The influence of a covariate on optimal designs in longitudinal studies with discrete-time survival endpoints

Longitudinal intervention studies on event occurrence can measure the timing of an event at discrete points in time. To design studies of this kind as inexpensively and efficiently as possible, researchers need to decide on the number of subjects and the number of measurements for each subject. Different combinations of these design factors may produce the same level of power, but each combination can have different costs. When applying a cost function, the optimal design gives the optimal number of subjects and measurements, thus maximizing the power for a given budget and achieving sufficient power at minimal costs. Only very limited research has been conducted on the effect of a predictive covariate on optimal designs for a treatment effect estimator. Here, we go one step further than previous studies on optimal designs and demonstrate the extent to which a binary covariate influences the optimal design. An examination of various covariate effects and prevalences shows how substantially the covariate affects the optimal design and this effect is partly associated with the cost ratio between sampling subjects and measurements, and the survival pattern. So since the optimal design is sensitive to misspecification of these factors, we advise researchers to carefully specify the covariate effect and prevalence.