ssizeEpiCont.default {powerSurvEpi}R Documentation

Sample Size Calculation for Cox Proportional Hazards Regression with nonbinary covariates for Epidemiological Studies

Description

Sample size calculation for Cox proportional hazards regression with nonbinary covariates for Epidemiological Studies.

Usage

ssizeEpiCont.default(power, theta, sigma2, psi, rho2, alpha = 0.05)

Arguments

power postulated power.
theta postulated hazard ratio.
sigma2 variance of the covariate of interest.
psi proportion of subjects died of the disease of interest.
rho2 square of the multiple correlation coefficient between the covariate of interest and other covariates.
alpha type I error rate.

Details

This is an implementation of the sample size calculation formula derived by Hsieh and Lavori (2000) for the following Cox proportional hazards regression in the epidemiological studies:

h(t|x_1, boldsymbol{x}_2)=h_0(t)exp(β_1 x_1+boldsymbol{β}_2 boldsymbol{x}_2,

where the covariate X_1 is a nonbinary variable and boldsymbol{X}_2 is a vector of other covariates.

Suppose we want to check if the hazard ratio of the main effect X_1=1 to X_1=0 is equal to 1 or is equal to exp(β_1)=theta. Given the type I error rate α for a two-sided test, the total number of subjects required to achieve a sample size of 1-β is

n=frac{(z_{1-α/2}+z_{1-β})^2}{ [log(theta)]^2 σ^2 psi (1-rho^2) },

where σ^2=Var(X_1), psi is the proportion of subjects died of the disease of interest, and rho is the multiple correlation coefficient of the following linear regression:

x_1=b_0+boldsymbol{b}^Tboldsymbol{x}_2.

That is, rho^2=R^2, where R^2 is the proportion of variance explained by the regression of X_1 on the vector of covriates boldsymbol{X}_2.

Value

The total number of subjects required.

Note

(1) Hsieh and Lavori (2000) assumed one-sided test, while this implementation assumed two-sided test. (2) The formula can be used to calculate ssize for a randomized trial study by setting rho2=0.

References

Hsieh F.Y. and Lavori P.W. (2000). Sample-size calculation for the Cox proportional hazards regression model with nonbinary covariates. Controlled Clinical Trials. 21:552-560.

See Also

ssizeEpiCont

Examples

  # example in the EXAMPLE section (page 557) of Hsieh and Lavori (2000).
  # Hsieh and Lavori (2000) assumed one-sided test, 
  # while this implementation assumed two-sided test. 
  # Hence alpha=0.1 here (two-sided test) will correspond
  # to alpha=0.05 of one-sided test in Hsieh and Lavori's (2000) example.
  ssizeEpiCont.default(power = 0.806, theta = exp(1), sigma2 = 0.3126^2, 
    psi = 0.738, rho2 = 0.1837, alpha = 0.1)


[Package powerSurvEpi version 0.0.5 Index]