# SSizeLogisticCon: 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 continuous predictor.

## Usage

 ```1 2 3 4``` ```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 the difference between at the mean of X and at one SD above the mean. `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 continuous predictor, and \log(OR) is the the change in log odds for the difference between at the mean of X and at one SD above the mean. The sample size formula we used for testing if β_1=0 or equivalently OR=1, is Formula (1) in Hsieh et al. (1998):

n=(Z_{1-α/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.

## 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.

`powerLogisticCon`

## Examples

 ```1 2 3``` ``` ## 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) ```

### Example output

```[1] 317
```

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