Correcting for selection bias in estimation of within-individual variance

Consider a variable whose expected value distributes among individuals in a population, and which also has an important component of within-individual variance. In a screening study that involves repeated observations only for those individuals whose initial observation exceeds an arbitrary cutoff point, the usual estimator of within-individual variance is biased. Assuming normality and independence, this note gives the derivation of the expected value of the estimator and uses it to obtain an unbiased estimator. The results generalize to the bivariate case that involves selection on only one variable of the pair. A companion paper provides an example with use of blood pressure.