Objective Criteria for Partitioning Gaussian-distributed Reference Values into Subgroups

Abstract Background: The aim of this study was to develop new and useful criteria for partitioning reference values into subgroups applicable to gaussian distributions and to distributions that can be transformed to gaussian distributions. Methods: The proposed criteria relate to percentages of the subgroups outside each of the reference limits of the combined distribution. Critical values suggested as partitioning criteria for these percentages were derived from analytical bias quality specifications for using common reference intervals throughout a geographic area. As alternative partitioning criteria to the actual percentages, these were transformed mathematically to critical distances between the reference limits of the subgroup distributions, to be applied to each pair of reference limits, the upper and the lower, at a time. The new criteria were tested using data on various plasma proteins collected from ∼500 reference individuals, and the outcomes were compared with those given by the currently widely applied and recommended partitioning model of Harris and Boyd, the “Harris-Boyd model”. Results: We suggest 4.1% as the critical minimum percentage outside that would justify partitioning into subgroups, and 3.2% as the critical maximum percentage outside that would justify combining them. Percentages between these two values should be classified as marginal, implying that nonstatistical considerations are required to make the final decision on partitioning. The correlation between the critical percentages and the critical distances was mathematically precise in the new model, whereas this correlation is rather approximate in the Harris-Boyd model because focus on the difference between means in this model makes high precision hard to achieve. The application examples suggested that the new model is more radical than the Harris-Boyd model. Conclusions: New percentage and distance criteria, to be used for partitioning gaussian-distributed data, have been developed. The distance criteria, applied separately to both reference limit pairs of the subgroup distributions, seemed more reliable and correlated more accurately with the critical percentages than the distance criteria of the Harris-Boyd model. As opposed to the Harris-Boyd model, the new model is easily adjustable to new critical values of the percentages, should they need to be changed in the future.

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Impact of Subgroup Prevalences on Partitioning of Gaussian-distributed Reference Values

Clinical Chemistry ◽

10.1093/clinchem/48.11.1987 ◽

2002 ◽

Vol 48 (11) ◽

pp. 1987-1999 ◽

Cited By ~ 49

Author(s):

Ari Lahti ◽

Per Hyltoft Petersen ◽

James C Boyd

Keyword(s):

Reference Interval ◽

Reference Population ◽

Reference Intervals ◽

Source Population ◽

Distributed Data ◽

New Model ◽

Common Reference ◽

Reference Limits ◽

Partitioning Problem ◽

Analytical Expressions

Abstract Background: The aims of this report were to examine how unequal subgroup prevalences in the source population may affect reference interval partitioning decisions and to develop generally applicable guidelines for partitioning gaussian-distributed data. Methods: We recently proposed a new model for partitioning reference intervals when the underlying data distribution is gaussian. This model is based on controlling the proportions of the subgroup distributions that fall outside each of the common reference limits, using the distances between the reference limits of the subgroup distributions as functions to these proportions. We examine the significance of the unequal prevalence effect for the partitioning problem and quantify it for distance partitioning criteria by deriving analytical expressions to express these criteria as a function of the ratio of prevalences. An application example, illustrating various aspects of the importance of the prevalence effect, is also presented. Results: Dramatic shrinkage of the critical distances between reference limits of the subgroups needed for partitioning was observed as the ratio of prevalences, the larger one divided by the smaller one, was increased from unity. Because of this shrinkage, the same critical distances are not valid for all ratios of prevalences, but specific critical distances should be used for each particular value of this ratio. Although proportion criteria used in determining the need for reference interval partitioning are not dependent on the prevalence effect, this effect should be accounted for when these criteria are being applied by adjusting the sample sizes of the subgroups to make them correspond to the ratio of prevalences. Conclusions: The prevalences of subgroups in the reference population should be known and observed in the calculations for every reference interval study, irrespective of whether distance or proportion criteria are being used to determine the need for reference interval partitioning. We present detailed methods to account for the prevalences when applying each of these types of criteria. Analytical expressions for the distance criteria, to be used when high precision is needed, and approximate distances, to be used in practical work, are derived. General guidelines for partitioning gaussian distributed data are presented. Following these guidelines and using the new model, we suggest that partitioning can be performed more reliably than with any of the earlier models because the new model not only offers an improved correspondence between the critical distances and the critical proportions, but also accounts for the prevalence effect.

