ssizeEpiCont.default {powerSurvEpi}

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

numeric. postulated power.

theta

numeric. postulated hazard ratio.

sigma2

numeric. variance of the covariate of interest.

psi

numeric. proportion of subjects died of the disease of interest.

rho2

numeric. square of the multiple correlation coefficient between the covariate of interest and other covariates.

alpha

numeric. 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(\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 total number of subjects required to achieve a sample size of 1-\beta is

n=\frac{\left(z_{1-\alpha/2}+z_{1-\beta}\right)^2}{ [\log(\theta)]^2 \sigma^2 \psi (1-\rho^2) },

where z_{a} is the 100 a-th percentile of the standard normal distribution, \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.

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)