All participants in the study were ascertained through the ongoing Canadian Collaborative Project on the Genetic Susceptibility to MS (CCPGSMS), for which the methodology has been previously described 21.

Total genomic DNA, extracted from whole blood as part of the CCPGSMS, was used to type HLA-DRB1 alleles by an allele-specific PCR amplification method 22. All genotypes were generated blind to pedigree structure and disease status of the individual. Initially, HLA-DRB1 alleles were classified into 10 categories, HLA-DRB1*01 to HLA-DRB1*10. Four of them were then subdivided, *05 into *11/12, *06 into *13/14, *02 into *15/16, and *03 into *17/18. Since then, these "two-digit" genotypes have been refined by adding two or four more digits. The first two digits describe the type, which corresponds to the serological antigen carried by an allelotype. The third and fourth digits are used to list the allele subtypes, numbers being assigned in the order in which the DNA sequences were determined. Alleles whose numbers differ in the first four digits must differ in one or more nucleotide substitutions that change the amino acid sequence of the encoded protein. Alleles that differ only by synonymous nucleotide substitutions within the coding sequence are distinguished by the use of the fifth and sixth digits.

In our population, 24 PCRs were carried out to amplify allelotypes corresponding to alleles HLA-DRB1*01, HLA-DRB1*04, HLA-DRB1*07, HLA-DRB1*08, HLA-DRB1*09, HLA-DRB1*10, HLA-DRB1*11, HLA-DRB1*12, HLA-DRB1*13, HLA-DRB1*14, HLA-DRB1*15, HLA-DRB1*16, HLA-DRB1*17, and HLA-DRB1*18. Each HLA-DRB1 genotype was scored twice by independent observers.

For terrestrial life forms, the number of alleles per single nucleotide polymorphism (SNP) is limited to five: A, C, G, T, and X (deletion), although only two alleles have been seen for most human SNPs. For HLA-DRB1 and HLA-DRB2 SNPs, however, up to 4 and 5 nucleotides, respectively, have been observed. As proven in 24, the informative data for each bi-allelic parental mating type (PMT) can be organized into three strata, with two informative filial constellations each:

Mating            Offspring Genotypes

   A.A~A.C         A.A   A.C

   A.C~A.C         A.A   C.C (A.C children are non-informative)

   A.C~C.C         A.C   C.C

   ...

   T.T~T.X         T.T   T.X

   T.X~T.X         T.T   X.X (T.X children are non-informative)

   T.X~X.X         T.X   X.X

With three alleles, only two constellations need to be considered:

Mating            Offspring Genotypes

   A.A~C.G         A.C      A.G

   A.C~A.G         A.A   A.C   A.G   C.G

   ...

   X.X~T.G         G.X      T.X

   X.G~X.T         G.T   G.X   T.X   X.X

With four or five alleles, each stratum contains four informative filial genotypes, e.g.:

Mating            Offspring Genotypes

   A.C~G.T         A.G,   A.T   C.G   C.T

To determine, whether a particular allele confers risk, children with this allele need to be 'paired' within the same PMT stratum with children having the same other allele. For bi-allelic PMTs, this leaves three informative mating types per combination of alleles, each with two informative filial genotypes 24. For tri-allelic PMTs, two situations may arise. One homozygous parent, also yields only two filial genotypes, while two heterozygous parents, yield strata with four filial genotypes. For quad-allelic PMTs, both parents are necessarily heterozygous yielding, again, four possible filial genotypes.

After excluding non-informative children, all filial genotypes within a PMT stratum have the same expectation under the null hypothesis. Thus, for the special case of bi-allelic parents, it has been suggested 25 that the sign/McNemar test for exact ties be applied 26, i.e. to count how often either of the genes were transmitted, irrespective of the PMT. Stratification 24 yields a test statistic based on counts representing independently observed events (cases born, rather than alleles transmitted, which are subject to identical genetical and environmental confounders). Here, the need for stratification is even more apparent than for bi-allelic parents 272829, as there are, for instance, twice as many A alleles to be expected among the children of A.C~A.G parents than either C or G alleles.

When developing a test suitable for multi-allelic loci, it is useful to note that the sign test can be written in the two equivalent forms given at the ends of the following equation:

( a − b ) 2 a + b = 4 ( a 2 − b 2 ) 2 a + b = 2 ( a − a + b 2 ) 2 a + b 2 = ( a − a + b 2 ) 2 a + b 2 + ( b − a + b 2 ) 2 a + b 2 = ( a − a + b 2 ) 2 1 2 a + b 2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@855A@

