studies. This will involve outlier removal, either before or after transformation, followed by calculation of the mean and SD or median and relevant percentiles [14].

Comparison of the direct and indirect approaches

Important benefits of the indirect approach, relative to the direct approach, include that it is faster and cheaper as the indirect approach is based on data that have already been generated as part of routine care, thus excluding the resource-intensive components, i.e. patient identification, recruiting, specimen collection and measurement, of the direct approach. Indirect methods also use the same preanalytical and analytical techniques used for patient management and can provide very large numbers for assessment [47]. However, there are risks and difficulties associated with indirect approaches. The most important risk is the question as to whether the presence of diseased individuals influences the RIs. Furthermore, there is still no consensus on the best statistical method to derive indirect RIs. IFCC, C-RIDL is currently working on the study for the comparison of different statistical techniques for establishing indirect reference intervals with the existing direct methods to close this deficit in the literature.

Transference of reference intervals

Assuming the original RI study was performed using a robust methodology and statistical procedures, transferring a RI requires that certain conditions be fulfilled in order to be acceptable, prior to verifying and receiving a RI. There are two main scenarios in which RIs are transferred. First, reference values may originate from a different population/laboratory method than the receiving laboratory, and second, reference values may originate from a laboratory that shares the same laboratory method/population as the receiving laboratory. In the first instance, comparing the laboratory methods serves as an instructive early screening tool to assess the suitability of the reference values for the receiving laboratory. Laboratory methods can be compared by a method comparison study between the method used during the development of the RI and the method used by the receiving laboratory to determine the statistical validity of a RI transfer [49]. For a method comparison study, samples must be collected with an appropriate distribution of values spanning the RI, as an insufficient range may underestimate and a range too large may overestimate the strength of the correlation. The correlation between the two methods is subsequently analyzed and, if appropriate, linear regression analysis is performed to determine the slope and y-intercept values of the best-fit regression line [50]. These values are subsequently used to transfer the RI. According to the EP28-A3c guideline, the best-fit regression line should have a slope bias close to 1, a y-intercept close to 0 and a correlation coefficient (r2) close to 1 [13]. Furthermore, according to CLSI EP09-A3guidelines, the scatter and bias plots should be examined for constant scatter to ensure there are no dramatic differences between the variation at the upper and lower ends of the range of values [50].

If the preanalytical processes, the laboratory methods, and the populations are very similar to those of the laboratory where the RIs originated, the method comparison study is still recommended to confirm the comparability, although the bias between the laboratory methods is expected to be very small [50]. However, in this situation, subsequent verification using samples from healthy reference individuals may not be necessary, and the laboratory may opt to simply perform a subjective assessment by carefully inspecting the reference population demographics, geographic location, preanalytical and analytical procedures, analytical performance and the statistical methods used in the RI study. If these factors are all consistent with the receiving laboratory’s population and procedures, the RI may be transferred with further verification [13].

Verification of reference intervals

Following transference, the CLSI EP28-A3c guideline recommends subsequently verifying the transferred RI. The guideline emphasizes that three approaches can be used to verify RIs: (1) a subjective assessment, (2) using a small number of reference individuals (e.g. n=20) and (3) using a large number of reference individuals (e.g. n=60, but fewer than 120) [13]. Using a large number of reference individuals is not generally preferred by routine laboratories, as this is nearly the same as the sample size required for a RI study. The standard approach recommended by the guideline for routine practice in laboratories is to collect and analyze samples from 20 healthy subjects per age and/or sex partition from the receiving laboratory’s local population and to compare these reference values with the RI established from the larger, more robust, original study. The Dixon [26] or Tukey methods [27] should be applied to test and subsequently remove outliers, and new specimens should be obtained to replace those removed. If no more than 2 of the 20 samples (i.e. 10% of the test results) fall outside the RI, it may be received for use, at least provisionally. If 3 or 4 of the 20 samples fall outside the RI, a second set of 20 reference specimens should be obtained. If again 3 or more of the new specimens (i.e. ≥10% of the test results) or 5 or more of the original 20 fall outside the RI, the user should reexamine the analytical procedures used and consider possible differences in the biological characteristics of the two populations sampled [13]. Although this guideline appears straightforward, RI partitions, the presence of outliers and initial unsuccessful verification can further complicate the verification process [21].