Linkage analysis

The standard method of carrying out linkage analysis in humans is the lod score approach devised by Morton. (12) Essentially, for a given set of data, lod scores are calculated over a range of values of q between 0 and 0.5. Where the lod score reaches a maximum, provides the best (or maximum likelihood) estimate of q. The lod score is so called because it is the common log of the odds that q has a certain value q' rather than a value of 0.5, i.e.

By convention, a lod of 3 or more is accepted indicating that linkage has been detected, while a lod of -2 or less indicates that linkage can be excluded at that particular value of q. A lod of 3 corresponds to odds on linkage of 1000 : 1 and to a nominal P value of 0.0001. This therefore seems at first sight to be a very stringent criterion. However, linkage between two loci taken at random is inherently unlikely (13) and Morton's(!2) original argument took into account the low prior probability of linkage to arrive at a criterion that gave a posterior probability, or reliability, of 95 per cent. More recently workers have been concerned about the effects of carrying out many statistical tests in a genome-wide search for linkage and have sought to set an appropriate level of lod score to compensate for this. In fact, as it turns out, the original suggestion of a lod of about 3 is close to recent calculations of what lod is required to conclude in favour of genome-wide significance.(1J

As originally devised, the lod method deals purely with regular Mendelian traits. However, it can be readily adapted for detection of single genes that have incomplete penetrance by applying the general single major locus model discussed earlier. The main drawback is that the model (as specified by the penetrance values, and less critically the gene frequency) must be known accurately. Where the model is mis-specified there is a high risk that linkage will fail to be detected. (16)

A further difficulty is that diseases may show locus heterogeneity, i.e. there may be two or more different (and unlinked) loci where mutations result in similar phenotypes. There are many instances of this among rare Mendelian diseases. A good example is Usher's syndrome causing deafness and retinitis pigmentosa, which can result from mutations in any one of six different genesAD Subforms of common diseases can also show locus heterogeneity, the most relevant to psychiatry being early onset familial Alzheimer's disease where autosomal dominant forms can result from mutations in three different genes, called presenilin 1, presenilin 2, and amyloid precusor protein. Although methods exist for detecting linkage in the presence of heterogeneity ^l5) these have not so far in practice been of great help in psychiatric or other common disorders. Rather, the most frequent general strategy has been to focus on multiplex families (i.e. those containing multiple members with the disorder under study) and to make the following simplifying assumptions.

1. There are major gene subforms of the disorder in at least some families.

2. Although the mode of transmission is unknown, a reasonable guess at the defining parameters can be made.

3. Although there may be locus heterogeneity in the disorder as a whole, within any given family there is likely to be homogeneity.

This has worked very well for several disorders, including, as we have just mentioned, Alzheimer's disease, but has so far produced a rather confusing set of results from a large number of different centres for schizophrenia(!8,» and manic-depressive disorderA19 The most likely cause of this is that assumption 1 is incorrect and that subforms of these conditions resulting from major genes are very rare or perhaps non-existent. Consequently there has been a shift towards other methods of tackling linkage studies in psychiatry which do not rely on any assumptions about the mode of transmission. These concentrate on affected siblings or other pairs of relatives both affected by the disorder.

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