Weighted Least‐Squares Method for Right‐Censored Data in Accelerated Failure Time Model

Summary The classical accelerated failure time (AFT) model has been extensively investigated due to its direct interpretation of the covariate effects on the mean survival time in survival analysis. However, this classical AFT model and its associated methodologies are built on the fundamental assumption of data homoscedasticity. Consequently, when the homoscedasticity assumption is violated as often seen in the real applications, the estimators lose efficiency and the associated inference is not reliable. Furthermore, none of the existing methods can estimate the intercept consistently. To overcome these drawbacks, we propose a semiparametric approach in this article for both homoscedastic and heteroscedastic data. This approach utilizes a weighted least‐squares equation with synthetic observations weighted by square root of their variances where the variances are estimated via the local polynomial regression. We establish the limiting distributions of the resulting coefficient estimators and prove that both slope parameters and the intercept can be consistently estimated. We evaluate the finite sample performance of the proposed approach through simulation studies and demonstrate its superiority through real example on its efficiency and reliability over the existing methods when the data is heteroscedastic.