Exponential model for breast cancer partly interval censored data via multiple imputation

Abstract

The estimation problem for interval-censored data has been investigated by several authors. The application of conventional methods to interval censored data that has been considered by Lindsey and Ryan (1998) showed misleading results when they tended to underestimate the standard errors of the estimated parameters. In this thesis, we apply the likelihoods in the exponential model in order to estimate the parameters and function of survival when multiple imputation and left imputation methods are used for partly interval censored data. We pay particular attention to the performance of our model. In particular, we present the Likelihood Ratio Test (LRT) with their p-value. We undertake a simulation study with different percentage of exact observations (0%, 25%, 50%, and 75%) in order to quantify and analyze the relative performances of maximum likelihood estimation for exponential model. The numerical evidence suggests that the estimates from multiple imputation are more accurate. We apply the proposed method to a real breast cancer data.