ssizeEpiCont {powerSurvEpi} | R Documentation |
Sample size calculation for Cox proportional hazards regression with nonbinary covariates for Epidemiological Studies.
ssizeEpiCont(formula, dat, X1, 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 .
|
dat |
a nPilot by p data frame representing the pilot
data set, where nPilot is the number of subjects in the pilot study and
the p (>1) columns contains the covariate of interest and other
covariates.
|
X1 |
the covariate of interest. |
failureFlag |
a nPilot by 1 vector of indicators indicating if a subject is
failure (failureFlag=1 ) or alive (failureFlag=0 ).
|
power |
postulated power. |
theta |
postulated hazard ratio. |
alpha |
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(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 total number of subjects required to achieve a sample size of 1-β is
n=frac{(z_{1-α/2}+z_{1-β})^2}{ [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.
rho^2, σ^2, and psi will be estimated from a pilot study.
n |
the total number of subjects required. |
rho2 |
square of the correlation between X_1 and X_2. |
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.
# 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, X1 = X1, failureFlag = failureFlag, power = 0.806, theta = exp(1), alpha = 0.05)