powerEpi {powerSurvEpi} | R Documentation |
Power Calculation for Cox Proportional Hazards Regression with Two Covariates for Epidemiological Studies
Description
Power 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. Some parameters will be estimated based on a pilot data set.
Usage
powerEpi(X1, X2, failureFlag, n, theta, alpha = 0.05)
Arguments
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. |
Details
This is an implementation of the power calculation 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(\beta_1 x_1+\beta_2 x_2),
where the covariate X_1
is of our interest. The covariate X_1
should 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(\beta_1)=\theta
.
Given the type I error rate \alpha
for a two-sided test, the power
required to detect a hazard ratio as small as \exp(\beta_1)=\theta
is
power=\Phi\left(-z_{1-\alpha/2}+\sqrt{n[\log(\theta)]^2
p (1-p) \psi (1-\rho^2)}\right),
where z_{a}
is the 100 a
-th percentile of the standard normal distribution, \psi
is the proportion of subjects died of
the disease of interest, and
\rho=corr(X_1, X_2)=(p_1-p_0)\times \sqrt{\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)
.
p
, \rho^2
, and \psi
will be estimated from a pilot data set.
Value
power |
the power of the test. |
p |
proportion of subjects taking |
rho2 |
square of the correlation between |
psi |
proportion of subjects died of the disease of interest. |
Note
(1) The formula can be used to calculate
power for a randomized trial study by setting rho2=0
.
(2) When \rho^2=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 \theta
measures the difference of effect of a covariate
at two different levels on the subdistribution hazard for a particular failure,
while in Schoenfeld (1983), the hazard ratio \theta
measures
the difference of effect on the cause-specific 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
Examples
# generate a toy pilot data set
X1 <- c(rep(1, 39), rep(0, 61))
set.seed(123456)
X2 <- sample(c(0, 1), 100, replace = TRUE)
failureFlag <- sample(c(0, 1), 100, prob = c(0.5, 0.5), replace = TRUE)
powerEpi(X1 = X1, X2 = X2, failureFlag = failureFlag,
n = 139, theta = 2, alpha = 0.05)