fmecTest {nivm}

Odds Ratio/Difference Non-inferiority tests

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

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

Author(s)

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.

See Also

nicqTest

Examples

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