powerEpiCont.default {powerSurvEpi} | R Documentation |
Power calculation for Cox proportional hazards regression with nonbinary covariates for Epidemiological Studies.
powerEpiCont.default(n, theta, sigma2, psi, rho2, alpha = 0.05)
n |
total number of subjects. |
theta |
postulated hazard ratio. |
sigma2 |
variance of the covariate of interest. |
psi |
proportion of subjects died of the disease of interest. |
rho2 |
square of the multiple correlation coefficient between the covariate of interest and other covariates. |
alpha |
type I error rate. |
This is an implementation of the power calculation formula derived by Hsieh and Lavori (2000) for the following Cox proportional hazards regression in the epidemiological studies:
h(t|x_1, boldsymbol{x}_2)=h_0(t)exp(β_1 x_1+boldsymbol{β}_2 boldsymbol{x}_2),
where the covariate X_1 is a nonbinary variable and boldsymbol{X}_2 is a vector of other covariates.
Suppose we want to check if the hazard ratio of the main effect X_1=1 to X_1=0 is equal to 1 or is equal to exp(β_1)=theta. Given the type I error rate α for a two-sided test, the power required to detect a hazard ratio as small as exp(β_1)=theta is
power=Phi(-z_{1-α/2}+sqrt{n[log(theta)]^2 σ^2 psi (1-rho^2)}),
where σ^2=Var(X_1), psi is the proportion of subjects died of the disease of interest, and rho is the multiple correlation coefficient of the following linear regression:
x_1=b_0+boldsymbol{b}^Tboldsymbol{x}_2.
That is, rho^2=R^2, where R^2 is the proportion of variance explained by the regression of X_1 on the vector of covriates boldsymbol{X}_2.
The power of the test.
(1) Hsieh and Lavori (2000) assumed one-sided test, while this implementation assumed two-sided test.
(2) The formula can be used to calculate
power for a randomized trial study by setting rho2=0
.
Hsieh F.Y. and Lavori P.W. (2000). Sample-size calculation for the Cox proportional hazards regression model with nonbinary covariates. Controlled Clinical Trials. 21:552-560.
# example in the EXAMPLE section (page 557) of Hsieh and Lavori (2000). # Hsieh and Lavori (2000) assumed one-sided test, # while this implementation assumed two-sided test. # Hence alpha=0.1 here (two-sided test) will correspond # to alpha=0.05 of one-sided test in Hsieh and Lavori's (2000) example. powerEpiCont.default(n = 107, theta = exp(1), sigma2 = 0.3126^2, psi = 0.738, rho2 = 0.1837, alpha = 0.1)