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Critical comments to a recent EFLM recommendation for the review of reference intervals

Clinical Chemistry and Laboratory Medicine (CCLM) ◽

10.1515/cclm-2016-1112 ◽

2017 ◽

Vol 55 (3) ◽

Cited By ~ 5

Author(s):

Rainer Haeckel ◽

Werner Wosniok ◽

Farhad Arzideh ◽

Jakob Zierk ◽

Eberhard Gurr ◽

...

Keyword(s):

Gold Standard ◽

Reference Intervals ◽

Direct Approach ◽

Confidence Limits ◽

Common Reference ◽

Reference Limits ◽

Age Range

AbstractIn a recent EFLM recommendation on reference intervals by Henny et al., the direct approach for determining reference intervals was proposed as the only presently accepted “gold” standard. Some essential drawbacks of the direct approach were not sufficiently emphasized, such as unacceptably wide confidence limits due to the limited number of observations claimed and the practical usability for only a limited age range. Indirect procedures avoid these disadvantages of the direct approach. Furthermore, indirect approaches are well suited for reference limits with large variations during lifetime and for common reference limits.

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Partitioning biochemical reference data intosubgroups: comparison of existing methods

Clinical Chemistry and Laboratory Medicine (CCLM) ◽

10.1515/cclm.2004.123 ◽

2004 ◽

Vol 42 (7) ◽

Cited By ~ 14

Author(s):

Ari Lahti

Keyword(s):

Reference Data ◽

Reference Interval ◽

Reference Intervals ◽

New Method ◽

Poor Correlation ◽

Specific Reference ◽

Common Reference ◽

Reference Limits ◽

The Common ◽

The Ideal

AbstractFour existing methods for partitioning biochemical reference data into subgroups are compared. Two of these, the method of Sinton et al. and that of Ichihara and Kawai, are based on a quotient of a difference between the subgroups and the reference interval for the combined distribution. The criterion of Sinton et al. appears rather stringent and could lead to recommendations to apply a common reference interval in many cases where establishment of group-specific reference intervals would be more useful. The method of Ichihara and Kawai is similar to that of Sinton et al., but their criterion, based on a quantity derived from between-group and within-group variances, seems to lead to inconsistent results when applied to some model cases. These two methods have the common weakness of using gross differences between subgroup distributions as an indicator of differences between their reference limits, while distributions with different means can actually have equal reference limits and those with equal means can have different reference limits. The idea of Harris and Boyd to require that the proportions of the subgroup distributions outside the common reference limits be kept reasonably close to the ideal value of 2.5% as a prerequisite for using common reference limits seems to have been a major improvement. The other two methods considered, that of Harris and Boyd and the “new method” follow this idea. The partitioning criteria of Harris and Boyd have previously been shown to provide a poor correlation to those proportions, however, and the weaknesses of their method are summarized in a list of five drawbacks. Different versions of the new method offer improvements to these drawbacks.

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Albumin and calcium reference interval using healthy individuals and a data-mining approach

Annals of Clinical Biochemistry International Journal of Laboratory Medicine ◽

10.1177/0004563220944204 ◽

2020 ◽

Vol 57 (5) ◽

pp. 373-381 ◽

Cited By ~ 2

Author(s):

N Jassam ◽

A Luvai ◽

D Narayanan ◽

D Turnock ◽

G Lee ◽

...

