Jointly modeling longitudinal proportional data and survival times with an application to the quality of life data in a breast cancer trial

Abstract

Motivated by the joint analysis of longitudinal quality of life data and recurrence free survival times from a cancer clinical trial, we present in this paper two approaches to jointly model the longitudinal proportional measurements, which are confined in a finite interval, and survival data. Both approaches assume a proportional hazards model for the survival times. For the longitudinal component, the first approach applies the classical linear mixed model to logit transformed responses, while the second approach directly models the responses using a simplex distribution. A semiparametric method based on a penalized joint likelihood generated by the Laplace approximation is derived to fit the joint model defined by the second approach. The proposed procedures are evaluated in a simulation study and applied to the analysis of breast cancer data motivated this research.

Keywords: Censoring; Gauss–Hermite numerical integration; Laplace approximation; Logistic-normal distribution; Logit transformation; Random effects; Simplex distribution.