SSizeLogisticBin {powerMediation}

Calculating sample size for simple logistic regression with binary predictor

Description

Calculating sample size for simple logistic regression with binary predictor.

Usage

SSizeLogisticBin(p1, 
                 p2, 
                 B, 
                 alpha = 0.05, 
                 power = 0.8)

Arguments

p1

pr(diseased | X = 0), i.e. the event rate at X = 0 in logistic regression logit(p) = a + b X, where X is the binary predictor.

p2

pr(diseased | X = 1), the event rate at X = 1 in logistic regression logit(p) = a + b X, where X is the binary predictor.

B

pr(X = 1), i.e. proportion of the sample with X = 1

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 binary predictor, p_1 = pr(diseased | X = 0), p_2 = pr(diseased| X = 1), B = pr(X = 1), and p = (1 - B) p_1 + B p_2. The sample size formula we used for testing if \beta_1 = 0, is Formula (2) in Hsieh et al. (1998):

n = (Z_{1-\alpha/2}[p(1-p)/B]^{1/2} + Z_{power}[p_1(1-p_1)+p_2(1-p_2)(1-B)/B]^{1/2})^2/[ (p_1-p_2)^2 (1-B) ]

where n is the required total sample size 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

powerLogisticBin

Examples

    ## Example in Table I Design (Balanced design with high event rates) 
    ## of Hsieh et al. (1998 )
    ## the sample size is 1281
    SSizeLogisticBin(p1 = 0.4, p2 = 0.5, B = 0.5, alpha = 0.05, power = 0.95)