Efficient panel designs for longitudinal recurrent event studies recording panel counts

Many clinical trials are designed to study outcome measures recorded as the number of events occurring during specific intervals, called panel data. In such data, the intervals are specified by a planned set of follow-up times. As the collection of panel data results in a partial loss of information relative to a record of the actual event times, it is important to gain a thorough understanding of the impact of panel study designs on the efficiency of the estimates of treatment effects and covariates. This understanding can then be used as a base from which to formulate appropriate designs by layering in other concerns, e.g. clinical constraints, or other practical considerations. We compare the efficiency of the analysis of panel data with respect to the analysis of data recorded precisely as times of recurrences, and articulate conditions for efficient panel designs where the focus is on estimation of a treatment effect when adjusting for other covariates. We build from the efficiency comparisons to optimize the design of panel follow-up times. We model the recurrent intensity through the common proportional intensity framework, with the treatment effect modeled flexibly as piecewise constant over panels, or groups of panels. We provide some important considerations for the design of efficient panel studies, and illustrate the methods through analysis of designs of studies of adenomas.