powerEpiInt.default0: Power Calculation Testing Interaction Effect for Cox...

In powerSurvEpi: Power and Sample Size Calculation for Survival Analysis of Epidemiological Studies

Description

Power calculation testing interaction effect for Cox proportional hazards regression with two covariates for Epidemiological Studies. Both covariates should be binary variables. The formula takes into account the correlation between the two covariates.

Usage

powerEpiInt.default0(n, 
		     theta, 
		     p, 
		     psi, 
		     G, 
		     rho2, 
		     alpha = 0.05)

Arguments

n	integer. total number of subjects.
theta	numeric. postulated hazard ratio.
p	numeric. proportion of subjects taking the value one for the covariate of interest.
psi	numeric. proportion of subjects died of the disease of interest.
G	numeric. a factor adjusting the sample size. The sample size needed to detect an effect of a prognostic factor with given error probabilities has to be multiplied by the factor G when an interaction of the same magnitude is to be detected.
rho2	numeric. square of the correlation between the covariate of interest and the other covariate.
alpha	numeric. type I error rate.

Details

This is an implementation of the power calculation formula derived by Schmoor et al. (2000) 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 + γ (x_1 x_2)),

where both covariates X_1 and X_2 are binary variables.

Suppose we want to check if the hazard ratio of the interaction effect X_1 X_2=1 to X_1 X_2=0 is equal to 1 or is equal to \exp(γ)=θ. Given the type I error rate α for a two-sided test, the power required to detect a hazard ratio as small as \exp(γ)=θ is

power=Φ≤ft(-z_{1-α/2}+√{\frac{n}{G}[\log(θ)]^2 p (1-p) ψ (1-ρ^2)}\right),

where z_{a} is the 100 a-th percentile of the standard normal distribution, ψ is the proportion of subjects died of the disease of interest, and

ρ=corr(X_1, X_2)=(p_1-p_0)\times √{\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), and

G=\frac{[(1-q)(1-p_0)p_0+q(1-p_1)p_1]^2}{(1-q)q (1-p_0)p_0 (1-p_1) p_1}.

If X_1 and X_2 are uncorrelated, we have p_0=p_1=p leading to 1/[(1-q)q]. For q=0.5, we have G=4.

Value

The power of the test.

References

Schmoor C., Sauerbrei W., and Schumacher M. (2000). Sample size considerations for the evaluation of prognostic factors in survival analysis. Statistics in Medicine. 19:441-452.

See Also

powerEpiInt.default1, powerEpiInt2

Examples

  # Example at the end of Section 4 of Schmoor et al. (2000).
  powerEpiInt.default0(n = 184, 
		       theta = 3, 
		       p = 0.61, 
		       psi = 139 / 184, 
                       G = 4.79177, 
		       rho2 = 0.015^2, 
		       alpha = 0.05)
  

powerSurvEpi documentation built on March 1, 2021, 9:06 a.m.