Calculating statistical power for a Cox proportional hazards regression with a continuous predictor variable I have 322 samples with survival data (71 had events) and wish to calculate the power to detect an association with a linear predictor (no covariates) at $\alpha$=0.05 and hazard ratio=1.561. Been struggling to find any help I can understand as a non-mathematician.
The results of the model are:

*

*coef=-0.07427

*exp(coef)=0.92843

*se(coef)=0.11206

*Z=-0.663

*P=0.508

This information has been requested by a co-author as a reply to a reviewer.

@EdM's answer should be selected for this particular scenario.
In general, the way to perform a power calculation for a Cox proportional hazards model is to simulate data according to an exponential survival model parametrized by the median survival or the event-rate parameter. The simulation may continue to account for several other design dependent considerations such as:

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*Rate of accrual to study

*Rate of censoring/drop out

*The trigger for the primary analysis (accrual of events, number of years from start, etc.)

All of which are endemic considerations for truly prospective study designs. Once a simulation strategy is established and the parameters are supplied, the simulated data are fit using a Cox model and the corresponding inference at the pre-specified significance level is used to calculate the fraction of "significant" results for a given sample size. There are elegant mathematical approximations to identify the sample size which are best left to professional software. For analytic formulations like OLS, the power and sample size calculation are often equivalent formulations. However, for Cox model and other simulation-based results, there is no straightforward approach other than grid-search.
