SSizeLogisticCon {powerMediation}

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 the difference between at the mean of X and at one SD above the mean.

alpha

Type I error rate.

power

power for testing if the odds ratio is equal to one.

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 \log(OR) is the the change in log odds for the difference between at the mean of X and at one SD above the mean. 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.

Value

total sample size required.

Note

The test is a two-sided test. For one-sided tests, please double the significance level. For example, you can set alpha=0.10 to obtain one-sided test at 5% significance level.

Author(s)

Weiliang Qiu [e-mail]

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.

See Also

powerLogisticCon

Examples

    ## 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)