Sample size determination for the association between longitudinal and time-to-event outcomes using the joint modeling time-dependent slopes parameterization

Given their improvements in bias reduction and efficiency, joint models (JMs) for longitudinal and time-to-event data offer great potential to clinical trials. However, for JM to become more widely used, there is a need for additional development of design considerations. To this end, Chen et al previously developed two closed-form sample size formulas in the JM setting. In this current work, we expand upon this framework by utilizing the time-dependent slopes parameterization, where the change in the longitudinal outcome influences the hazard, in addition to the current value of the longitudinal process. Our extended formula for the required number of events can be used when testing significance of the association between the longitudinal and time-to-event outcomes. We find that if the data indeed are generated such that not only the current value, but also the slope of the longitudinal outcome influence the hazard of the time-to-event process, it is advisable to use the current formula developed utilizing the time-dependent slopes parameterization. In this setting, our proposed formula will provide a more accurate estimate of power compared to the method by Chen et al. To illustrate our proposed method, we present power calculations of a biomarker qualification study for Hutchinson-Gilford progeria syndrome, an ultra-rare premature aging disease.