Regression to the Mean in Half-Life Studies.

Half-life studies of environmental contaminants in humans are restricted to only a few measurements per subject taken after the initial exposure, the initial dose is usually unknown, and subjects are included in the study only if their body burden is above a threshold C. The assumption of a one compartment first order decay model leads to a repeated measures linear model relating the logarithm of the biomarker with time, with the negative of the coefficient of time being the decay rate. The usual least-squares estimate of the decay rate is biased due to regression to the mean. In this report, based on the repeated measure linear model, unbiased estimates of the decay rate have been developed by the method of least-squares. This has been done for the two cases: (1) when there is no covariate (Report I) and (2) when there is a categorical covariate (Report II). The maximum likelihood estimator of the decay rate is developed (Report III) under the assumption that the logarithm of the concentration of the contaminant for the k time points of each subject has a truncated multivariate normal distribution with AR (1).