Joint models for efficient estimation in proportional hazards regression models

Abstract

In survival studies, information lost through censoring can be partially recaptured through repeated measures data which are predictive of survival. In addition, such data may be useful in removing bias in survival estimates, due to censoring which depends upon the repeated measures. Here we investigate joint models for survival T and repeated measurements Y, given a vector of covariates Z. Mixture models indexed as f (T/Z) f (Y/T,Z) are well suited for assessing covariate effects on survival time. Our objective is efficiency gains, using non-parametric models for Y in order to avoid introducing bias by misspecification of the distribution for Y. We model (T/Z) as a piecewise exponential distribution with proportional hazards covariate effect. The component (Y/T,Z) has a multinomial model. The joint likelihood for survival and longitudinal data is maximized, using the EM algorithm. The estimate of covariate effect is compared to the estimate based on the standard proportional hazards model and an alternative joint model based estimate. We demonstrate modest gains in efficiency when using the joint piecewise exponential joint model. In a simulation, the estimated efficiency gain over the standard proportional hazards model is 6.4 per cent. In clinical trial data, the estimated efficiency gain over the standard proportional hazards model is 10.2 per cent.