# SSizeLogisticBin: Calculating sample size for simple logistic regression with... In powerMediation: Power/Sample Size Calculation for Mediation Analysis

## Description

Calculating sample size for simple logistic regression with binary predictor.

## Usage

 ```1 2 3 4 5``` ```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)) = 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.

## 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 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 sample size is 1281 SSizeLogisticBin(p1 = 0.4, p2 = 0.5, B = 0.5, alpha = 0.05, power = 0.95) ```

### Example output

```[1] 1281
```

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