Hypothesis Testing for the Deep Cox Model

Music City Center 

Deep learning has become enormously popular in the analysis of complex data, including event time measurements with censoring. To date, deep survival methods have mainly focused on prediction. Such methods are scarcely used in matters of statistical inference such as hypothesis testing. Due to their black-box nature, deep-learned outcomes lack interpretability which limits their use for decision-making in biomedical applications. Moreover, conventional tests fail to produce reliable type I errors due to the ability of deep neural networks to learn the data structure under the null hypothesis even if they search over the full space. This talk provides testing methods for the nonparametric Cox model -- a flexible family of models with a nonparametric link function to avoid model misspecification. Here we assume the nonparametric link function is modeled via a deep neural network. To perform hypothesis testing, we utilize sample splitting and cross-fitting procedures to get neural network estimators and construct the test statistic. These procedures enable us to propose a new significance test to examine the association of certain covariates with event times. We show that our test statistic converges to a normal distribution under the null hypothesis and establish its consistency, in terms of the Type II error, under the alternative hypothesis. Numerical simulations and a real data application demonstrate the usefulness of the proposed test.