Improving Statistical Power in Studies on Event Occurrence by Using an Optimal Design

Longitudinal studies on event occurrence aim to investigate if and when subjects experience a particular event, and the timing of these events may be measured continuously using thin precise units or discretely using time periods. To conduct such trials, a lot of labor, time, and money is needed, and to not waste these efforts, trials need to be carefully planned before they are actually conducted. The best way is to find a good or an optimal design in the planning phase of a trial and then implement it in real life. One can find a good design taking the statistical power and sample size into consideration, or find an optimal design taking the statistical power and sample size but also constraints like time limitations, feasibility, political, or ethical restrictions into account. In this way one can find a design that is actually feasible in reality, efficient and scientifically useful, and can be conducted using an available budget. The design of trials with continuous-time survival endpoints has been studied for years, but very little is known about the design of trials with discrete-time survival endpoints. The latter trials are conducted in many fields of science, for instance, in social and behavioral science, because observations are often recorded at intervals or at discrete points in time due to practical, financial, or ethical reasons, and therefore, it is important to carefully investigate that trials. When they are conducted in experimental setting, one or more groups of subjects receive a treatment, and they are compared to a group of subjects that receives a standard treatment or no treatment at all. The compared treatment groups might have an equal number of subjects or some of the groups might have more participants relative to the other groups. Moreover, subjects can be recruited at the same or at different points in time, each of them can be followed for the same or for different length of time, and the follow up time can be short or long. Hence, the interest here is to find a good number of subjects in both groups, a number of subjects in the experimental group and a duration of the trial, i.e. the number of time periods that subjects are observed for. To investigate these quantities, the generalized linear model (GLM) with logistic or complementary log-log link function, and the continuous-time parametric survival distribution can be applied. Moreover, a cost function can be considered