Features of complex genetic diseases showing HLA associations, such as incomplete penetrance, multiple disease-predisposing loci both within and outside the HLA region, heterogeneity, and interaction effects, make determination of their genetic basis more difficult than for traits showing classic monogenic Mendelian inheritance. Nonetheless, the direct involvement of HLA class II, and in some cases class I, genes in the disease process has been well documented for a number of complex diseases. Many of these diseases are of autoimmune origin, but cancers, infectious, and other diseases are also included. The issue of contributions to these diseases by other HLA region genes has been of interest for a number of years. Many reports of other associations within the HLA region have appeared in the literature. However, in many of these studies it has been difficult to determine whether an additional HLA region gene is involved in disease, versus the association's reflecting linkage disequilibrium (LD) with the peptide-presenting HLA molecules directly involved in disease.

A number of analytic strategies have been developed to remove the effects of LD with the peptide-presenting HLA genes directly involved in the disease. These include matched genotype strategies [1], and for family-based data the homozygous parent transmission disequilibrium test (HPTDT) [2] and the homozygous parent linkage test (HPLT) for affected sib pairs [3]. These three approaches only use a subset of the patient and control data. The haplotype method (henceforth referred to as the conditional haplotype method (CHM)) [4–6] and the conditional extended TDT (CETDT) [7, 8] use more of the data, but haplotypes need to be estimated. The logic of the CHM starts with the assumption that all HLA genes directly involved in disease susceptibility have been identified, e.g., HLA DR in RA. We then examine the relative frequencies of alleles at marker loci (e.g., single-nucleotide polymorphisms (SNPs), microsatellite markers, or other classical HLA loci) located on specific haplotypes stratified (to remove the effects of LD) by HLA DR in the case of RA, e.g., the high risk DRB1*0401 allele. Under the null hypothesis, the relative frequencies of the marker alleles on these stratified haplotypes should be the same in cases and controls. While fit to these expectations does not exclude the possibility that other genes in the HLA complex are involved in disease, lack of fit unequivocally shows that all disease-predisposing genes in the region have not been identified (provided that population stratification effects, for example, have not produced spurious results). The CHM tests for effects on individual haplotypes at the primary disease predisposing locus. Thomson [9] extended the CHM approach with development of a method to test for additional genetic effects over all haplotypes, henceforth referred to as the overall conditional haplotype method (OCHM). One advantage of the CHM, OCHM, and CETDT is that more of the data is used than with the matched genotype approach and the HPTDT and HPLT methods. However, care must be taken in all analyses and their interpretations with rare haplotypes and sparse cells.

Our aim in this study is to present a conditional genotype approach that tests for the presence of additional disease genes in a genetic region while accounting for LD with a primary disease gene. In the conditional genotype method (CGM), marker genotype frequencies are compared between cases and controls (AFBACs (affected family-based controls) in the case of family data [10, 11]). Our concentration in this paper is on the overall conditional genotype method (OCGM) in which genotype frequencies at marker loci are considered over all genotypes at the primary disease locus (in fact only all common genotypes are considered). We have developed an appropriate test statistic and applied this method to the Genetic Analysis Workshop 15 (GAW15) Problem 3 data (with answers known).

We have developed a simple but powerful approach using genotypes (the conditional genotype method (CGM) and overall conditional genotype method (OCGM) method) to detect association of a secondary locus in LD with a major disease locus that is model free and does not require estimation of haplotype frequencies. Even with strong LD as seen with the DR and C loci in this data set, we were able to detect the effect of the C locus after allowing for the effect of the primary DR locus. This was possible even though D' = 1 for these two loci, as both alleles C and c occur with allele DRX. In this case DRX refers to all alleles that are not DR4 and not DR1, namely, allele 1 of the simulation for the DR locus. The allele frequencies of these two haplotypes were 0.15 and 0.50, respectively. This allowed discrimination between risk effects of the genotypes comprising these two haplotypes, and hence detection of the C locus effect once the primary effect of the DR locus was taken into account. The only situation in which the CGM and OCGM, as well as other methods, would not be useful is when there is an absolute 100% correlation between all alleles at both loci. In such cases, cross ethnic studies may be useful in that the LD pattern may differ and not show 100% correlation.

One could also take the observed (obs) and expected (exp) fp(B _h B _k ) values from Eq. 3 and consider the observed and expected allele frequencies at the B locus under the null; obtained simply by the method of allele (gene) counting. In effect, this is the same as the overall conditional haplotype method (OCHM) [9] but the genotype approach obviates the need to estimate LD values in controls between the A and B genes as proposed in its initial implementation. Another difference is that whereas the genotype-based implementation uses ratios of A locus genotype frequencies in patients versus controls, the haplotype-based implementation as originally proposed uses allele frequencies. The effect of this on type I and type II errors is not known and further work would be required to determine the appropriate test statistic for the OCHM or a resampling approach could be applied. Thus, we have shown theoretically how allele frequency data can also be tested without resorting to estimation of haplotype frequencies using the OCHM. The OCHM has not been applied in this current research.

Our theory, applied to GAW15 Problem 3 data, and power analyses of the OCGM, as well as discussion of the CGM, CHM, and OCHM, show the utility of all these approaches for detecting additional disease genes in LD with a primary disease gene in a genetic region. Additionally, all of these methods are useful in detecting primary disease-predisposing genes in a region if they are not known. Also, they can be used in across-genome studies to detect the effects of other disease genes that have risk effects that are not strictly multiplicative with a primary disease gene under study, and hence the effects may be easier to detect in samples stratified by the genotypes of the primary disease gene.