On semiparametric modelling, estimation and inference for survival data subject to dependent censoring

When modelling survival data, it is common to assume that the survival time T is conditionally independent of the censoring time C given a set of covariates. However, there are numerous situations in which this assumption is not realistic. The goal of this paper is therefore to develop a semiparametric normal transformation model which assumes that, after a proper nonparametric monotone transformation, the vector (T, C) follows a linear model, and the vector of errors in this bivariate linear model follows a standard bivariate normal distribution with a possibly nondiagonal covariance matrix. We showthat this semiparametric model is identifiable, and propose estimators of the nonparametric transformation, the regression coefficients and the correlation between the error terms. It is shown that the estimators of the model parameters and the transformation are consistent and asymptotically normal. We also assess the finite-sample performance of the proposed method by comparing it with an estimation method under a fully parametric model. Finally, our method is illustrated using data from the AIDS Clinical Trial Group 175 study.

Automated summary

This paper introduces a semiparametric normal transformation model to address the potential conditional dependencies in survival data, showing the identifiability and consistency of estimators using nonparametric monotone transformation and a linear model. The proposed method is evaluated against an estimation method under a fully parametric model to assess its finite-sample performance.