ssizeEpi.default {powerSurvEpi}R Documentation

Sample Size Calculation for Cox Proportional Hazards Regression with two covariates for Epidemiological Studies (Covariate of interest should be binary)

Description

Sample size calculation for Cox proportional hazards regression with two covariates for Epidemiological Studies. The covariate of interest should be a binary variable. The other covariate can be either binary or non-binary. The formula takes into account competing risks and the correlation between the two covariates.

Usage

ssizeEpi.default(power, theta, p, psi, rho2, alpha = 0.05)

Arguments

power postulated power.
theta postulated hazard ratio.
p proportion of subjects taking value one for the covariate of interest.
psi proportion of subjects died of the disease of interest.
rho2 square of the correlation between the covariate of interest and the other covariate.
alpha type I error rate.

Details

This is an implementation of the sample size formula derived by Latouche et al. (2004) for the following Cox proportional hazards regression in the epidemiological studies:

h(t|x_1, x_2)=h_0(t)exp(β_1 x_1+β_2 x_2),

where the covariate X_1 is of our interest. The covariate X_1 has to be a binary variable taking two possible values: zero and one, while the covariate X_2 can be binary or continuous.

Suppose we want to check if the hazard of X_1=1 is equal to the hazard of X_1=0 or not. Equivalently, we want to check if the hazard ratio of 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 power of 1-β is

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

where psi is the proportion of subjects died of the disease of interest, and

rho=corr(X_1, X_2)=(p_1-p_0)timessqrt{frac{q(1-q)}{p(1-p)}},

and p=Pr(X_1=1), q=Pr(X_2=1), p_0=Pr(X_1=1|X_2=0), and p_1=Pr(X_1=1 | X_2=1).

Value

The required sample size to achieve the specified power with the given type I error rate.

Note

(1) The calculated sample size will be round up to an integer.

(2) The formula can be used to calculate sample size required for a randomized trial study by setting rho2=0.

(3) When rho2=0, the formula derived by Latouche et al. (2004) looks the same as that derived by Schoenfeld (1983). Latouche et al. (2004) pointed out that in this situation, the interpretations are different hence the two formulae are actually different. In Latouched et al. (2004), the hazard ratio exp(β_1)=theta measures the difference of effect of a covariate at two different levels on cause-specific hazard for a particular failure, while in Schoenfeld (1983), the hazard ratio theta measures the difference of effect on subdistribution hazard.

References

Schoenfeld DA. (1983). Sample-size formula for the proportional-hazards regression model. Biometrics. 39:499-503.

Latouche A., Porcher R. and Chevret S. (2004). Sample size formula for proportional hazards modelling of competing risks. Statistics in Medicine. 23:3263-3274.

See Also

ssizeEpi

Examples

  # Examples at the end of Section 5.2 of Latouche et al. (2004)
  # for a cohort study.
  ssizeEpi.default(power = 0.80, theta = 2, p = 0.39 , psi = 0.505,
    rho2 = 0.132^2, alpha = 0.05)

[Package powerSurvEpi version 0.0.5 Index]