Calculating reference intervals for laboratory measurements

Influence of demographic factors and sport type on growth hormone-responsive markers in elite athletes

CONTEXT

GH-responsive markers of the IGF system and of collagen turnover hold promise as the basis of a GH doping test.

OBJECTIVE

The purpose of this study was to determine the influence of age, gender, body mass index (BMI), ethnicity, and sporting type on GH-responsive serum markers in a large cohort of elite athletes from different ethnic backgrounds.

DESIGN

The study was designed as a cross-sectional study.

PARTICIPANTS

A total of 1103 elite athletes (699 males, 404 females), aged 22.2 +/- 5.2 yr, from 12 countries and 10 major sporting categories participated in this study.

MAIN OUTCOME MEASURES

Serum IGF-I, IGF binding protein-3 (IGFBP-3), acid labile subunit (ALS), and collagen markers [N-terminal propeptide of type I procollagen (PINP), C-terminal telopeptide of type I collagen (ICTP), N-terminal propeptide of type III procollagen (PIIINP)] were measured.

RESULTS

There was a significant negative correlation (r = -0.14 to -0.58, P < 0.0005) between age and each of the GH-responsive markers. Serum IGF-I, IGFBP-3, and ALS were all lower (P < 0.05), whereas the collagen markers PINP, ICTP, and PIIINP were higher (P < 0.05) in men than in women. Multiple regression analysis indicated that age, gender, BMI, and ethnicity accounted for 23-54% of total between-subject variability of the markers. Age and gender cumulatively accounted for 91% of the attributable variation of IGF-I and more than 80% for PINP, ICTP, and PIIINP. Gender exerted the greatest effect on ALS (48%), and BMI accounted for less than 12% attributable variation for all markers. The influence of ethnicity was greatest for IGFBP-3 and ALS; however, for the other markers, it accounted for less than 6% attributable variation. Analysis of 995 athletes indicated that sporting type contributed 5-19% of attributable variation.

CONCLUSIONS

Age and gender were major determinants of variability of GH-responsive markers except for IGFBP-3 and ALS. Ethnicity is unlikely to confound the validity of a GH doping test based on IGF-I and these collagen markers.

Estimation of an age-specific reference interval for pulse wave velocity: a meta-analysis

OBJECTIVE

To estimate an age-specific reference interval for carotid-femoral pulse wave velocity (PWV), an index of aortic stiffness, and to determine the predictive values of the reference range for detecting those at moderate and high risk of cardiovascular disease (CVD).

DESIGN AND METHODS

We searched MEDLINE using PubMed from 1995 to 2005 for all studies in which Carotid-Femoral PWV was measured using a Complior (Colson, Paris, France) apparatus in Caucasian non-pregnant adults. Twenty-five studies were included, covering 30 groups of subjects; these groups were classified a priori into low (normal), moderate, and high CVD risk categories, with 2008, 5979, and 180 (total 8167) subjects, respectively. Individual-level data were simulated for each group, and an age-specific reference interval was calculated by using fractional polynomial functions.

RESULTS

We plotted an age-adjusted normal curve for PWV with 2.5, 5, 50, 90, 95, and 97.5 centile limits. Applying this reference interval to the moderate- and high-risk groups using simulations yielded sensitivities of 34.3 [95% confidence interval (CI) 33.2-35.3] and 57.2 (95% CI 55.2-59.3), respectively, specificities of 95.3 (95% CI 94.8-95.8) and 95.3 (95% CI 94.4-96.2), respectively, and positive likelihood ratios of 7.3 and 12.2, respectively.

CONCLUSION

We constructed an age-adjusted reference curve for PWV. Using the 95th centile of this curve as a threshold (e.g. 10.94, 11.86, and 13.18 m/s for 20, 40, and 60 years old) shows construct validity, as it appears to identify medium and high CVD risk groups reasonably accurately. This reference range needs to be tested using other datasets.

Methods to estimate the optimal threshold for normally or log-normally distributed biological tests

Putting a screening or a diagnostic test into everyday use requires the determination of its threshold. The authors present methods that yield a point and an interval estimation of the threshold that maximize the population utility whenever the test results are normally or log-normally distributed among healthy and among diseased subjects, with equal variances. These methods were assessed for bias, coverage probability, coverage symmetry, and confidence-interval width using simulation. They proved to be asymptotically nonbiased and to have a satisfactory coverage probability whenever the sample sizes of the healthy and the diseased subjects are equal to or greater than 50. The methods were next applied to determine an optimal threshold for the antibody load used to diagnose congenital toxoplasmosis at birth. The methods are easy to implement and impose few constraints; however, the sample sizes should be carefully determined according to the required accuracy.

