powerMediation (version 0.3.4)

SSizeLogisticBin: 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.

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 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.

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

# NOT RUN {
    ## 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)
# }