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Statistical power to detect violation of the proportional hazards assumption when using the Cox regression model
Authors:Peter C Austin
Institution:1. Institute for Clinical Evaluative Sciences, Toronto, ON, Canada;2. Institute of Health Management, Policy and Evaluation, University of Toronto, Toronto, ON, Canada;3. Schulich Heart Research Program, Sunnybrook Research Institute, Toronto, ON, Canada
Abstract:The use of the Cox proportional hazards regression model is wide-spread. A key assumption of the model is that of proportional hazards. Analysts frequently test the validity of this assumption using statistical significance testing. However, the statistical power of such assessments is frequently unknown. We used Monte Carlo simulations to estimate the statistical power of two different methods for detecting violations of this assumption. When the covariate was binary, we found that a model-based method had greater power than a method based on cumulative sums of martingale residuals. Furthermore, the parametric nature of the distribution of event times had an impact on power when the covariate was binary. Statistical power to detect a strong violation of the proportional hazards assumption was low to moderate even when the number of observed events was high. In many data sets, power to detect a violation of this assumption is likely to be low to modest.
Keywords:Data-generating process  survival analysis  proportional hazards model  simulations  Monte Carlo simulations  power and sample size calculation
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