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| 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.] | 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 Schoenfeld (1983), Hsieh and Lavori (2000) and Collett (2003) corresponding to a group regression estimate (ratio of hazards) in a Cox regression model. |
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| In particular Collett(2003) gives the total sample size, d, required as | In particular from Schoenfeld (1983) the total number of events, d, required is |
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| d = $$\frac{(z_text{a/2} + z_text{b/2})^text{2}}{p(1-p)log(hr)^text{2}}$$ | d = $$\frac{(z_text{a/2} + z_text{b})^text{2}}{p(1-p)[log(hr)]^text{2}}$$ |
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| for two-sided type I error, a, power 1-b, event rate in population p and hazard ratio, hr. | 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. |
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| __Reference__ | Hsieh and Lavori (2000) further give sample size formulae for the number of deaths using continuous covariates in the Cox regression. |
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| Collett, D (2003) Modelling Survival Data in Medical Research Second Edition. Chapman and Hall:London | dc = $$\frac{(z_text{a/2} + z_text{b})^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 the covariate of interest with the others in the case of more than one continuous covariate. This method is computed using this [attachment:coxcN.xls spreadsheet.] The ratio for a continuous covariate could be comparing rates at one sd above the mean to that at the mean. This approach is similar to Hsieh's approaches to sample size calculations for the odds ratio in a logistic regression (see [:FAQ/power/llogPow:here]). This method may also be computed using the powerEpiCont function in R as illustrated [:FAQ/power/hazNR: here]. 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.] The free downloadable software [http://www.brixtonhealth.com/pepi4windows.html WINPEPI] also computes this sample size and power for comparing survival curves. __References__ Collett, D (2003) Modelling Survival Data in Medical Research. Second Edition. Chapman and Hall:London Hsieh FY and Lavori PW (2000) [http://www.sciencedirect.com/science/article/pii/S0197245600001045 Sample size calculations for the Cox proportional hazards regression models with nonbinary covariates] ''Controlled Clinical Trials'' '''21''' 552-560. Schoenfeld DA (1983) Sample size formulae for the proportional hazards regression model. ''Biometrics'' '''39''' 499-503. |
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 Schoenfeld (1983), Hsieh and Lavori (2000) and Collett (2003) corresponding to a group regression estimate (ratio of hazards) in a Cox regression model.
In particular from Schoenfeld (1983) the total number of events, d, required is
d = $$\frac{(z_text{a/2} + z_text{b})text{2}}{p(1-p)[log(hr)]text{2}}$$
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) further 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})text{2}}{\sigmatext{2}\[log(hr)]^text{2}}
with $$\sigma^text{2}$$ equal to the variance of the covariate.
dc2 = $$\frac{dc}{1-Rtext{2}}$$ where $$Rtext{2}$$ is the squared multiple correlation regression of the covariate of interest with the others in the case of more than one continuous covariate. This method is computed using this [attachment:coxcN.xls spreadsheet.] The ratio for a continuous covariate could be comparing rates at one sd above the mean to that at the mean.
This approach is similar to Hsieh's approaches to sample size calculations for the odds ratio in a logistic regression (see [:FAQ/power/llogPow:here]). This method may also be computed using the powerEpiCont function in R as illustrated [:FAQ/power/hazNR: here].
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.] The free downloadable software [http://www.brixtonhealth.com/pepi4windows.html WINPEPI] also computes this sample size and power for comparing survival curves.
References
Collett, D (2003) Modelling Survival Data in Medical Research. Second Edition. Chapman and Hall:London
Hsieh FY and Lavori PW (2000) [http://www.sciencedirect.com/science/article/pii/S0197245600001045 Sample size calculations for the Cox proportional hazards regression models with nonbinary covariates] Controlled Clinical Trials 21 552-560.
Schoenfeld DA (1983) Sample size formulae for the proportional hazards regression model. Biometrics 39 499-503.