As (a−b)/a+b~as.χ12 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaWaaSGbaeaadaqadaqaaiabdggaHjabgkHiTiabdkgaIbGaayjkaiaawMcaaaqaamaakaaabaGaemyyaeMaey4kaSIaemOyaigaleqaaaaakiabc6ha+naaBaaaleaacqWGHbqycqWGZbWCcqGGUaGlaeqaaOGaeq4Xdm2aa0baaSqaaiabigdaXaqaaiabikdaYaaaaaa@3DB6@ and the "standardized residuals" (a−a+b2)/12a+b2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSGbaeaadaqadaqaaiabdggaHjabgkHiTmaaleaabaGaemyyaeMaey4kaSIaemOyaigabaGaeGOmaidaaaGaayjkaiaawMcaaaqaamaakaaabaWaaSqaaeaacqaIXaqmaeaacqaIYaGmaaWaaSqaaeaacqWGHbqycqGHRaWkcqWGIbGyaeaacqaIYaGmaaaabeaaaaaaaa@3B37@ and (b−a+b2)/12a+b2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSGbaeaadaqadaqaaiabdkgaIjabgkHiTmaaleaabaGaemyyaeMaey4kaSIaemOyaigabaGaeGOmaidaaaGaayjkaiaawMcaaaqaamaakaaabaWaaSqaaeaacqaIXaqmaeaacqaIYaGmaaWaaSqaaeaacqWGHbqycqGHRaWkcqWGIbGyaeaacqaIYaGmaaaabeaaaaaaaa@3B39@ are symmetric, each follows asymptotically a standard Gaussian distribution, allowing the contributions from different PMT strata to be combined in an additive fashion.

To test the effect of allele A, for instance, the following strata are informative:

Mating      Informative Offspring Genotypes

A.A~A.x:

A.x~A.x:

A.x~x.x:

A.x~y.y:

A.x~A.y:

A.x~x.y:

A.y~x.y:

A.x~y.z:

The informative children A.A in the A.x~A.x and A.x~A.y strata differ from the 'non-A' (x.x or x.y) counterparts by two alleles. As in 24, this will be accounted for by assigning twice the weight to these strata, rather than assuming that the effects of the two alleles transmitted to the same child are independently observed.

With more than two alleles, several comparisons could be made within the A.x~A.y stratum, e.g.,

Mating      Informative Offspring Genotypes

A.x~A.y:

A.x~A.y:

In both cases, the term to the left (A.A or A.x/A.y) would have more A alleles than the corresponding term on the right (A.x/A.y or x.y, respectively). Averaging across these comparisons yields the same term (A.x+A.y)/2 on both sides which, as the heterozygous children born to two heterozygous children in the biallelic case, can be ignored, resolving this seeming ambiguity. Again, stratification is essential for developing a sound statistical approach to deal with this complex situation.

From column card in Figure 1, the maximum number of informative strata for the influence of a given allele is 3 × 4 + 3 × 12 + 6 = 54 out of the 105. Of course, if a particular PMT is not observed, the corresponding strata need not be included. Column w gives the weight to be applied to this stratum's contribution based on the number of alleles differing.

This stratification now allows for different degrees of 'dominance' to be considered. An allele is "dominant" or "recessive", if having a single copy confers the same risk as having two copies or no copy, respectively.

When both parents are heterozygous for the allele of interest, only those children are counted where both alleles are equal to or different from the allele of interest (n* = n_{A. A} + n_¬A.¬A). Thus, among these strata, the effective sample size depends on the allele considered.

Using the results of 30, the strata's contributions can be combined into an allele-specific test statistic by forming a single test statistic from the sum of the effect estimates and their variances, respectively, e.g.,

T A = ∑ x ≠ y ≠ z ∈ { C,G,T,X } ∑ P M T ∈ P M T ( A ) w P M T ( n A + | P M T − n A − | P M T ) ∑ x ≠ y ≠ z ∈ { C,G,T,X } ∑ P M T ∈ P M T ( A ) w P M T 2 ( n A + | P M T + n A − | P M T ) ~ a s . N ( 0 , 1 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@B07D@

where x is the subset of the 54 PMTs informative (relevant and not empty) for nucleotide A, while nA+|PMT MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemOBa42aiajqBaaaleacqcKamajqbgeabnacqcehaaadbKaKafacqcKamajqgUcaRaaaliadqcKG8baFcWaKaniuaaLamajqd2eanjadqc0Gubavaeqcqceaaaa@3EA7@ and nA−|PMT MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemOBa42aaSbaaSqaaiabdgeabnaaCaaameqabaGaeyOeI0caaSGaeiiFaWNaemiuaaLaemyta0Kaemivaqfabeaaaaa@3494@ states the number of subjects with a preponderance of A or non-A alleles, respectively within the stratum indicated (i.e., n_{A. A}, n_{A. x}, or n_A.+, see above).

From the above, nucleotide-specific test statistics can be obtained by performing the following steps:

1) Select the PMTs where at least one parent is heterozygous for the nucleotide considered (Figure 1).

2) Among the strata where both parents are heterozygous for the nucleotide considered, eliminate the counts of children that are also heterozygous for this nucleotide.

3) By number of parental copies of the nucleotide of interest (1, 2, or 3), count the number of children with more (1 or 2) vs the number of children with less (0 or 1, respectively) alleles of this nucleotide.

4) Perform the stratified McNemar test 24 based on these six numbers and the weights assigned to each of the three categories of strata according to the degree of dominance to be considered (Figure 1).

Statistical analyses were done using S-PLUS 8.0 http://www.insightful.com and the muStat library (available from http://csan.insightful and http://cran.r-project.org). Surface and cartoon representations were produced using PyMOL http://www.pymol.org. The program VOLUMES (R. Esnouf., unpublished data) was used with a 1.4 Å radius probe to map the extent of the P4 pocket cavity.