Joint Analysis of Longitudinal Proportional Measurements and Survival Times Based on Generalized Mean‐Variance Mixed Model and Cox Proportional Hazards Model

Longitudinal proportional data, which are restricted in a closed interval, are frequently observed together with survival data in clinical trials and other medical studies. In this paper, we propose a new model for the joint analysis of longitudinal proportional and survival data. This model uses generalized mean‐variance mixed model for longitudinal outcomes, which avoids parametric assumption for their distribution, and Cox proportional hazards model for survival times. A procedure is developed to estimate the parameters in the proposed model based on quasi‐likelihood for longitudinal data and partial likelihood for survival data with a Laplace approximation for the joint likelihood. A random weighting method is proposed to calculate the variance of these parameter estimators. The performance of the proposed model and estimation procedures are assessed through simulation studies and the application to the analysis of data from a randomized clinical trial on early breast cancer.