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| dc = dc$$(/1-R^text{2})$$ where $$R^text{2}$$ is the squared multiple correlation regression one covaraite on the others. | dc = $$\frac{dc}{1-R^text{2}}$$ where $$R^text{2}$$ is the squared multiple correlation regression one covaraite on the others. |
Survival analysis sample size calculations
Total sample size 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 sample size, d, required as
d = $$\frac{(z_text{a/2} + z_text{b/2})text{2}}{p(1-p)log(hr)text{2}}$$
for 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.
d = $$\frac{(z_text{1-a} + z_text{1-b))text{2}}{\sigmatext{2}\hr^text{2}}
dc = $$\frac{dc}{1-Rtext{2}}$$ where $$Rtext{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.