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

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. Along with their asymptotic properties, the claimed robustness advantage is also studied theoretically via appropriate influence function analysis. We have studied the finite sample level and power of the proposed MDPDE based Wald-type test through extensive simulations. 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.