Survival analysis sample size calculations

The total number of events may be evaluated for comparing hazard rates (per unit time) using this [attachment:coxsamp.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.]

In particular Collett(2003) gives the total number of events, d, required as

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

for a two-sided type I error, a, power 1-b, event rate in population p, hazard ratio, hr 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.

dc = $$\frac{(z_text{a/2} + z_text{b/2})^{text{2}}{\sigma}text{2}\log(hr)^text{2}}

with $$\sigma^text{2}$$ equal to the variance of the covariate.

dc2 = $$\frac{dc}{1-R^{text{2}}$$ where $$R}text{2}$$ is the squared multiple correlation regression of one covariate on the others in the case of more than one continuous covariate.

This approach is similar to Hsieh's approaches to power for the odds ration in a logistic regression (see [:FAQ/llogPow here.]

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.