Keyword(s):

Metrological Traceability ◽

Reference Interval ◽

Reference Population ◽

Reference Intervals ◽

Healthy Individuals ◽

Reference Limit ◽

Common Reference ◽

Age Related ◽

Upper Reference Limit ◽

Analytical Platforms

Background Harmonization of reference intervals for analytes that have a sound calibration and metrological traceability is a widely recommended practice. The UK Pathology Harmony has recently harmonized reference intervals for calcium and albumin. In this study, we have determined the reference intervals for calcium and albumin on the UK’s most commonly used analytical platforms. Method A prospective reference population of healthy individuals was recruited according to the IFCC CRIDL criteria. A second indirect population was collected from 14 primary care setting and measured in laboratories using various analytical platforms and methods (Roche, Abbott, Beckman and Siemens analytical platforms). Results In total, 299 subjects were recruited; the central 95th centile values for calcium for three out of four analytical platforms were in a close agreement with UK Pathology Harmony reference intervals of 2.2–2.6 mmol/L. Reference intervals of BCG methods from both cohorts and irrespective of analytical platforms were higher for both lower and upper reference limits than those for BCP. In comparison, the indirect study showed an age-related variation. The younger population reference intervals varied by up to 5.7% at the lower reference limit and up to 12% at the upper reference limit compared with Pathology Harmony reference intervals, and the older population showed a variation of up to 14% at both limits. Conclusion While calcium reference intervals can be a subject for harmonization, albumin reference intervals studied showed large variation which is unsupportive of embracing a common reference interval for albumin.

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Reference ranges for clinical electrophysiology of vision

Documenta Ophthalmologica ◽

10.1007/s10633-021-09831-1 ◽

2021 ◽

Author(s):

C. Quentin Davis ◽

Ruth Hamilton

Keyword(s):

Reference Values ◽

False Negative ◽

Reference Interval ◽

Reference Intervals ◽

Clinical Electrophysiology ◽

Reference Ranges ◽

Physiological Measurement ◽

Negative Results ◽

Reference Limits ◽

Suitable Reference

Abstract Introduction Establishing robust reference intervals for clinical procedures has received much attention from international clinical laboratories, with approved guidelines. Physiological measurement laboratories have given this topic less attention; however, most of the principles are transferable. Methods Herein, we summarise those principles and expand them to cover bilateral measurements and one-tailed reference intervals, which are common issues for those interpreting clinical visual electrophysiology tests such as electroretinograms (ERGs), visual evoked potentials (VEPs) and electrooculograms (EOGs). Results The gold standard process of establishing and defining reference intervals, which are adequately reliable, entails collecting data from a minimum of 120 suitable reference individuals for each partition (e.g. sex, age) and defining limits with nonparametric methods. Parametric techniques may be used under some conditions. A brief outline of methods for defining reference limits from patient data (indirect sampling) is given. Reference intervals established elsewhere, or with older protocols, can be transferred or verified with as few as 40 and 20 suitable reference individuals, respectively. Consideration is given to small numbers of reference subjects, interpretation of serial measurements using subject-based reference values, multidimensional reference regions and age-dependent reference values. Bilateral measurements, despite their correlation, can be used to improve reference intervals although additional care is required in computing the confidence in the reference interval or the reference interval itself when bilateral measurements are only available from some of subjects. Discussion Good quality reference limits minimise false-positive and false-negative results, thereby maximising the clinical utility and patient benefit. Quality indicators include using appropriately sized reference datasets with appropriate numerical handling for reporting; using subject-based reference limits where appropriate; and limiting tests for each patient to only those which are clinically indicated, independent and highly discriminating.

