mcnby_ni {EQUIVNONINF}R Documentation

Bayesian test for noninferiority in the McNemar setting with the difference of proportions as the parameter of interest

Description

The program determines through iteration the largest nominal level α_0 such that comparing the posterior probability of the alternative hypothesis K_1: δ > -δ_0 to the lower bound 1-α_0 generates a critical region whose size does not exceed the target significance level α. In addition, exact values of the power against specific parameter configurations with δ = 0 are output.

Usage

mcnby_ni(N,DEL0,K1,K2,K3,NSUB,SW,ALPHA,MAXH)

Arguments

N

sample size

DEL0

noninferiority margin to the difference of the parameters of the marginal binomial distributions under comparison

K1

Parameter 1 of the Dirichlet prior for the family of trinomial distributions

K2

Parameter 2 of the Dirichlet prior for the family of trinomial distributions

K3

Parameter 3 of the Dirichlet prior for the family of trinomial distributions

NSUB

number of subintervals for partitioning the range of integration

SW

width of the search grid for determining the maximum of the rejection probability on the common boundary of the hypotheses

ALPHA

target significance level

MAXH

maximum number of interval halving steps to be carried out in finding the maximally raised nominal level

Details

The program uses 96-point Gauss-Legendre quadrature on each of the NSUB intervals into which the range of integration is partitioned.

Value

N

sample size

DEL0

noninferiority margin to the difference of the parameters of the marginal binomial distributions under comparison

K1

Parameter 1 of the Dirichlet prior for the family of trinomial distributions

K2

Parameter 2 of the Dirichlet prior for the family of trinomial distributions

K3

Parameter 3 of the Dirichlet prior for the family of trinomial distributions

NSUB

number of subintervals for partitioning the range of integration

SW

width of the search grid for determining the maximum of the rejection probability on the common boundary of the hypotheses

ALPHA

target significance level

MAXH

maximum number of interval halving steps to be carried out in finding the maximally raised nominal level

ALPHA0

result of the search for the largest admissible nominal level

SIZE0

size of the critical region corresponding to α_0

SIZE_UNC

size of the critical region of test at uncorrected nominal level α

POW

power against 7 different parameter configurations with δ =0

Author(s)

Stefan Wellek <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>

References

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 5.2.3.

Examples

mcnby_ni(25,.10,.5,.5,.5,10,.05,.05,5)

[Package EQUIVNONINF version 1.0.2 Index]