Joint Modelling of Longitudinal Measurements and Time-to-Event Outcomes With a Cure Fraction Using Functional Principal Component Analysis

In studying the association between clinical measurements and time-to-event outcomes within a cure model, utilizing repeated observations rather than solely baseline values may lead to more accurate estimation. However, there are two main challenges in this context. First, longitudinal measurements are usually observed at discrete time points and second, for diseases that respond well to treatment, a high censoring proportion may occur by the end of the trial. In this article, we propose a joint modelling approach to simultaneously study the longitudinal observations and time-to-event outcome with an assumed cure fraction. We employ the functional principal components analysis (FPCA) to model the longitudinal data, offering flexibility by not assuming a specific form for the longitudinal curve. We used a Cox's proportional hazards mixture cure model to study the survival outcome. To investigate the longitudinal binary observations, we adopt a quasi-likelihood method which builds pseudo normal distribution for the binary data and use the E-M algorithm to estimate the parameters. The tuning parameters are selected using the Akaike information criterion. Our proposed method is evaluated through extensive simulation studies and applied to a clinical trial data to study the relationship between the longitudinal prostate specific antigen (PSA) measurements and overall survival in men with metastatic prostate cancer.