powerSurvEpi (version 0.0.9)

powerEpiCont.default: Power Calculation for Cox Proportional Hazards Regression with Nonbinary Covariates for Epidemiological Studies

Description

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

Usage

powerEpiCont.default(n, theta, sigma2, psi, rho2, alpha = 0.05)

Arguments

n

total number of subjects.

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.

Value

• The power of the test.

Details

This is an implementation of the power calculation formula derived by Hsieh and Lavori (2000) for the following Cox proportional hazards regression in the epidemiological studies: $$h(t|x_1, \boldsymbol{x}_2)=h_0(t)\exp(\beta_1 x_1+\boldsymbol{\beta}_2 \boldsymbol{x}_2),$$ 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 $\exp(\beta_1)=\theta$. Given the type I error rate $\alpha$ for a two-sided test, the power required to detect a hazard ratio as small as $\exp(\beta_1)=\theta$ is $$power=\Phi\left(-z_{1-\alpha/2}+\sqrt{n[\log(\theta)]^2 \sigma^2 \psi (1-\rho^2)}\right),$$ where $\sigma^2=Var(X_1)$, $\psi$ is the proportion of subjects died of the disease of interest, and $\rho$ is the multiple correlation coefficient of the following linear regression: $$x_1=b_0+\boldsymbol{b}^T\boldsymbol{x}_2.$$ 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 $\boldsymbol{X}_2$.

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

powerEpiCont

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.
  powerEpiCont.default(n = 107, theta = exp(1), sigma2 = 0.3126^2, 
    psi = 0.738, rho2 = 0.1837, alpha = 0.1)