Tang, Chuan-FaZhang, Fan2023-10-112023-10-112023-05May 2023May 2023https://hdl.handle.net/10735.1/9911Survival analysis is a powerful statistical methodology utilized in various disciplines to study time-to-event data, particularly when the time to the event of interest is censored. The Cox model proposed by (Cox, 1972), also called the proportional hazards model, has been one of the most frequently used models for survival analysis due to its flexibility without specifying error distribution. However, the proportionality and log-linearity assumptions limit the use of the model and therefore have led to the development of more adaptable models, such as the isotonic proportional hazards model proposed by (Chung et al., 2018), which relaxes the log linearity to the more flexible monotonicity assumption. This dissertation proposes goodness-of-fit tests for the Cox model under the constraints that the hazard func- tion is monotonic with respect to continuous covariates. The proposed tests are diagnostics for the log-linearity assumption for the Cox model, while the minor assumption about the monotonicity relationship between the hazard and the covariate is satisfied. Three popular scenarios regarding the continuous covariate of interest are discussed to develop the test, including time-independent univariate covariate, time-independent univariate covariate together with additional linear-effect covariates, and time-dependent univariate covariate. We proposed partial-likelihood-ratio-based tests with bootstrapped critical values for the Cox model versus the isotonic proportional hazards model. Simulation studies under each scenario show the controlled type-I error and the consistency of the test. Several data examples have been discussed to apply the goodness-of-fit tests, including the heart failure clinical records data, lung cancer data from North Central Cancer Treatment Group, breast cancer data from the German Breast Cancer Study Group, monoclonal gammopathy data and the AIDS Clinical Trials Grup 175 dataset.application/pdfEnglishStatisticsThesis2023-10-11