ssizeEpiCont | R Documentation |
Sample size calculation for Cox proportional hazards regression with nonbinary covariates for Epidemiological Studies.
ssizeEpiCont(formula,
dat,
var.X1,
var.failureFlag,
power,
theta,
alpha = 0.05)
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 |
power |
numeric. postulated power. |
theta |
numeric. postulated hazard ratio. |
alpha |
numeric. type I error rate. |
This is an implementation of the sample size 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 total
number of subjects required to achieve a sample size of 1-\beta
is
n=\frac{\left(z_{1-\alpha/2}+z_{1-\beta}\right)^2}{
[\log(\theta)]^2 \sigma^2 \psi (1-\rho^2)
},
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
.
rho^2
, \sigma^2
, and \psi
will be estimated from a pilot study.
n |
the total number of subjects required. |
rho2 |
square of the correlation between |
sigma2 |
variance of the covariate of interest. |
psi |
proportion of subjects died of the disease of interest. |
(1) Hsieh and Lavori (2000) assumed one-sided test, while this implementation assumed two-sided test.
(2) The formula can be used to calculate
ssize 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.
ssizeEpiCont.default
# 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)
ssizeEpiCont(formula = X1 ~ X2,
dat = dat,
var.X1 = "X1",
var.failureFlag = "failureFlag",
power = 0.806,
theta = exp(1),
alpha = 0.05)
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