Semiparametric regression analysis of partly interval-censored failure time data with application to an AIDS clinical trial

Abstract

Failure time data subject to various types of censoring commonly arise in epidemiological and biomedical studies. Motivated by an AIDS clinical trial, we consider regression analysis of failure time data that include exact and left-, interval-, and/or right-censored observations, which are often referred to as partly interval-censored failure time data. We study the effects of potentially time-dependent covariates on partly interval-censored failure time via a class of semiparametric transformation models that includes the widely used proportional hazards model and the proportional odds model as special cases. We propose an EM algorithm for the nonparametric maximum likelihood estimation and show that it unifies some existing approaches developed for traditional right-censored data or purely interval-censored data. In particular, the proposed method reduces to the partial likelihood approach in the case of right-censored data under the proportional hazards model. We establish that the resulting estimator is consistent and asymptotically normal. In addition, we investigate the proposed method via simulation studies and apply it to the motivating AIDS clinical trial.

Keywords: AIDS clinical trial; EM algorithm; partly interval-censored data; semiparametric transformation models; survival analysis.

Figure 1:

Log-likelihood function evaluated at the final parameter estimates when different values of r are considered in the semiparametric transformation model with G(x) = r⁻¹ log(1 + rx). The vertical dashed line corresponds to the r value that yields the largest log-likelihood.

Figure 2:

Estimated survival functions by considering different combinations of covariates under the semiparametric transformation model $\Lambda (t\mid S(\cdot ),Z)=G\left({\int }_0^t\text{exp}\{\beta S(s)+\gamma Z\}d\Lambda (s)\right)$, where S(·) denotes the time-dependent covariate log₁₀(CD4) and Z is the treatment indicator. For example, “S25+Z1” corresponds to the covariates combination with S being the 25th percentile of log₁₀(CD4) and Z being 1 (i.e., the treatment group). “PH” and “PO” represent the proportional hazards and proportional odds models, respectively, while “Selected” represents the selected model among the transformations G(x) = r⁻¹ log(1 + rx) with r values ranging from 0 to 3 with an increment of 0.1.