Optimal designs for epidemiologic longitudinal studies with binary outcomes

Abstract

Alternating presence and absence of a medical condition in human subjects is often modelled as an outcome of underlying process dynamics. Longitudinal studies provide important insights into research questions involving such dynamics. This article concerns optimal designs for studies in which the dynamics are modelled as a binary continuous-time Markov process. Either one or both the transition rate parameters in the model are to be estimated with maximum precision from a sequence of observations made at discrete times on a number of subjects. The design questions concern the choice of time interval between observations, the initial state of each subject and the choice between number of subjects versus repeated observations per subject. Sequential designs are considered due to dependence of the designs on the model parameters. The optimal time spacing can be approximated by the reciprocal of the sum of the two rates. The initial distribution of the study subjects should be taken into account when relatively few repeated samples per subject are to be collected. A study with a reasonably large size should be designed in more than one phase because there are then enough observations to be spent in the first phase to revise the time spacing for the subsequent phases.