Assessing uncertainty in reference intervals via tolerance intervals: application to a mixed model describing HIV infection

We define the reference interval as the range between the 2.5th and 97.5th percentiles of a random variable. We use reference intervals to compare characteristics of a marker of disease progression between affected populations. We use a tolerance interval to assess uncertainty in the reference interval. Unlike the tolerance interval, the estimated reference interval does not contains the true reference interval with specified confidence (or credibility). The tolerance interval is easy to understand, communicate and visualize. We derive estimates of the reference interval and its tolerance interval for markers defined by features of a linear mixed model. Examples considered are reference intervals for time trends in HIV viral load, and CD4 per cent, in HIV-infected haemophiliac children and homosexual men. We estimate the intervals with likelihood methods and also develop a Bayesian model in which the parameters are estimated via Markov-chain Monte Carlo. The Bayesian formulation naturally overcomes some important limitations of the likelihood model.

A new approach to sample size calculation for reference interval studies

A new criterion is proposed for determining the sample size required for a study performed for the purpose of establishing reference intervals. The basic idea behind the criterion is to compare the empirical coverage (i.e. the probability content) of the reference region obtained from the sample with its target value (e.g. 95 per cent) and to set suitable limits delta1, delta2 to the difference between both quantities which must not be exceeded with sufficiently large probability beta (e.g. beta=90 per cent). For the most frequently used parametric and distribution-free methods of estimating univariate reference limits, implicit formulae are derived relating the sample size to the design parameters delta1, delta2 and beta. For symmetric specification of (delta1, delta2), explicit approximation formulae for the computation of n are given. Exact values obtained by means of suitable numerical techniques are presented in a set of tables covering specifications of delta1, delta2 and beta which can be recommended for real applications. The tables can be used both for one- and two-sided reference intervals.

Centile Charts II: Alternative Nonparametric Approach for Establishing Time-Specific Reference Centiles and Assessment of the Sample Size Required

Background: Reference intervals, and more generally centile estimates, are used to characterize a reference population for the purposes of interpreting an individual patient’s clinical measurement. We describe methods of calculating reference intervals where these centiles vary with a covariate, usually age or time.

Methods: The US Food and Drug Administration and the IFCC have made recommendations on two approaches: the parametric approach, which models the structural characteristics of the data set with a theoretical distribution, and the nonparametric approach, which makes no particular assumption about this structure. In this report we propose a nonparametric procedure that relies on the principles of regression and show how sample size determination can be assessed. We also show how the sample size calculation is influenced by the distribution of the times measured.

Results: We illustrated our method on three data sets and compared the results for our proposed nonparametric method with parametric estimates. We showed that the bias is reduced and that the nonparametric method is less likely to produce fluctuating profiles.

Conclusions: To achieve adequate precision the sample size needs to be larger than 120, as has often been recommended. If there is doubt about the parametric model, then threshold sample sizes may need to be as high as 500.

Centile Charts I: New Method of Assessment for Univariate Reference Intervals

Background: We introduce a new criterion, the percentile inclusion probability, for comparing methods for calculating reference intervals. The criterion is compared with a previously published measure of reliability suggested by Linnet (Linnet K. Clin Chem 1987;33:381–6), the ratio of the width of the confidence interval for the percentile to that of the reference interval.

Methods: Data were simulated from a range of theoretical statistical distributions representing the shapes of data sets encountered in clinical investigations. The two-stage transformation of the data to a gaussian distribution recommended by the IFCC was compared with a nonparametric approach.

Results: The percentile inclusion probability criterion identified that the parametric approach is in some cases seriously affected by bias. Using different parametric models, we compared nonparametric and parametric methods for two sets of clinical data and showed that the parametric approach is susceptible to model choice.

Conclusions: Sample sizes significantly greater than those currently recommended are required to establish reference intervals, regardless of whether parametric or nonparametric methods are used. Parametric methods are preferable when the data are truly gaussian, but are only marginally better than nonparametric methods when data transformation is needed to achieve a gaussian shape.

Reference Centiles for Serum Ferritin and Percentage of Transferrin Saturation, with Application to Mutations of the HFE Gene

Background: The gene that causes most cases of hereditary hemochromatosis is designated HFE. Individuals with mutations in the HFE gene may have increased serum iron, transferrin saturation, and ferritin concentrations relative to individuals with the wild-type genotype.

