SSizeLogisticCon:
Calculating sample size for simple logistic regression with continuous predictor
Description
Calculating sample size for simple logistic regression with continuous predictor.
Usage
SSizeLogisticCon(p1, OR, alpha = 0.05, power = 0.8)
Arguments
p1
the event rate at the mean of the continuous predictor X in logistic regression
$logit(p) = a + b X$,
OR
expected odds ratio.
$\log(OR)$ is the change in log odds for an increase of one unit in $X$.
alpha
Type I error rate.
power
power for testing if the odds ratio is equal to one.
Value
total sample size required.
Details
The logistic regression mode is
$$
\log(p/(1-p)) = \beta_0 + \beta_1 X
$$
where $p=prob(Y=1)$, $X$ is the continuous predictor, and $\beta_1$ is the
log odds ratio.
The sample size formula we used for testing if $\beta_1=0$ or equivalently
$OR=1$, is Formula (1) in Hsieh et al. (1998):
$$
n=(Z_{1-\alpha/2} + Z_{power})^2/[ p_1 (1-p_1) [log(OR)]^2 ]
$$
where $n$ is the required total sample size, $OR$ is the
odds ratio to be tested, $p_1$ is the event rate at the mean
of the predictor $X$, and $Z_u$ is the $u$-th
percentile of the standard normal distribution.
References
Hsieh, FY, Bloch, DA, and Larsen, MD.
A SIMPLE METHOD OF SAMPLE SIZE CALCULATION FOR LINEAR AND LOGISTIC REGRESSION.
Statistics in Medicine. 1998; 17:1623-1634.
## Example in Table II Design (Balanced design (1)) of Hsieh et al. (1998 )## the sample size is 317 SSizeLogisticCon(p1 = 0.5, OR = exp(0.405), alpha = 0.05, power = 0.95)