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We use a deep neural network (DNN) to approximate the logarithm of a conditional hazard function given covariates and obtain a DNN likelihood-based estimator of the conditional hazard function. Such an estimation approach enhances model flexibility and hence relaxes structural and functional assumptions on conditional hazard or survival functions. We establish the nonasymptotic error bound and functional asymptotic normality of the proposed estimator. Subsequently, we develop new one-sample tests for goodness-of-fit evaluation and two-sample tests for treatment comparison. Notably, we design a new test specifically tailored for testing nonparametric Cox models. The consistency of these tests is established by analyzing the power functions. 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