A multivariate normal regression model for survival data subject to different types of dependent censoring

Abstract

In survival analysis observations are often right censored and this complicates considerably the analysis of these data. Right censoring can have several underlying causes: administrative censoring, loss to follow up, competing risks, etc. The (latent) censoring times corresponding to the latter two types of censoring are possibly related to the survival time of interest, and in that case this should be taken into account in the model. A unifying model is presented that allows these censoring mechanisms in one single model, and that is also able to incorporate the effect of covariates on these times. Each time variable is modeled by means of a transformed linear model, with the particularity that the error terms of the transformed times follow a multivariate normal distribution allowing for non-zero correlations. It is shown that the model is identified and the model parameters are estimated through a maximum likelihood approach. The performance of the proposed method is compared with methods that assume independent censoring using finite sample simulations. The results show that the proposed method exhibits major advantages in terms of reducing the bias of the parameter estimates. However, a strong deviation from normality and/or a strong violation of the homogeneous variance assumption may lead to biased estimates. Finally, the model and the estimation method are illustrated using the analysis of data coming from a prostate cancer clinical trial.