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This work presents novel and powerful tests for comparing non-proportional hazard functions, based on sample-space partitions. Right censoring introduces two major difficulties which make the existing sample-space partition tests for uncensored data non-applicable: (i) the actual event times of censored observations are unknown; and (ii) the standard permutation procedure is invalid in case the censoring distributions of the groups are unequal. We overcome these two obstacles, introduce invariant tests, and prove their consistency. Extensive simulations reveal that under non-proportional alternatives, the proposed tests are often of higher power compared with existing popular tests for non-proportional hazards. Efficient implementation of our tests is available in the R package KONPsurv, which can be freely downloaded from {https://github.com/matan-schles/KONPsurv

A dynamic treatment regime is a set of decision rules for how to treat a patient at multiple time points. At each time point, a treatment decision is made depending on the patient’s medical history up to that point. We consider the infinite-horizon setting in which the number of decision points is very large. Specifically, we consider long trajectories of patients’ measurements recorded over time. At each time point, the decision whether to intervene or not is conditional on whether or not there was a change in the patient’s trajectory. We present change-point detection tools and show how to use them in defining dynamic treatment regimes. The performance of these regimes is assessed using an extensive simulation study. We demonstrate the utility of the proposed change-point detection approach using two case studies: detection of sepsis in preterm infants in the intensive care unit and detection of a change in glucose levels of a diabetic patient.

A longitudinal discriminant analysis is applied to build predictive models based on repeated measurements of serum hepatitis C virus RNA. These models are evaluated through the partial area under the receiver operating curve index (PA index) and, the final selection of the best model is based on cross-validated estimates of the PA index. Models are compared by building 95% bootstrap confidence interval for the difference in PA index between two models. Data from a randomised trial, in which chronic HCV patients were enrolled, are used to illustrate the application of the proposed method to predict treatment outcome.