### A Simulation Study to Evaluate the Performance of Extended Cox model in Testing Treatment Effect with Possible Non-proportional Hazards

#### Abstract

**Background:** Many randomized clinical studies with long-term follow-up regularly measure time-to-event outcomes, such as survival time to compare an experimental treatment with a standard treatment or placebo control. In this comparison, one tests whether the two treatments have the same survival function or equivalently the same hazard function over a given time period in order to evaluate effect of treatment. However, when comparing treatments in terms of their time to event distribution, there may be reason to believe that the hazard curves will cross, and in such cases standard comparison techniques could lead to misleading results. It was shown that extended Cox model performed well to test effect of treatment in case of crossing survival curves at 20% and 40% administratively censored time. However, most of the studies did not assess the statistical properties of this approach under high censoring rates.

**Objective:** In this paper, the main objective of the study was to evaluate whether the power and type I error rate of extended Cox model was robust with variations in censoring rates under five possible treatment effects based on data from simulations.

**Methodology: **a simulation study was designed to compare the performance of the extended Cox and the data are replicated 1000 times to estimate type I error rate and empirical power of the test.

**Results**: type I error rates for the test from the model approached the nominal level of 0.05 at 10% and 30% of censoring rates regardless of sample size per treatment group considered in the study, however, type I error rates are slightly inflated at 70% of censoring rate. Moreover, with respect to powers of the test, extended Cox model performed reasonably well with powers of test above 80% in case of crossing survival curves under censoring rates of 10% and 30% to test treatment effect without including baseline covariates in the model. Although 70% censoring rate appeared to have influence on the power of test, test from extended Cox model exhibits moderate power in this situation, particularly for sample of size 200 per treatment group. Furthermore, extended Cox model with heavy side function performed well under the early treatment effect in which hazards is expected to crosses. Using the extended Cox model with baseline covariate in case of crossing survival curves did not generally yield dramatic decrease in power.

**Conclusions: **70% censoring rate appeared to have influence on the power of test and type I error rate although test exhibits moderate power for sample of size 200 per treatment group.

Keywords: **Simulation, ****Type I error rate, Cox Proportional Hazards,**** Power of the test, Extended Cox Model**

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