Sample size and power determination in joint modeling of longitudinal and time-to-event data
Embargo Date
2026-02-05
OA Version
Citation
Abstract
The joint model (JM) is a statistical framework in which longitudinal and time-to-event data are simultaneously modeled. Joint models have grown in popularity over the last several years due to their improvements in bias reduction and efficiency in estimating treatment effect, compared to the current standard of modeling the longitudinal and time-to-event outcomes separately. Given the improvements offered by the JM framework in elucidating treatment effect, there is great potential for JM in a clinical trials setting. However, acknowledging the importance of proper study design in clinical trials, there is a need for advancements and improved guidance in JM study design, particularly with regards to sample size and power calculations. As a response to this, this work offers guidance on clinical trial design when utilizing the joint modeling framework as an analysis approach.
This dissertation consists of three main parts: the first part proposes a formula for the required number of events when testing significance of the association between the longitudinal and time-to-event outcomes when utilizing the time-dependent slopes JM parameterization. This proposed formula is recommended when not only the current value, but also the slope of the longitudinal outcome, influences the hazard of the time-to-event process. The second part of this work proposes a two-stage adaptive design for testing overall treatment effect within the joint modeling framework. We find that if the data are generated such that there is an indirect effect of treatment on the time-to-event outcome via the longitudinal process, in addition to any direct effects of treatment on the time-to-event outcome, it is advisable to use the current proposed formula for the number of additional required events developed using the joint modeling methodology, as our proposed formula will provide a more accurate estimate of the required number of additional events compared to the current standard. In the third part of this dissertation, we offer sample size and power formulas for three clinical trial designs when using the JM framework: superiority by a margin, non-inferiority, and equivalence. In summary, we argue the continuing development of joint modeling design considerations will allow for the more frequent use of joint models in clinical trials.