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Randomly censored survival data are frequently encountered in appliedsciences including biomedical or reliability applications and clinical trialanalyses. Testing the significance of statistical hypotheses is crucial in suchanalyses to get conclusive inference but the existing likelihood based tests,under a fully parametric model, are extremely non-robust against outliers inthe data. Although, there exists a few robust parameter estimators (e.g.,M-estimators and minimum density power divergence estimators) given randomlycensored data, there is hardly any robust testing procedure available in theliterature in this context. One of the major difficulties in this context isthe construction of a suitable consistent estimator of the asymptotic varianceof M estimators; the latter is a function of the unknown censoringdistribution. In this paper, we take the first step in this direction byproposing a consistent estimator of asymptotic variance of the M-estimatorsbased on randomly censored data without any assumption on the form of thecensoring scheme. We then describe and study a class of robust Wald-type testsfor parametric statistical hypothesis, both simple as well as composite, undersuch set-up, along with their general asymptotic and robustness properties.Robust tests for comparing two independent randomly censored samples and robusttests against one sided alternatives are also discussed. Their advantages andusefulness are demonstrated for the tests based on the minimum density powerdivergence estimators with specific attention to clinical trial analyses.

Robust Wald-Type Tests under Random Censoring with Applications to Clinical Trial Analyses