mcnby_ni: Bayesian test for noninferiority in the McNemar setting with...

In EQUIVNONINF: Testing for Equivalence and Noninferiority

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 <[e-mail]>
Peter Ziegler <[e-mail]>

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)

Example output

Loading required package: BiasedUrn
 N = 25  DEL0 = 0.1  ALPHA = 0.05  K1 = 0.5  K2 = 0.5  K3 = 0.5  NSUB = 10  SW = 0.05 
 ALPHA0 = 0.03453125 SIZE0 = 0.04687917 SIZE_UNC = 0.05698492
  POW = 0.002491023 0.02412256 0.1791303 0.2547076 0.1937482 0.1476818 0.115195

EQUIVNONINF documentation built on July 12, 2021, 5:08 p.m.