Description Usage Arguments Details Value References See Also Examples
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. Some parameters will be estimated based on a pilot study.
1 2 3 4 5 6 | powerEpiInt(X1,
X2,
failureFlag,
n,
theta,
alpha = 0.05)
|
X1 |
numeric. a |
X2 |
numeric. a |
failureFlag |
numeric.a |
n |
integer. total number of subjects. |
theta |
numeric. postulated hazard ratio. |
alpha |
numeric. 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(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}{δ}[\log(θ)]^2 ψ}\right),
where z_{a} is the 100 a-th percentile of the standard normal distribution,
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).
p_{00}, p_{01}, p_{10}, p_{11}, and ψ will be estimated from the pilot data.
power |
the power of the test. |
p |
estimated Pr(X_1=1) |
q |
estimated Pr(X_2=1) |
p0 |
estimated Pr(X_1=1 | X_2=0) |
p1 |
estimated Pr(X_1=1 | X_2=1) |
rho2 |
square of the estimated corr(X_1, X_2) |
G |
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 |
mya |
estimated number of subjects taking values X_1=0 and X_2=0. |
myb |
estimated number of subjects taking values X_1=0 and X_2=1. |
myc |
estimated number of subjects taking values X_1=1 and X_2=0. |
myd |
estimated number of subjects taking values X_1=1 and X_2=1. |
psi |
proportion of subjects died of the disease of interest. |
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.
powerEpiInt.default0
, powerEpiInt2
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