On the Relation between Change and Initial Value

Abstract Given a series of consecutive measurements on a random sample of individuals, it is often of interest to investigate whether there exists a relationship between the rate of change and the initial value. Assuming that the observations deviate in a random manner from the true values, straightforward regression computations will yield biased results. It is shown that, in the case of the normal distribution, the maximum likelihood (ML) estimates of the second-order moments of the true slope and the true initial value are obtained by simple adjustments of the corresponding moments of the estimated quantities. An asymptotic formula for the standard error of the regression coefficient of slope on initial value is derived, and the methods are applied to longitudinal blood pressure data. The case with concomitant variables is discussed briefly.