Semiparametric inference procedure for the accelarated failure time model with interval-censored data - Karimi, Mostafa (2019)
In this thesis new inference procedures are proposed for estimating the parameters of the accelerated failure time (AFT) model in the presence of interval-censored data. In the literature, a variety of semiparametric inference procedures are suggested by previous research for estimating the parameters of AFT models with censored data, and rank-based methods are popular among all. The main difficulty with the existing rank-based methods is that they involve nonparametric estimation of the probability distribution of the model’s error terms. Another problem is estimating the covariance matrix of the parameter estimators, since the existing methods involve derivative of the hazard function of the model’s error terms. Considering the stated problems, the major objectives of this thesis include developing new rank-based estimating procedures for AFT models with intervalcensored data based on the actual rank and the expected rank estimating functions, for both univariate and multivariate models. Other research objectives include developing new resampling methods for estimating the covariance matrix of the estimators based on random sampling within censoring intervals and based on the perturbed estimating function. The findings of this research provide two new iterative algorithms for estimating the parameters of the AFT model with interval-censored data, and also two new resampling techniques for estimating the covariance matrix of estimators. The rank-based methods, estimating algorithms, and resampling techniques that are developed do not involve the difficulties of the existing estimating procedures. A computationally simple two-step iterative algorithm, called estimationapproximation algorithm, is introduced for estimating the parameters of the model on the basis of the rank estimators. Also, a one-step iterative algorithm, called expected rank algorithm, is introduced which is more complicated than the estimation-approximation algorithm, but more accurate. For estimating the covariance matrix of the proposed estimators two new resampling techniques are proposed, one based on random sampling within censoring interval and another based on perturbed estimating function. Inference procedures are developed for modelling multiple events intervalcensored data through AFT models. Computational properties of the proposed parameter estimating methods and the proposed resampling techniques are comprehensively discussed. The proposed inference procedures are assessed through simulation studies and their performance in applications is demonstrated through analysing real data sets in health science and transportation. The significance of the study from the results of the numerical analysis shows that the proposed estimators and their corresponding resampling methods are accurate and computationally simpler than the existing methods. The results also imply that influential factors such as the length of censoring intervals and the distribution of the error terms do not significantly affect their efficiency and accuracy. The main contribution of this research is developing statistical approaches, and introducing new algorithms and resampling methods for analysing interval-censored data through AFT models.