An unsolved problem in the design of a repetitive screening trial is the determination of a procedure which yields the optimal number of screens for efficient evaluation. An approach to this problem described in this paper is to use lead time properties of cases detected at screening to define a stopping rule. Previous results are generalized by allowing the intervals between screens to be arbitrary, and the probability of detecting preclinical disease to vary among screens.

Additional theory important in the design and evaluation of a periodic screening program is presented. The distributions of doubly bounded preclinical state forward and backward recurrence times of the stochastic screening model are derived. Properties of these distributions are used to obtain an expression for estimating the mean lead time gained by screening, an alternative theoretical expression for the mean lead time and an equation for calculating an estimate of the probability of detecting preclinical disease.

A stochastic model for a periodic screening program is presented in which the natural history of a chronic disease is assumed to follow a progressive path from a preclinical state to a clinical state. The sampling of preclinical state sojourn times by screening examinations generates bounds on the preclinical state recurrence times. The distribution of the bounded forward recurrence time is derived and used to obtain the distribution and mean of the lead time, and relationships for calculating the proportion of preclinical cases detected. These expressions are derived in terms of the preclinical state sojourn-time distribution and adjustible parameters important in the design of a periodic screening program.