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Optimal designs for trials with discrete-time survival endpoints.

Abstract Introduction Randomised controlled trials require a lot of labour, time and money. To avoid wasting these efforts and to get scientifically useful results, they need to be carefully planned beforehand. There has been a lack of knowledge on planning designs of longitudinal experiments where events are observed in discrete time, but recently some relevant articles about that topic have been published. In experiments of that type, subjects are observed in time periods and a design is a combination of the total number of subjects, the number of time periods they are observed for and the allocation of subjects to the control and experimental groups. A good design is the combination of these factors that guarantees a sufficient level of statistical power at minimal costs. The optimal design methodology is introduced on a basic level and an example shows that designs based on standard calculations are not necessarily the best choice. The aim of this review was to discuss the optimal designs for trials with discrete-time survival endpoints. Conclusion This article should help researchers in planning longitudinal experiments where events are observed in discrete time. Introduction In many fields of science, researchers study a particular event in people’s lives as they are interested in the timing and/or causation of event occurrence, such as recovery from anorexia nervosa1. A method to identify and investigate such events is to follow a group of subjects across time in a longitudinal study until they either experience the event or drop out from the study due to other reasons. In the planning phase of a study it is important to select an appropriate metric of time, that is, a meaningful scale of time in which the event can occur. Time can be measured continuously or discretely. Time is measured continuously when the precise timing of event occurrence is known, and is measured discretely when the event is measured at preselected points in time or in time intervals. Measuring discretely rather than continuously implies the exact time of event occurrence is unknown and so it results in a loss of information. The choice for measuring time discretely rather than continuously should therefore be well justified2. In retrospective studies, time is often measured discretely because subjects may not be able to remember the exact time of event occurrence. In prospective studies, the budget may be limited and endpoints are assessed periodically. In addition, measuring too frequently may cause participation burden and increased rates of attrition and may also raise ethical objections, especially when taking a measurement puts a high burden on the participants. In epidemiology, discrete-time survival analysis is used in studies on the onset of alcohol and tobacco use and in studies on disease progress and relapse. The metric of time is an important choice because it has an influence on the sample size to achieve a prespecified power level. Here we focus on the power to detect treatment effects in randomised controlled trials that compare one experimental condition with a control3,4. To conduct longitudinal trials where people are followed over time, a lot of labour, time and money are needed. Therefore, trials need to be carefully planned before they are actually conducted, and the best way is to calculate the optimal design in the planning phase of a trial. The optimal design is one of the designs that performs best with respect to some optimality criterion, for instance, the power of the test on treatment effect. Power is related to sample size and sufficient sample size ensures an effect of treatment is detected with large probability. To plan a trial, researchers need to consider many aspects, for instance, how many participants should be recruited, how many of them should be randomised to the experimental condition and for how long they should be followed up. Guidelines on sample sizes and optimal designs for trials with continuous-time survival data have been studied in the past5–12 and are implemented in software packages such as nQuery Advisor 7.013, PASS14 or Study Size15. These guidelines cannot be used for trials with discrete-time survival data because another metric of time is used. When subjects are measured discretely an important question is for how many time intervals they should be measured. This question is irrelevant for trials with * Corresponding author Email: K.jozwiak@nki.nl