# fmecTest: Odds Ratio/Difference Non-inferiority tests In nivm: Noninferiority Tests with Variable Margins

## Description

Rohmel and Keier (2013) developed these non-inferioirty tests with variable margins. One margin function, NiM3, has the variable margin measuring a constant difference in proportions (0.10 in paper) after a threshold (0.20 proportion in the control group), or tests for differences defined in terms of a constant odds ratio (1.71 in paper) at values less than the threshold. The `fmecTest` with type='max' gives the maximum of two p-values, either a difference in proportions test (one-sided asymptotic method of Farrington and Manning, 1990) or an odds ratio test (one-sided Fisher's exact). This test is NiM3/T2 in Rohmel and Keier (2013). We also provide an exact version of this test with `fmecExact`, denoted NiM3/T3 in Rohmel and Keier (2013). When type='switch' the tests are like T1 of Rohmel and Keier (2013).

## Usage

 ```1 2 3 4 5 6 7``` ```fmecTest(x1, n1, x2, n2, threshold = 0.2, delta = 0.1, alternative = c("less","greater"), type = c("max", "switch")) fmecExact(x1, n1, x2, n2, threshold = 0.2, delta = 0.1, alternative = c("less", "greater"), type = c("max", "switch"), ngrid = 1000) ```

## Arguments

 `x1` number of failures in control group `n1` number of individuals in control group `x2` number of failures in test group `n2` number of individuals in test group `threshold` threshold on proportion in control group: above it use constant difference margin, below it use difference margin with constant odds ratio `delta` difference margin at threshold `alternative` must be 'less'. the value 'greater' is not supported at this time. `type` either 'max' (maximum of Fisher's exact p-value or Farrington and Manning p-value) or 'switch' (Fisher's exact p-value below threhold and Farington and Manning p-value above threhold). `ngrid` grid size for the search for the maximum p-value. Search over the control proportion values 0:ngrid/ngrid.

## Details

For details see Rohmel and Keier (2013, Section 3). These functions only use NiM3.

## Value

a list of class 'htest':

 `statistic` the threshold, delta (difference margin at threshold), and odds ratio at threshold `data.name` gives x1,x2,n1,n2 as a character string `method` description of test `p.value` one-sided p-value `null.value` delta, the difference margin at threshold `alternative` direction of alternative hypothesis

Michael P. Fay

## References

Farrington, CP and Manning G (1990). "Test statistics and sample size formulae for comparative binomial trials with null hypothesis of non-zero risk difference or non-unit relative risk" Statistics in Medicine 9:1447-1454.

Rohmel, J, and Kieser, M (2013). "Investigations on non-inferiority - - the Food and Drug Administration draft guidance on treatments for nosocomial pneumonia as a case for exact tests for binomial proportions" Statistics in Medicine 32:2335-2348.

`nicqTest`

## Examples

 ```1 2``` ```fmecTest(6,10,2,12,alternative="less",type="max") fmecExact(6,10,2,12,alternative="less",type="max") ```

### Example output

```Loading required package: bpcp

Odds Ratio/Difference Test type=max

data:  x1=6 n1=10 x2=2 n2=12
threshold = 0.2000, difference = 0.1000, odds ratio = 1.7143, p-value =
0.01064
alternative hypothesis: true difference in proportions is less than 0.1

Exact Odds Ratio/Difference Test type=max

data:  x1=6 n1=10 x2=2 n2=12
threshold = 0.2000, difference = 0.1000, odds ratio = 1.7143, p-value =
0.008839
alternative hypothesis: true difference in proportions is less than 0.1
```

nivm documentation built on May 2, 2019, 8:22 a.m.