Laplace approximated quasi-likelihood method for heteroscedastic survival data

Abstract

The classical accelerated failure time model is the major linear model for right censored survival data. It requires the survival data to exhibit homoscedasticity of variance and excludes heteroscedastic survival data that are often seen in practical applications. The least squares method for the classical accelerated failure time model has been extended to accommodate the heteroscedasticity in survival data. However, the estimating equations are discrete and hence they are time consuming and may not be feasible for large datasets. This paper proposes a Laplace approximated quasi-likelihood method with a continuous estimating equation. It utilizes the Laplace approximation to approximate the survival function in the quasi-likelihood, in which the variance function is approximated by a spline function. Then it shows the asymptotic distribution of the Laplace approximated estimator, its estimation bias and the formula for confidence interval estimation for the parameter of interest. The finite sample performance of the proposed approach is evaluated through simulation studies and follows real data examples for illustration.