powerEpiCont.default | 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 |
integer. total number of subjects. |
theta |
numeric. postulated hazard ratio. |
sigma2 |
numeric. variance of the covariate of interest. |
psi |
numeric. proportion of subjects died of the disease of interest. |
rho2 |
numeric. square of the multiple correlation coefficient between the covariate of interest and other covariates. |
alpha |
numeric. 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(\beta_1 x_1+\boldsymbol{\beta}_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(\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 \sigma^2 \psi (1-\rho^2)}\right),
where z_{a}
is the 100 a
-th percentile of the standard normal distribution, \sigma^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}^T\boldsymbol{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.
powerEpiCont
# 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)
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