Evaluating predictors of competing risk outcomes when censoring depends on time-dependent covariates, with application to safety and efficacy of HIV treatment

Clayton copula for survival data with dependent censoring: An application to a tuberculosis treatment adherence data

Ignoring the presence of dependent censoring in data analysis can lead to biased estimates, for example, not considering the effect of abandonment of the tuberculosis treatment may influence inferences about the cure probability. In order to assess the relationship between cure and abandonment outcomes, we propose a copula Bayesian approach. Therefore, the main objective of this work is to introduce a Bayesian survival regression model, capable of taking into account the dependent censoring in the adjustment. So, this proposed approach is based on Clayton's copula, to provide the relation between survival and dependent censoring times. In addition, the Weibull and the piecewise exponential marginal distributions are considered in order to fit the times. A simulation study is carried out to perform comparisons between different scenarios of dependence, different specifications of prior distributions, and comparisons with the maximum likelihood inference. Finally, we apply the proposed approach to a tuberculosis treatment adherence dataset of an HIV cohort from Alvorada-RS, Brazil. Results show that cure and abandonment outcomes are negatively correlated, that is, as long as the chance of abandoning the treatment increases, the chance of tuberculosis cure decreases.

Estimation of the cumulative incidence function under multiple dependent and independent censoring mechanisms

Competing risks occur in a time-to-event analysis in which a patient can experience one of several types of events. Traditional methods for handling competing risks data presuppose one censoring process, which is assumed to be independent. In a controlled clinical trial, censoring can occur for several reasons: some independent, others dependent. We propose an estimator of the cumulative incidence function in the presence of both independent and dependent censoring mechanisms. We rely on semi-parametric theory to derive an augmented inverse probability of censoring weighted (AIPCW) estimator. We demonstrate the efficiency gained when using the AIPCW estimator compared to a non-augmented estimator via simulations. We then apply our method to evaluate the safety and efficacy of three anti-HIV regimens in a randomized trial conducted by the AIDS Clinical Trial Group, ACTG A5095.