Inferences on Accelerated Life Model with Various Types of Censored Data

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In survival data analysis, the Accelerated Life Model (ALM) is one of the most widely used statistical models. However, until now there has been little work done in statistical literature on the ALM for complicated types of censored data, such as doubly censored data, interval censored data, etc., while these types of censored data are frequently encountered in practice. Some of the relevant existing works treat the log form of ALM as a linear regression model and make statistical inferences on the ALM based on the least squares method. In this dissertation, we first use a simulation study to demonstrate that the log form of ALM is not a linear regression model, which motivates us to develop estimation methods for the ALM with various types of censored survival data via the \textit{weighted empirical likelihood} approach (Ren, 2001, 2008). We develop a weighted empirical likelihood-based estimation method for the ALM in a unified way for various types of censored data. We also provide an algorithm to implement the estimation method and present some simulation results.