A modified regression model to adjust for intraindividual variation in serum biomarker concentrations

Department of Epidemiology
German Institute of Human Nutrition
Arthur-Scheunert-Allee 114-116
14558 Nuthetal
Germany
E-mail: khoff{at}mail.dife.de

Dear Sir:

I read with interest the recent article by Gillespie et al (1) suggesting a new method for predicting the mean retinol concentration of a person from a single measurement. The basic idea is to adjust for intraindividual variation. Gillespie et al applied the method to reduce prevalence estimates of inadequate serum retinol concentrations by using laboratory-quality data and a subsample of repeated measurements. The centerpiece of the method is the linear regression model,

where However, the chosen regression model did not adequately address the problem of eliminating the intraindividual variance component. First, it is possible that the estimate of the slope parameter ß₁ is larger than 1, which means that the prevalence estimate of inadequate concentrations will be exaggerated. To see this failure, consider a simple hypothetical example of 3 persons with first retinol concentration measurements of 1.9, 2.0, and 2.1 µmol/L and corresponding second retinol concentration measurements of 1.7, 2.0, and 2.3 µmol/L. The resulting individual means are 1.8, 2.0, and 2.2 µmol/L, and the estimate for ß₁ is equal to 2. In general, the proposed method may fail if both measurements are highly correlated and the second concentrations vary more than the first ones. Instead of regression on the first measurement, all single measurements should be included in the model. If this is done, the estimated regression slope cannot be larger than 1, which can be proven. In the hypothetical example, the estimate is 0.8 if all 6 measurements are used.

Second, the linear regression model should predict a person's "usual" serum retinol concentration defined as the long-term daily average. Although Gillespie et al adopt a similar interpretation of their approach, they actually use the mean of only 2 measurements as the dependent variable in the model. Because the mean of 2 repeated measurements still has an intraindividual variance component, this component must be subtracted before regression analysis is applied. Principally, the usual retinol concentration has to be estimated in a preliminary step. The problem of estimating usual or long-term exposure by repeated short-term measurements has been intensively studied in food-consumption and environmental surveys, and several statistical methods aimed at eliminating the intraindividual variance component are available (2-4).

In summary, I propose applying a modified regression model with another dependent variable and another independent variable. Regression of the estimated usual retinol concentration on a single concentration by using all single measurements allows elimination of the distracting effect of intraindividual variation. Applying this modified model should yield lower prevalence estimates of inadequate serum retinol concentrations than those obtained by Gillespie et al.

REFERENCES

1. Gillespie C, Ballew C, Bowman BA, Donehoo R, Serdula MK. Intraindividual variation in serum retinol concentrations among participants in the third National Health and Nutrition Examination Survey, 1988–1994. Am J Clin Nutr 2004;79:625-32.
2. Buck RJ, Hammerstrom KA, Ryan PB. Estimating long-term exposures from short-term measurements. J Expo Anal Environ Epidemiol 1995;5:359-73.
3. Nusser SM, Carriquiry AL, Dodd KW, Fuller WA. A semiparametric transformation approach to estimating usual daily intake distributions. J Am Stat Assoc 1996;91:1440-9.
4. Hoffmann K, Boeing H, Dufour A, et al. Estimating the distribution of usual dietary intake by short-term measurements. Eur J Clin Nutr 2002;56(suppl):S53-62.