# powerLogisticBin: Calculating power for simple logistic regression with binary... In powerMediation: Power/Sample Size Calculation for Mediation Analysis

## Description

Calculating power for simple logistic regression with binary predictor.

## Usage

 ```1 2 3 4 5``` ```powerLogisticBin(n, p1, p2, B, alpha = 0.05) ```

## Arguments

 `n` total number of sample size. `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.

## Details

The logistic regression mode is

\log(p/(1-p)) = β_0 + β_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 β_1=0, is Formula (2) in Hsieh et al. (1998):

n=(Z_{1-α/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.

Estimated power.

## 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 stwxq@channing.harvard.edu

## 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.

`powerLogisticBin`

## Examples

 ```1 2 3 4``` ``` ## Example in Table I Design (Balanced design with high event rates) ## of Hsieh et al. (1998 ) ## the power = 0.95 powerLogisticBin(n = 1281, p1 = 0.4, p2 = 0.5, B = 0.5, alpha = 0.05) ```

### Example output

```[1] 0.9500671
```

powerMediation documentation built on March 24, 2021, 1:06 a.m.