In their classic form, allelic association studies are more straightforward o carry out than linkage studies. A sample of cases affected by a disorder (or subjects who have scores higher than a given threshold on a quantitative measure) is compared with controls who do not have the disorder (or subject whose scores are near average). The frequency of alleles at the marker locus is then compared in the two groups. The significance of the difference can then be compared in the usual way for contingency table analysis using a c2 test (or Fisher's exact test if expected frequencies are small). In addition to significance it is useful to have a measure of the strength of association. A variety of statistics can provide this but probably the most useful and intuitively appealing is the relative risk, i.e. the proportion of cases among those carrying the marker allele or risk factor, P1, divided by the proportion of cases, P2, among those not carrying the factor. As we can calculate from T§bl§.3, RR = P1/P2 = (a/(a + b))/(c/(c + a)). If the disorder is uncommon, i.e. a and c are small relative to b and d, RR can be approximated by another, easier-to-obtain statistic, the odds ratio, OR = a * d/(b * c). If a positive marker disease association has been found the odds ratio will be significantly greater than 1.

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Table 3 Case-control allelic association

Before the current era of molecular genetics many association studies of disease with classical markers were carried out most notably with blood groups and with the HLA system. One of the earliest well-replicated findings was an association between blood group O and duodenal ulcer. The odds ratio was less than 2 in most studies and Edwards(23> pointed out that the proportion of variance in liability to the disorder explained by the association was only about 1 per cent. Even though later disease association studies on HLA, with other diseases such as type I diabetes and various auto immune disorders, were stronger, it has been pointed out that here too only a small proportion of variance is accounted for. Although this could in one respect be considered disappointing, it demonstrates that allelic association can detect small gene effects in polygenic or multifactorial traits and may therefore prove to be more useful than linkage.

How does allelic association arise and what does its detection tell us? There are three principal mechanisms of association. The first is linkage disequilibrium. Normally pairs of alleles at two different loci occur together no more often than would be expected by chance (i.e. they are in 'equilibrium'). In most cases this is the result of independent assortment. However, even if loci are linked they will usually approach equilibrium very rapidly with the proportion of associated alleles decreasing by 1 - q each generation. Only where the two loci are very close together does disequilibrium tend to persist. For example, where the distance is 1 cM corresponding to a recombination rate of one meiosis in 100, the time taken for an association to go half way to equilibrium is 69 generations. For a distance of 0.1 cM the time taken is 693 generations, or about 20 000 years. The second cause of association is when a polymorphism within a gene itself has a functional effect which results in susceptibility to a disease. The third, and in most cases least interesting, phenomenon is population stratification. This occurs where there has been recent admixture of populations or two or more ethnically distinct populations living side by side with little interbreeding. If the populations differ in terms of the frequency of alleles of the genetic markers and in the frequency of the disease being studied, marker disease associations can arise if there is not careful ethnic matching of patients and controls.

Another way of overcoming stratification is not to study unrelated cases and controls but to study families and derive the controls 'internally'. The most familiar method in current use is the transmission disequilibrium test.(24) This requires affected individuals to have at least one parent who is heterozygous at the test locus. The affecteds can therefore each receive one of two alleles from such parents. A 2 * 2 contingency table can then be constructed of whether a particular allele is the transmitted or the non-transmitted allele. This is illustrated in Table.,.! for a marker with two alleles, A1 and A2. The entries in each cell of the table, a, b, c, and d are counts of the number of parents transmitting or not transmitting each allele to their affected offspring. The significance of the transmission disequilibrium test is simply assessed by a McNemar c2 test.











Table 4 Transmission disequilibrium test: affected subjects with at least one parent heterozygous for allele A

Assuming that stratification can be overcome there are broadly two ways to proceed with association studies. The first is to concentrate on polymorphisms in or near candidate genes, i.e. genes that encode for proteins that are likely to be involved in the disorder. This has so far been the commonest type of association study in psychiatry as in most other common diseases, and there are some interesting early results relating to, for example, polymorphisms at the serotonin 5-HT 2a receptor in schizophrenia, the serotonin transporter in affective disorders, and the dopamine (DAT -,) transporter in attention-deficit-hyperactivity disorder. The second is to attempt a systematic search through a chromosomal region or, more ambitiously, the entire genome with the aim of detecting linkage disequilibrium. It follows from what we have discussed earlier that a genome-wide search for linkage disequilibrium has a particular attraction in the study of polygenic disorders in that it should be capable of detecting genes of small effect. The disadvantages are twofold. There are problems to do with multiple statistical testing and there are feasibility issues to do with the amount of genotyping necessary to scan the entire genome. This has led some authorities to conclude that systematic genome scans for genes involved in complex disorders are not practicable. (H)

Let us deal with the second problem first. It follows from our discussion of the mechanisms underlying association that it will require a very large number of markers to scan the entire genome. This is because linkage disequilibrium is usually only detectable over very short distances of a centimorgan or less. This means that thousands of evenly spaced markers will be needed. If we add to this the problem that small effects require large samples of subjects to provide adequate power of detection, the task becomes daunting. Let us suppose that we wish to test 3000 markers on 1000 subjects (500 patients and the same number of controls). This would mean 3 million genotypings—a huge amount of work. Fortunately two recent developments make this more achievable. DNA pooling methods (25) allow the initial screening to be carried out on combined samples such that all of the controls can be processed as one batch and all of the patients as the other. Positive findings can then be followed up by doing individual genotyping. This means that the initial screen involves 6000 rather than 3 million genotypings. The other innovative development in very high throughput genetic analysis involves hydridizing DNA to microarrays of hundreds of oligonucleotides bound to 'chips' which means that a very large number of biallelic single nucleotide polymorphisms can be tested for very rapidly.

The problem of multiple testing can be overcome either, as in the DNA pooling approach, by carrying out a two-stage analysis with fairly liberal test criteria in the first stage followed by stringent criteria in the second stage, or by simply setting a very stringent criterion at the beginning. It has recently been shown that, even with an alpha level set at 1 * 10-6, detection of linkage disequilibrium with genes of small effect is feasible with realistic sample sizes. (26) In short, the linkage disequilibrium mapping approach using either DNA pooling or single nucleotide polymorphisms on chips is likely to greatly advance the discovery of susceptibility loci and quantitative trait loci over the next few years.

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