Methods: We generated reference centiles for percentage of transferrin saturation and serum ferritin concentrations in normal (wild-type), healthy Caucasian adults. We then examined transferrin and ferritin concentrations relative to these centiles in 81 individuals homozygous for the major hemochromatosis mutation C282Y and 438 individuals with the compound heterozygous HFE genotype C282Y/H63D.

Results: Serum ferritin concentrations, but not percentage of transferrin saturation, in normal, healthy women tended to increase sharply as they progressed through menopause. Transferrin and serum ferritin centiles for normal, healthy females were lower than the corresponding centiles in normal, healthy males. C282Y homozygotes had abnormally high transferrin saturation and serum ferritin values relative to the wild types. Compound heterozygotes appeared to be a mixture of individuals with unexceptional transferrin and ferritin values and those with abnormally large values similar to the homozygotes, with equal proportions of each.

Conclusions: There are age- and sex-related differences in reference centiles for the percentage of transferrin saturation and serum ferritin concentrations in normal, healthy adults. Individuals homozygous for the C282Y mutation in the HFE gene have abnormal transferrin saturation and serum ferritin values relative to the reference population; penetrance with the compound heterozygotes, as reflected by abnormal transferrin and ferritin values, is less than with the homozygotes.

Quantitative assessment of cutaneous thermal and vibration sensation and thermal pain detection thresholds in healthy children and adolescents

Quantitative sensory testing (QST) is a noninvasive, computer-assisted method for assessing function in peripheral small and large sensory fibers. In order to use QST for clinical neurological assessment in children, it is necessary: (1) to determine whether children can reliably perform these tests and (2) to characterize normal ranges in healthy children. Values of cold sensation, warm sensation, cold pain, heat pain, and vibration sensation detection thresholds were determined in the hand and foot with the method of limits (MLI) and method of levels (MLE) in 101 healthy children aged 6-17 years using a commercially available device. Both MLI and MLE were well-accepted by children, and there was good reproducibility between two sessions. The MLE takes longer to perform but produces lower thermal detection thresholds than the MLI. In the MLI, vibration and warm sensation showed higher thresholds in the foot than hand, whereas cold pain showed lower thresholds in the foot than hand. Based on these results, QST may be used to document and monitor the clinical course of sensory abnormalities in children with neurological disorders or neuropathic pain.

Goodness-of-fit statistics for age-specific reference intervals

The age-specific reference interval is a commonly used screening tool in medicine. It involves estimation of extreme quantile curves (such as the 5th and 95th centiles) of a reference distribution of clinically normal individuals. It is crucial that models used to estimate such intervals fit the data extremely well. However, few procedures to assess goodness-of-fit have been proposed in the literature, and even fewer have been evaluated systematically. Here we consider procedures based on the distribution of the Z-scores (standardized residuals) from a model and on Pearson chi(2) statistics for observed and expected counts in groups defined by age and the estimated reference centile curves. Two of the procedures (Q and grid tests) are mainly inferential, whereas the third (permutation bands and B-tests) is essentially graphical. We obtain approximations to the null distributions of several relevant test statistics and examine their size and power for a range of models based on real data sets. We recommend Q-tests in all situations where Z-scores are available since they are general, simple to calculate and usually have the highest power among the three classes of test considered. For the cases considered the grid tests are always inferior to the Q- and B- tests.

Typical error versus limits of agreement

We have shown that the SEM (typical error) and LOA are very similar when defined at the same level of abstraction. The calculation of these sample statistics does not depend on sample size, but the precision of their estimate for the population parameter does. Only the latter concept involves the t-statistic. They do differ in the type of measurement error that is described (true score error versus test-retest error) and the coverage probability of the reference interval (0.6 versus 0.95). Bland and Altman and Atdinson and Nevill have promoted the citation of either the SEM or the LOA to help researchers in their discussion of the impact of error to real uses of the measurement tol. What is vital in this discussion is the researcher having a thorough understanding of the underlying theory behind the measurement error statistic(s) that is/are employed, especially the definition of error and the coverage probability that is selected. Such issues have been built into the title of the 95% LOA statistic, and are also an inherent part of SEM. Whilst the concept of typical error appears to be easy to understand and teach, this is only because the underlying theory and definition of what the statistic actually represents is not communicated. Only if all researchers adopt one single statistic (e.g. typical error) for measurement error is it remotely possible to push underlying theory into the background, since there would be a baseline of comparison for all. Because this scenario is highly unlikely, it is important that any measurement error statistic is well defined and understood by researchers.