Analysis and Goodness-of-Fit Tests for Time-to-Event Models
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The Cox proportional hazards model and the proportional odds model are some of the popular survival models often chosen to analyze censored time-to-event data. The properties of these models have been studied in detail by several authors. In recent years, the linear transformation models have gained substantial interest. Linear transformation models are a general class of models that contain the Cox proportional hazards and proportional odds models as special cases. It thus provides a lot more flexibility in terms of model selection. The linear transformation models have been studied in the comparatively simpler right censoring scenario and some authors have analyzed the transformation models in the presence of measurement error. In this dissertation, I consider the problem of analyzing the semiparametric transformation models in the more general interval censoring setup when a covariate is measured with error. To the best of my knowledge this is an unexplored combination. I propose a semiparametric methodology to estimate the parameters of the linear transformation models. I use a flexible two-stage imputation technique to address the interval censoring and covariate measurement error. Finite sample performance of the proposed method is judged via simulation studies. Finally, the suggested method is applied to analyze a real dataset from an AIDS clinical trial. In the above discussion, I mentioned that the linear transformation models are a general class of models. A natural question that arises then is which model to select. I propose a new class of omnibus supremum tests based on martingale residuals for testing the goodness-of-fit of a specific model within the linear transformation models when the observations are subject to right censoring. The performance of the proposed test is judged via simulation studies. A guideline for extending this methodology to the interval censoring scenario is also provided.
linear transformation models
Mandal, Soutrik (2018). Analysis and Goodness-of-Fit Tests for Time-to-Event Models. Doctoral dissertation, Texas A & M University. Available electronically from