ssizeEpiInt.default0 {powerSurvEpi} | R Documentation |
Sample Size Calculation Testing Interaction Effect for Cox Proportional Hazards Regression
Description
Sample size 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
ssizeEpiInt.default0(power,
theta,
p,
psi,
G,
rho2,
alpha = 0.05)
Arguments
power |
numeric. postulated power. |
theta |
numeric. postulated hazard ratio. |
p |
numeric. proportion of subjects taking 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 |
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 sample size 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(\beta_1 x_1+\beta_2 x_2 + \gamma (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(\gamma)=\theta
.
Given the type I error rate \alpha
for a two-sided test, the total
number of subjects required to achieve a power of 1-\beta
is
n=\frac{\left(z_{1-\alpha/2}+z_{1-\beta}\right)^2 G}{
[\log(\theta)]^2 \psi (1-p) p (1-\rho^2)
},
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)
, 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 total number of subjects required.
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
ssizeEpiInt.default1
, ssizeEpiInt2
Examples
# Example at the end of Section 4 of Schmoor et al. (2000).
ssizeEpiInt.default0(power = 0.8227,
theta = 3,
p = 0.61,
psi = 139 / 184,
G = 4.79177,
rho2 = 0.015^2,
alpha = 0.05)