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Functional reference limits: a case study of serum ferritin

Journal of Laboratory Medicine ◽

10.1515/labmed-2020-0127 ◽

2021 ◽

Vol 45 (2) ◽

pp. 69-77

Author(s):

Gorkem Sezgin ◽

Tze Ping Loh ◽

Corey Markus

Keyword(s):

Serum Ferritin ◽

Reference Population ◽

Reference Intervals ◽

Reference Limit ◽

Subclinical Disease ◽

Routinely Collected Data ◽

Reference Limits ◽

Relevant Reference ◽

The Relationship

Abstract Reference intervals depend on the distribution of results within a reference population and can be influenced by subclinical disease. Functional reference limits present an opportunity to derive clinically relevant reference limits from routinely collected data sources, which consist of mixed populations of unhealthy and healthy groups. Serum ferritin is a good example of the utility of functional reference limits. Several studies have identified clinically relevant reference limits through examining the relationship between serum ferritin and erythrocyte parameters. These ferritin functional limits often represent the inflection point at which erythrocyte parameters change significantly. Comparison of ferritin functional reference limits with those based on population distributional reference limits reveals that the lower reference limit may fall below the point at which patients become clinically unwell. Functional reference limits may be considered for any biomarker that exhibits a correlated relationship with other biomarkers.

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A self-consistent set of reference values for 23 clinical chemical analytes.

Clinical Chemistry ◽

10.1093/clinchem/35.3.448 ◽

1989 ◽

Vol 35 (3) ◽

pp. 448-452 ◽

Cited By ~ 3

Author(s):

U E Spichiger ◽

D J Vonderschmitt

Keyword(s):

Reference Values ◽

Iterative Procedure ◽

Blood Donors ◽

Reference Population ◽

Reference Intervals ◽

Men And Women ◽

A Value ◽

Self Consistent ◽

Reference Limits ◽

Clinical Chemical

Abstract Heparinized plasma of 528 blood donors was subjected to the 23 most frequently ordered chemical and enzymatic tests. The central fraction of the distribution of all results for each test was estimated. Out of the 528 donors a reference population has been selected. Because of the lack of other criteria, the result for any test of a blood donor was selected as a value belonging to the reference population if the results for the other 22 analytes of this particular donor lay within their own central fraction. On this basis an iterative procedure for the selection was programmed, considering the interaction between tests. The procedure was stopped when the reference limits for all 23 tests were converging. Fractions from 0.90 to 0.98 were applied to results for men and women donors separately. The elimination procedure and the criteria to select the best fitted fraction are discussed. The derived reference intervals are designated a "self-consistent set of reference values."

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Equivalence limits of reference intervals for partitioning of population data. Relevant differences of reference limits

LaboratoriumsMedizin ◽

10.1515/labmed-2016-0002 ◽

2016 ◽

Vol 40 (3) ◽

Author(s):

Rainer Haeckel ◽

Werner Wosniok ◽

Farhad Arzideh

Keyword(s):

Population Data ◽

Reference Intervals ◽

International Standards ◽

Reference Limit ◽

Permissible Limits ◽

First Case ◽

Reference Limits ◽

External Sources ◽

The Difference ◽

Simple Equations

Abstract:Reference limits need to be compared with each other for two main purposes: to evaluate the clinical relevance of a possible difference, if limits are obtained from the same population but at different time periods, or to check if limits derived from two different subpopulations can be considered as identical. The comparison of reference limits required for the periodic reviewing of applied reference limits and for checking the transferability of reference limits adopted from external sources according to international standards is an example for the first case. In the second case, a decision is intended whether the full population has to be partitioned (stratified) into the subpopulations under consideration (e.g. males and females). In both situations, differences may be due either to analytical errors, to biological differences or to both effects. The difference between reference limits may be acceptable if it is within permissible limits. For establishing permissible limits, the concept of equivalence limits was adopted to assess the relevance of differences between two reference limits. The concept bases on the permissible uncertainty at a particular reference limit. The permissible uncertainty is quantified by the permissible analytical standard deviation derived from the empirical biological variation as recently proposed. It is defined separately for lower and upper reference limits. The concept proposed can be condensed to simple equations.

