Screening and diagnosis when within-individual observations are Markov-dependent

The statistical model currently used for determining the amount of regression to the mean that will occur in a screening study includes an assumption that repeat observations within the same subject are mutually independent. This assumption has been used in the determination of the number of repeat observations within an individual that is required to reduce the amount of regression to the mean or the probability of misclassification to a given value. In this paper the model is extended to the case in which repeat observations within an individual are Markov-dependent. New expressions are given for the regression to the mean, based on the time delay between screening and re-examination, and on the use of an average of several measurements for both screening and re-examination. The extended model is used to describe the conditional distribution of the long-term mean of an individual, given several measurements, and this distribution is suggested as a diagnostic tool. A method is presented for estimation of the autocorrelation coefficient in very short time series observed in several individuals. The autocorrelation in diastolic blood pressure is estimated from a set of repeat observations, one day apart, on a group of subjects.