powerMediation (version 0.2.9)

powerLogisticCon: Calculating power for simple logistic regression with continuous predictor

Description

Calculating power for simple logistic regression with continuous predictor.

Usage

powerLogisticCon(n, 
                 p1, 
                 OR, 
                 alpha = 0.05)

Arguments

n

total sample size.

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.

Value

Estimated power.

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

SSizeLogisticCon

Examples

# NOT RUN {
    ## Example in Table II Design (Balanced design (1)) of Hsieh et al. (1998 )
    ## the power is 0.95
    powerLogisticCon(n=317, p1=0.5, OR=exp(0.405), alpha=0.05)
# }