D-optimal designs for a continuous predictor in longitudinal trials with discrete-time survival endpoints

In designing an experiment with one single, continuous predictor, the questions are composed of what is the optimal number of the predictor's values, what are these values, and how many subjects should be assigned to each of these values. In this study, locally D‐optimal designs for such experiments with discrete‐time event occurrence data are studied by using a sequential construction algorithm. Using the Weibull survival function for modeling the underlying time to event function, it is shown that the optimal designs for a linear effect of the predictor have two points that coincide with the design region's boundaries, but the design weights highly depend on the predictor effect size and its direction, the survival pattern, and the number of time points. For a quadratic effect of the predictor, three or four design points are needed.