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| where n is the total sample size, p the probability of occurrence of the event in the population, hr the hazard ratio, type I error a, $$\Phi$$ the inverse normal function and z the Standard Normal (or probit) function. | 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. |
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.
Reference
Collett, D (2003) Modelling Survival Data in Medical Research Second Edition. Chapman and Hall:London