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Nonparametric and semiparametric methods are commonly used in survivalanalysis to mitigate the bias due to model misspecification. However, suchmethods often cannot estimate upper-tail survival quantiles when a sizableproportion of the data are censored, in which case parametric likelihood-basedestimators present a viable alternative. In this article, we extend a popularfamily of parametric survival models which make the Accelerated Failure Time(AFT) assumption to account for heteroscedasticity in the survival times. Theconditional variances can depend on arbitrary covariates, thus addingconsiderable flexibility to the homoscedastic model. We present anExpectation-Conditional-Maximization (ECM) algorithm to efficiently compute theHAFT maximum likelihood estimator with right-censored data. The methodology isapplied to the heavily censored data from a colon cancer clinical trial, forwhich a new type of highly stringent model residuals is proposed. Based onthese, the HAFT model was found to eliminate most outliers from itshomoscedastic counterpart.

A Heteroscedastic Accelerated Failure Time Model for Survival Analysis