Abstract: Recently, the accelerated failure time model has been extended to accommodate heteroscedastic survival data. However, the existing methods often require stringent assumptions or complex algorithms. In this paper, a weighted least squares method is developed based on Laplace approximation for quasi-likelihood subject to conditionally independent censoring. The Laplace approximation is used to approximate the quasi-survival function of the censored observations, which results in simpler and more computationally efficient estimation than the existing methods. The consistency and asymptotic distribution of the resulting estimator are also established. Extensive simulations are conducted to evaluate the performance of the proposed method. Finally, we apply the new proposed method to Stanford heart transplant data and colon cancer data to demonstrate its use in real applications.

Key words and phrases: Heteroscedasticity, Laplace approximation, local polynomial regression.