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.
1  powerEpiInt.default1(n, theta, psi, p00, p01, p10, p11, alpha = 0.05)

n 
total number of subjects. 
theta 
postulated hazard ratio. 
psi 
proportion of subjects died of the disease of interest. 
p00 
proportion of subjects taking values X_1=0 and X_2=0, i.e., p_{00}=Pr(X_1=0,\mbox{and}, X_2=0). 
p01 
proportion of subjects taking values X_1=0 and X_2=1, i.e., p_{01}=Pr(X_1=0,\mbox{and}, X_2=1). 
p10 
proportion of subjects taking values X_1=1 and X_2=0, i.e., p_{10}=Pr(X_1=1,\mbox{and}, X_2=0). 
p11 
proportion of subjects taking values X_1=1 and X_2=1, i.e., p_{11}=Pr(X_1=1,\mbox{and}, X_2=1). 
alpha 
type I error rate. 
This is an implementation of the power calculation formula derived by Schmoor et al. (2000) for the following Cox proportional hazards regression in the epidemoilogical studies:
h(tx_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 twosided test, the power required to detect a hazard ratio as small as \exp(γ)=θ is:
power=Φ≤ft(z_{1α/2}+√{\frac{n}{δ}[\log(θ)]^2 ψ}\right),
where
δ=\frac{1}{p_{00}}+\frac{1}{p_{01}}+\frac{1}{p_{10}} +\frac{1}{p_{11}},
ψ is the proportion of subjects died of the disease of interest, and p_{00}=Pr(X_1=0,\mbox{and}, X_2=0), p_{01}=Pr(X_1=0,\mbox{and}, X_2=1), p_{10}=Pr(X_1=1,\mbox{and}, X_2=0), p_{11}=Pr(X_1=1,\mbox{and}, X_2=1).
The power of the test.
Schmoor C., Sauerbrei W., and Schumacher M. (2000). Sample size considerations for the evaluation of prognostic factors in survival analysis. Statistics in Medicine. 19:441452.
powerEpiInt.default0
, powerEpiInt2
1 2 3 4 5 6 7  # Example at the end of Section 4 of Schmoor et al. (2000).
# p00, p01, p10, and p11 are calculated based on Table III on page 448
# of Schmoor et al. (2000).
powerEpiInt.default1(n = 184, theta = 3, psi = 139 / 184,
p00 = 50 / 184, p01 = 21 / 184, p10 = 78 / 184, p11 = 35 / 184,
alpha = 0.05)

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