Accelerated failure time modeling via nonparametric mixtures

An accelerated failure time (AFT) model assuming a log‐linear relationship between failure time and a set of covariates can be either parametric or semiparametric, depending on the distributional assumption for the error term. Both classes of AFT models have been popular in the analysis of censored failure time data. The semiparametric AFT model is more flexible and robust to departures from the distributional assumption than its parametric counterpart. However, the semiparametric AFT model is subject to producing biased results for estimating any quantities involving an intercept. Estimating an intercept requires a separate procedure. Moreover, a consistent estimation of the intercept requires stringent conditions. Thus, essential quantities such as mean failure times might not be reliably estimated using semiparametric AFT models, which can be naturally done in the framework of parametric AFT models. Meanwhile, parametric AFT models can be severely impaired by misspecifications. To overcome this, we propose a new type of the AFT model using a nonparametric Gaussian‐scale mixture distribution. We also provide feasible algorithms to estimate the parameters and mixing distribution. The finite sample properties of the proposed estimators are investigated via an extensive stimulation study. The proposed estimators are illustrated using a real dataset.