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We study parametric inference on a rich class of hazard regression models inthe presence of right-censoring. Previous literature has reported someinferential challenges, such as multimodal or flat likelihood surfaces, in thisclass of models for some particular data sets. We formalize the study of theseinferential problems by linking them to the concepts of near-redundancy andpractical non-identifiability of parameters. We show that the maximumlikelihood estimators of the parameters in this class of models are consistentand asymptotically normal. Thus, the inferential problems in this class ofmodels are related to the finite-sample scenario, where it is difficult todistinguish between the fitted model and a nested non-identifiable (i.e.,parameter-redundant) model. We propose a method for detecting near-redundancy,based on distances between probability distributions. We also employ methodsused in other areas for detecting practical non-identifiability andnear-redundancy, including the inspection of the profile likelihood functionand the Hessian method. For cases where inferential problems are detected, wediscuss alternatives such as using model selection tools to identify simplermodels that do not exhibit these inferential problems, increasing the samplesize, or extending the follow-up time. We illustrate the performance of theproposed methods through a simulation study. Our simulation study reveals alink between the presence of near-redundancy and practical non-identifiability.Two illustrative applications using real data, with and without inferentialproblems, are presented.

On near-redundancy and identifiability of parametric hazard regression models under censoring