Analysis and Goodness-of-Fit Tests for Time-to-Event Models
Abstract
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.
Subject
interval censoringlinear transformation models
multiple imputation
semiparametric methods
martingale
goodness-of-fit tests
Citation
Mandal, Soutrik (2018). Analysis and Goodness-of-Fit Tests for Time-to-Event Models. Doctoral dissertation, Texas A & M University. Available electronically from https : / /hdl .handle .net /1969 .1 /174133.