Proc. SD Rus. Acad. Sci. (biol.ser. ),1: 3-13 (1992)
ON DISTRIBUTION OF LINKAGE TEST .
Ginsburg E.Kh, Axenovich T.I.
Institut of Cytology and Genetics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090 Russia
The criterion of likelihood ratio l(Q, Â) is usually used when the linkage is tested in samples of pedigrees. The adequacy of the solution (null hypothesis H0 is rejected in favour of the alternative one H1 or vice versa), is the batter, the more exactly are known the two distributions (distributions of l(Q, Â) when H0 is true and when H1 is true). An exact determination of the l(Q, Â) distribution is usually impossible, and some approximations are used instead of it. If the alternative hypothesis is complex (H1: 0<= Q<0,5), the c2 distribution may be used in some situations. The problem of determination of the l(Q, Â) distribution for a simple alternative hypothesis H1 with a limited sample size, in particular, has not been sufficiently investigated. This paper suggests to approximate the l(Q, Â) distribution by the first four terms of Edgeworth's series. The accuracy of the approximation is illustrated with some genetic stochastical simulations. This approach may be useful when planning samples for the linkage analysis i. e.: to estimate the minimum number of pedigrees in the sample under the given errors of type I and type II, to estimate the criterion power given a definite sample size and type I error etc.
l(Q,Â) is natural log [Pr(Â|Q)/Pr(Â|Q=0.5)]
here Pr stays for probability, Q is "theta" -- recombinationb fraction and Â is pedigree data
c2 = chi-square