Abstract
Inference for point processes is more efficient when the exact event occurrence times are known. However, collecting exact times is sometimes difficult due to a study design or practical restrictions. Yet, even then, the grouped number of events, that is, the number of events in intervals of the observation period, is available. Having only the grouped number of recurrent events with time-dependent covariates available, we investigate the precision in estimation of a parameter representing a treatment effect. The study includes only time-dependent covariate which is a function of the cumulative number of recurrent events. The time-dependent covariate is observed at a designated design point and the observation period is divided into two or three intervals. Our results suggest that the lowest bias in estimation of the treatment effect is obtained when the design-point coincides with one of the partition points. High efficiency in parameter estimation is obtained when we take the design-point as the partition point for division of the observation period into two intervals. Additionally, in the case of the division into three intervals, high efficiency is obtained when dividing the first half of the observation period equally into two intervals and setting the design point at the second partition point.
