Sample Size and Power Determination in Joint Models of Survival and Longitudinal Data]
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Liddy Chen, Parexel  Haitao Chu, University of Minnesota  *Joseph G Ibrahim, UNC 

Keywords: Sample size, Power estimation, Joint modeling; Survival analysis, Longitudinal data, Repeated measurements

Due to the rapid development of biomarkers in both cancer and virology clinical trials, joint modeling of survival and longitudinal data has gained its popularity in recent years because it reduces bias and provides improvements of efficiency in the assessment of treatment effects and other prognostic effects. Statistical design, such as sample size and power calculations, is a crucial first step in clinical trials. Although much effort has been put into inferential methods in joint modeling, such as estimation and hypothesis testing, the design aspects have not been formally considered. We present closed-form sample size formulas for estimating the effect of the longitudinal process in joint modeling and extend existing time-to-event sample size formulas to the joint modeling setting for estimating the overall treatment effect. We discuss the impact of the within subject variability on power, data collection strategies, such as spacing and frequency of repeated measurements, to maximize power. When the within subject variability is large, different data collection strategies can influence the power of the study in a significant way. Optimal frequency of repeated measurements depends the nature of the trajectory function, where higher degree polynomial trajectories require more frequent measurements. While repeated measurements taken at later time points of the follow-up period can improve power, it is very crucial to ensure enough repeated measurements of the longitudinal data for each subject. We show that this can lead to a biased estimate of the longitudinal effect and result in a significant loss of power. Also, ignoring the longitudinal marker in the analysis can result in a biased estimate of the treatment effect. All of these properties are demonstrated with simulation studies.