Robust Hypothesis Testing and Model Selection for Parametric Proportional Hazard Regression Models

TL;DR

This paper develops robust hypothesis testing and model selection methods for parametric proportional hazards models using MDPDEs, improving robustness against outliers and demonstrating effectiveness through simulations and real data examples.

Contribution

It introduces robust Wald-type tests and model selection procedures for parametric proportional hazards models based on MDPDEs, with theoretical and empirical validation.

Findings

Proposed tests show high robustness in simulations.

Method outperforms semi-parametric methods in outlier scenarios.

Real data applications demonstrate practical utility.

Abstract

The semi-parametric Cox proportional hazards regression model has been widely used for many years in several applied sciences. However, a fully parametric proportional hazards model, if appropriately assumed, can often lead to more efficient inference. To tackle the extreme non-robustness of the traditional maximum likelihood estimator in the presence of outliers in the data under such fully parametric proportional hazard models, a robust estimation procedure has recently been proposed extending the concept of the minimum density power divergence estimator (MDPDE) under this set-up. In this paper, we consider the problem of statistical inference under the parametric proportional hazards model and develop robust Wald-type hypothesis testing and model selection procedures using the MDPDEs. We have also derived the necessary asymptotic results which are used to construct the testing procedure for general composite hypothesis and study its asymptotic powers. The claimed robustness properties are studied theoretically via appropriate influence function analyses. We have studied the finite sample level and power of the proposed MDPDE based Wald type test through extensive simulations where comparisons are also made with the existing semi-parametric methods. The important issue of the selection of appropriate robustness tuning parameter is also discussed. The practical usefulness of the proposed robust testing and model selection procedures is finally illustrated through three interesting real data examples.