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Joint Models for Multivariate Longitudinal and Multivariate Survival Data
Author(s) -
Chi YuehYun,
Ibrahim Joseph G.
Publication year - 2006
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2005.00448.x
Subject(s) - multivariate statistics , univariate , proportional hazards model , multivariate analysis , survival analysis , covariate , statistics , survival function , econometrics , population , hazard ratio , marginal model , joint probability distribution , mathematics , medicine , regression analysis , confidence interval , environmental health
Summary Joint modeling of longitudinal and survival data is becoming increasingly essential in most cancer and AIDS clinical trials. We propose a likelihood approach to extend both longitudinal and survival components to be multidimensional. A multivariate mixed effects model is presented to explicitly capture two different sources of dependence among longitudinal measures over time as well as dependence between different variables. For the survival component of the joint model, we introduce a shared frailty, which is assumed to have a positive stable distribution, to induce correlation between failure times. The proposed marginal univariate survival model, which accommodates both zero and nonzero cure fractions for the time to event, is then applied to each marginal survival function. The proposed multivariate survival model has a proportional hazards structure for the population hazard, conditionally as well as marginally, when the baseline covariates are specified through a specific mechanism. In addition, the model is capable of dealing with survival functions with different cure rate structures. The methodology is specifically applied to the International Breast Cancer Study Group (IBCSG) trial to investigate the relationship between quality of life, disease‐free survival, and overall survival.