mcnby_ni_pp {EQUIVNONINF}

Computation of the posterior probability of the alternative hypothesis of noninferiority in the McNemar setting, given a specific point in the sample space

Description

Evaluation of the integral on the right-hand side of Equation (5.24) on p. 88 of Wellek S (2010) Testing statistical hypotheses of equivalence and noninferiority. Second edition.

Usage

mcnby_ni_pp(N,DEL0,N10,N01)

Arguments

N

sample size

DEL0

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

N10

count of pairs with (X,Y) = (1,0)

N01

count of pairs with (X,Y) = (0,1)

Details

The program uses 96-point Gauss-Legendre quadrature on each of 10 subintervals 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

N10

count of pairs with (X,Y) = (1,0)

N01

count of pairs with (X,Y) = (0,1)

PPOST

posterior probability of the alternative hypothesis K_1: \delta > -\delta_0 with respect to the noninformative prior determined according to Jeffrey's rule

Note

The program uses Equation (5.24) of Wellek S (2010) corrected for a typo in the middle line which must read

\int_{\delta_0}^{(1+\delta_0)/2}\Big[ B\big(n_{01}+1/2,n-n_{01}+1\big)\,\, p_{01}^{n_{01}-1/2}(1-p_{01})^{n-n_{01}}

.

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, \S 5.2.3.

Examples

mcnby_ni_pp(72,0.05,4,5)