powerMediation (version 0.2.9)

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.

See Also

powerLogisticCon

Examples

# NOT RUN {
    ## 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)
# }