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Reference Values for 30 Common Biochemistry Analytes Across 5 Different Analyzers in Neonates and Children 30 Days to 18 Years of Age

Clinical Chemistry ◽

10.1373/clinchem.2019.306431 ◽

2019 ◽

Vol 65 (10) ◽

pp. 1317-1326 ◽

Cited By ~ 9

Author(s):

Monsurul Hoq ◽

Susan Matthews ◽

Vicky Karlaftis ◽

Janet Burgess ◽

Jessica Cowley ◽

...

Keyword(s):

Reference Values ◽

Polynomial Regression ◽

Total Error ◽

Reference Intervals ◽

Specific Reference ◽

Mixed Effect ◽

Fractional Polynomial ◽

Reference Limits ◽

Effect Regression ◽

The Mean

Abstract BACKGROUND Age-specific reference intervals (RIs) have been developed for biochemistry analytes in children. However, the ability to interpret results from multiple laboratories for 1 individual is limited. This study reports a head-to-head comparison of reference values and age-specific RIs for 30 biochemistry analytes for children across 5 analyzer types. METHODS Blood was collected from healthy newborns and children 30 days to <18 years of age. Serum aliquots from the same individual were analyzed on 5 analyzer types. Differences in the mean reference values of the analytes by the analyzer types were investigated using mixed-effect regression analysis and by comparing maximum variation between analyzers with analyte-specific allowable total error reported in the Westgard QC database. Quantile regression was used to estimate age-specific RIs using power variables in age selected by fractional polynomial regression for the mean, with modification by sex when appropriate. RESULTS The variations of age-specific mean reference values between analyzer types were within allowable total error (Westgard QC) for most analytes, and common age-specific reference limits were reported as functions of age and/or sex. Analyzer-specific reference limits for all analytes on 5 analyzer types are also reported as functions of age and/or sex. CONCLUSIONS This study provides quantitative and qualitative measures of the extent to which results for individual children can or cannot be compared across analyzer types, and the feasibility of RI harmonization. The reported equations enable incorporation of age-specific RIs into laboratory information systems for improving evidence-based clinical decisions in children.

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Valid analytical performance specifications for combined analytical bias and imprecision for the use of common reference intervals

Annals of Clinical Biochemistry International Journal of Laboratory Medicine ◽

10.1177/0004563217752963 ◽

2018 ◽

Vol 55 (5) ◽

pp. 612-615

Author(s):

Per Hyltoft Petersen ◽

Flemming Lund ◽

Callum G Fraser ◽

Sverre Sandberg ◽

György Sölétormos

Keyword(s):

Clinical Chemistry ◽

Reference Intervals ◽

International Federation ◽

Analytical Performance ◽

Microsoft Excel ◽

Gaussian Distributions ◽

Common Reference ◽

Performance Specifications ◽

Constant Percentage

Background Many clinical decisions are based on comparison of patient results with reference intervals. Therefore, an estimation of the analytical performance specifications for the quality that would be required to allow sharing common reference intervals is needed. The International Federation of Clinical Chemistry (IFCC) recommended a minimum of 120 reference individuals to establish reference intervals. This number implies a certain level of quality, which could then be used for defining analytical performance specifications as the maximum combination of analytical bias and imprecision required for sharing common reference intervals, the aim of this investigation. Methods Two methods were investigated for defining the maximum combination of analytical bias and imprecision that would give the same quality of common reference intervals as the IFCC recommendation. Method 1 is based on a formula for the combination of analytical bias and imprecision and Method 2 is based on the Microsoft Excel formula NORMINV including the fractional probability of reference individuals outside each limit and the Gaussian variables of mean and standard deviation. The combinations of normalized bias and imprecision are illustrated for both methods. The formulae are identical for Gaussian and log-Gaussian distributions. Results Method 2 gives the correct results with a constant percentage of 4.4% for all combinations of bias and imprecision. Conclusion The Microsoft Excel formula NORMINV is useful for the estimation of analytical performance specifications for both Gaussian and log-Gaussian distributions of reference intervals.

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