Adjusting for measurement error to assess health effects of variability in biomarkers

Abstract

Longitudinal studies of health effects often relate individuals' biomarker levels to disease progression. Repeated measurements also provide an opportunity to assess within-individual biomarker variability, and it is reasonable to postulate that this measure might provide additional information about a particular outcome variable. Given the existing precedent for application of adjustment methods to account for measurement error in subject-specific average levels of a covariate, this concept motivates the application of such methods to incorporate variability as well. In this paper, we investigate the nature of the relationship between the decline of CD4 cell count induced by infection with human immunodeficiency virus, and CD4 level and variability prior to infection. We first describe the distribution of repeated CD4 measurements prior to infection using a model that accounts both for random average levels and random subject-specific variance components. Based on this model, we define true unobservable random variables that correspond to prior level and stability. We perform a linear regression analysis, using these latent variables as covariates, by means of a full maximum likelihood approach. We compare the resulting parameter estimates with those based on regressions employing sample-based estimates of pre-infection levels and variances, and empirical Bayes estimates of these quantities. Although the final inferences are similar to those based on the unadjusted analysis, we find that the magnitude of association with prior level decreases, while that with prior stability increases. Stratified analyses indicate that smoking status affects the relationship between prior CD4 level and initial CD4 decline. We point out advantages associated with the maximum likelihood approach in this particular application.