# brkTest: Barnard-Rohmel-Kieser Test In nivm: Noninferiority Tests with Variable Margins

## Description

A variable margin difference in proportion test for non-inferiority. The test is based on Barnard's test.

## Usage

 `1` ```brkTest(x1, n1, x2, n2, threshold = 0.2, delta = 0.1, control = brkControl()) ```

## Arguments

 `x1` number of events in the control group `n1` number of individuals in the control group `x2` number of events in the test group `n2` number of events in the test group `threshold` proportion in the control group associated with the threshold, above that threshold use a constant difference margin, below the threshold use a difference margin with a constant odds ratio. We use only continuous variable margins that meet at the threshold. `delta` difference in proportions at the threshold `control` list of parameters for algorithm control, see `brkControl`

## Details

This test is labeled T4 in Rohmel and Keiser (2013).

## Value

a list of class `brk`, with elements:

 `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 `FullResults` a list with 4 matrices, each n1+1 by n2+1 representing the total sample space. R=a matrix with logical values with TRUE elements representing the rejection region, its 'sig.level' attribute gives the significance level of the test; PVALbounds=a matrix of p-value bounds, pb; PVALsymbols=a matrix of symbols that describe the pb, '<=' means 'p<=pb', '=' means 'p=pb' and '>' means 'p>pb'; PVALUES=a matrix giving the p-value expression, e.g., 'p<=.00321' or 'p>0.025'.

Michael P. Fay

## References

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 "Investigations on non-inferiority - - the Food and Drug Administration draft guidance on treatments for nosocomial pneumonia as a case for exact tests for binomial proportions" Statistics in Medicine 32:2335-2348.

See Also `nicqTest`, ~~~

## Examples

 ```1 2 3``` ```x<-brkTest(3,8,0,6) x x\$FullResults\$PVALUES ```

### Example output

```Loading required package: bpcp

Barnard-Rohmel-Kieser Test

data:  x1=3 n1=8 x2=0 n2=6
threshold = 0.2000, difference = 0.1000, odds ratio = 1.7143

One-sided p-value:
p>0.025
Note: to save computational time, only bound on p-value calculated.

For rejection region and p-values for any possible
result with these sample sizes, save output as x,
and see the list x\$FullResults
x2=0          x2=1          x2=2         x2=3         x2=4
x1=0 "p>0.025"     "p>0.025"     "p>0.025"    "p>0.025"    "p>0.025"
x1=1 "p>0.025"     "p>0.025"     "p>0.025"    "p>0.025"    "p>0.025"
x1=2 "p>0.025"     "p>0.025"     "p>0.025"    "p>0.025"    "p>0.025"
x1=3 "p>0.025"     "p>0.025"     "p>0.025"    "p>0.025"    "p>0.025"
x1=4 "p=0.011699"  "p>0.025"     "p>0.025"    "p>0.025"    "p>0.025"
x1=5 "p=0.003668"  "p>0.025"     "p>0.025"    "p>0.025"    "p>0.025"
x1=6 "p=0.000852"  "p=0.008467"  "p>0.025"    "p>0.025"    "p>0.025"
x1=7 "p<=0.000293" "p=0.002501"  "p=0.013915" "p>0.025"    "p>0.025"
x1=8 "p<=0.000293" "p<=0.000293" "p=0.001404" "p=0.006229" "p=0.024348"
x2=5      x2=6
x1=0 "p>0.025" "p>0.025"
x1=1 "p>0.025" "p>0.025"
x1=2 "p>0.025" "p>0.025"
x1=3 "p>0.025" "p>0.025"
x1=4 "p>0.025" "p>0.025"
x1=5 "p>0.025" "p>0.025"
x1=6 "p>0.025" "p>0.025"
x1=7 "p>0.025" "p>0.025"
x1=8 "p>0.025" "p>0.025"
```

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