mcnby_ni_pp {EQUIVNONINF} R Documentation

## 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: δ > -δ_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_{δ_0}^{(1+δ_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 <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_pp(72,0.05,4,5)


[Package EQUIVNONINF version 1.0.2 Index]