gofhwex: Critical constants of the exact UMPU test for approximate...

In EQUIVNONINF: Testing for Equivalence and Noninferiority

Description

The function computes the critical constants defining the uniformly most powerful unbiased test for equivalence of the population distribution of the three genotypes distinguishable in terms of a single nucleotide polymorphism (SNP), to a distribution being in Hardy-Weinberg equilibrium (HWE).
The test is conditional on the total count S of alleles of the kind of interest, and the parameter θ, in terms of which equivalence shall be established, is defined by θ = \frac{π_2^2}{π_1(1-π_1-π_2)}, with π_1 and π_2 denoting the population frequence of homozygotes of the 1st kind and heterozygotes, respectively.

Usage

gofhwex(alpha,n,s,del1,del2) 

Arguments

alpha	significance level
n	number of genotyped individuals
s	observed count of alleles of the kind of interest
del1	absolute value of the lower equivalence limit to θ/4 - 1
del2	upper equivalence limit to θ/4 - 1

Value

alpha	significance level
n	number of genotyped individuals
s	observed count of alleles of the kind of interest
del1	absolute value of the lower equivalence limit to θ/4 - 1
del2	upper equivalence limit to θ/4 - 1
C1	left-hand limit of the critical interval for the observed number X_2 of heterozygotes
C2	right-hand limit of the critical interval for the observed number X_2
GAM1	probability of rejecting the null hypothesis when it turns out that X_2=C_1
GAM2	probability of rejecting the null hypothesis for X_2=C_2

Author(s)

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

References

Wellek S: Tests for establishing compatibility of an observed genotype distribution with Hardy-Weinberg equilibrium in the case of a biallelic locus. Biometrics 60 (2004), 694-703.

Goddard KAB, Ziegler A, Wellek S: Adapting the logical basis of tests for Hardy-Weinberg equilibrium to the real needs of association studies in human and medical genetics. Genetic Epidemiology 33 (2009), 569-580.

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 9.4.2.

Examples

gofhwex(0.05,475,429,1-1/1.96,0.96)

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