Survival analysis power calculations

Power may be evaluated for comparing hazard rates (per unit time) using this [attachment:coxpow.xls spreadsheet] which uses a simple formula taken from Collett (2003) [http://stats.stackexchange.com/questions/7508/power-analysis-for-survival-analysis illustrated here] corresponding to a group regression estimate (ratio of hazards) in a Cox regression model. Alternatively the effect size can be expressed in terms of ratios of group survival rates as used by the power calculator given [http://www.stattools.net/SSizSurvival_Pgm.php here.]

Rearranging the equation given in Collett(2003)

Power = $$2 \Phi(\sqrt{np(1-p)hr^text{2}}-z_text{a/2})-1$$

where n is the total sample size, p the probability of occurrence of the event in the population, hr the hazard ratio, a the two-sided type I error, $$\Phi$$ the inverse normal function and z the Standard Normal (or probit) function.

Hsieh and Lavori (2000) give sample size formulae for the number of deaths using continuous covariates in the Cox regression.

d = $$\frac{(z_text{1-a} + z_text{1-b))^{text{2}}{\sigma}text{2}\hr^text{2}}

dc = $$\frac{dc}{1-R^{text{2}}$$ where $$R}text{2}$$ is the squared multiple correlation regression one covaraite on the others.

References

Collett, D (2003) Modelling Survival Data in Medical Research Second Edition. Chapman and Hall:London

Hsieh FY and Lavori PW (2000) Sample size calculations for the Cox proportional hazards regression models with nonbinary covariates Controlled Clinical Trials 21 552-560.