Semi-parametric accelerated failure time regression analysis with application to interval-censored HIV/AIDS data

This paper demonstrates a way to investigate a potentially non-linear relationship between an interval-censored response variable and a continuously distributed explanatory variable. A potentially non-linear effect of a continuous explanatory variable on the response is incorporated into an accelerated failure time model, forming a partial linear model. A sieve maximum likelihood estimator (MLE) is suggested to simultaneously estimate all the parameters. The sieve MLE is shown to be asymptotically efficient and normally distributed. Simulation studies show that the proposed estimators for the scale and regression parameters are robust and efficient, and the estimator for the non-linear function is able to capture the shape of a variety of smooth non-linear functions. The model is applied to observational HIV data, where the response variable is the time to suppression of HIV viral load after initiation of antiretroviral therapy, and baseline viral load is investigated as a potentially non-linear effect.