powerEpiCont {powerSurvEpi} | R Documentation |
Power Calculation for Cox Proportional Hazards Regression with Nonbinary Covariates for Epidemiological Studies
Description
Power calculation for Cox proportional hazards regression with nonbinary covariates for Epidemiological Studies. Some parameters will be estimated based on a pilot data set.
Usage
powerEpiCont(formula,
dat,
var.X1,
var.failureFlag,
n,
theta,
alpha = 0.05)
Arguments
formula |
a formula object relating the covariate of interest
to other covariates to calculate the multiple correlation coefficient. The
variables in formula must be in the data frame |
dat |
a |
var.X1 |
character. name of the column in the data frame |
var.failureFlag |
character. name of the column in the data frame |
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 Hsieh and Lavori (2000) for the following Cox proportional hazards regression in the epidemiological studies:
where the covariate is a nonbinary variable and
is a vector of other covariates.
Suppose we want to check if
the hazard ratio of the main effect to
is equal to
or is equal to
.
Given the type I error rate
for a two-sided test, the power
required to detect a hazard ratio as small as
is
where is the
-th percentile of the standard normal distribution,
,
is the proportion of subjects died of
the disease of interest, and
is the multiple correlation coefficient
of the following linear regression:
That is, , where
is the proportion of variance
explained by the regression of
on the vector of covriates
.
will be estimated from a pilot study.
Value
power |
The power of the test. |
rho2 |
square of the correlation between |
sigma2 |
variance of the covariate of interest. |
psi |
proportion of subjects died of the disease of interest. |
Note
(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
.
References
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.
See Also
Examples
# generate a toy pilot data set
set.seed(123456)
X1 <- rnorm(100, mean = 0, sd = 0.3126)
X2 <- sample(c(0, 1), 100, replace = TRUE)
failureFlag <- sample(c(0, 1), 100, prob = c(0.25, 0.75), replace = TRUE)
dat <- data.frame(X1 = X1, X2 = X2, failureFlag = failureFlag)
powerEpiCont(formula = X1 ~ X2,
dat = dat,
var.X1 = "X1",
var.failureFlag = "failureFlag",
n = 107,
theta = exp(1),
alpha = 0.05)