In its usual form, the multifactorial model of disease transmission assumes that the liabilities to disease have a multivariate normal distribution. This paper studies how sensitive to this assumption are the quantitative results from the model. Accordingly, bounds are established for the probability of a child having a disease, given that both parents have it and taking the heritability of the disease to be known. Unfortunately, these bounds turn out to be wide. For example, a probability that is 0.38 under the trivariate normal model may be as low as 0.12 or as high as 0.78 under other trivariate models, even if attention is restricted to those of variables-in-common form. The broader statistical issue of the meaning of trivariate dependence, as distinct from bivariate dependence, is also discussed.

Affected sib pairs with typed but unaffected parents, conveniently termed foursomes, have become a major source of information on genetic susceptibility to common disease. So far most methods of analysis have been based on extensions of the single locus analyses developed, and successfully applied, to the mendelian disorders. However, unifactorial methods are not suited to multifactorial disorders. The power of methods of detecting linkage in the presence of more than one locus with one or more susceptibility alleles is considered.

The relevance of familial clustering to predicting the presence of loci with susceptibility or resistance alleles sufficiently frequent and effective to have an appreciable influence on population incidence is discussed. The mathematical problem of clustering due to numerous alleles of small effect was resolved by Pearson in 1901 in relation to claims that the mendelian model of an allele at a single locus determining a distinct phenotype was necessary to explain the familial concentrations that had been observed in several species. The apparent inconsistency between the mendelian and polygenic models was resolved by Fisher's demonstration in 1918 that there was no essential difference between these two extreme forms of phenotypic determination. Although constant penetrance models are unrealistic, and no longer necessary since Pearson's analysis, the assumption is implicit in most recent analyses and has the advantage of simplicity in providing a lower limit on the sample sizes necessary.

The transcription map of the human genome published by Schuler et al. (1996) is a valuable resource in which approximately one quarter of all human genes have been mapped with respect to genetic framework markers using radiation hybrids. We have taken information from this map to provide potential genes within the TSC1 candidate region on chromosome 9q34. In so doing we have been able to provide an independent assay of the quality of the radiation hybrid mapping by using somatic cell hybrids and a 2 Mb cosmid contig covering the TSC1 region as mapping tools. In addition, we have built sequence contigs of ESTs for 25 clusters. This has shown that about 20% of the relevant EST clusters in the Unigene resource (Boguski & Schuler 1995) contain chimaeric clones.

Complex segregation analysis was conducted in a series of patients with hereditary non-polyposis colorectal cancer (HNPCC) ascertained through probands registered in the Cancer Registry of the Health Care District of Modena, Northern Italy. Altogether there were 125 nuclear families segregating for HNPCC, for a total of 672 individuals. The analysis favoured a two-locus model, with both susceptibility genes rare and dominant. The gene frequency of the deleterious allele at the major locus is estimated to be low qm=0·004 and for the second locus the estimate is even lower q=0·00003. Both genes defining the two-locus model seem to be highly penetrant. The lifetime penetrance of the abnormal gene at the major locus is estimated to be 0·73 for female, while the estimation for male is higher, 0·85.

A non-linear time series version of a model for the transmission of fragile X previously described in Ashley & Sherman (1995) is developed. The model retains the biological features of the Ashley/Sherman model but is easier to generalize and in particular allows the inclusion of covariates such as haplotype to model different paths and random effects to model family effects. The model is fitted to data from Murray et al. (1997) and its properties are illustrated in a simulation study.

The sex chromosomes enable direct determination of haplotypes, and the analysis of 8 microsatellite markers from the FRAX region on Xq27-q28 contributes 7219 independent haplotypes from our study in Wessex. Allelic association increases with frequency of alleles, and is less for trinucleotide than dinucleotide repeats. The estimate of ε, the exponential decline of association with distance in kb, is 0.0023. The swept radius 1/ε estimates the distance at which disequilibrium falls to e−1 ≈ .37 of its initial value. The current study estimates the swept radius of association to be 433 kb, which is surprisingly close to estimates for SNPs, and suggests that a marker density of 1/100 kb should be powerful in regions such as FRAX. An explanation for these results is offered, and some speculations made about what will be found when SNPs are subjected to an equally intensive study in multiple regions.

Loss of heterozygosity (LOH) analysis in B-cell chronic lymphocytic leukemia (BCLL) has indicated that a frequent genetic event is loss of alleles from an approximately 500 kb region in 13q14.3, distal to the retinoblastoma gene. We have used DNA markers from this region to isolate and characterize a series of bacterial artificial chromosomes (BACs) which span the region between markers D13S319 and D13S25, which represents the common region of LOH. This entire region appears to be contained within only two minimally overlapping BACs, representing a maximum distance of approximately 350 kb. This BAC contig has been used to position known STS, EST and gene markers within the region. We have also used a modified differential display/RNA fingerprinting procedure designed to isolated transcribed sequences from YACs to isolate two transcribed units from the region which have also been positioned within the contig. The construction of a BAC contig with minimal redundancy provides the ideal resource from which to begin to identify candidate genes related to BCLL.

Ann. Hum. Genet. (1997), 61, 319–333

Correction and additional citation

The author has noticed two errors he failed to correct in this paper, as follows:

(i) Page 329: ‘Thus if the case has genotype AA and the control is BC one adds 0.5 to TAB and 0.5 to TAC’ should read ‘Thus if the case has genotype AD and the control is BC one adds 0.5 to each of TAB, TAC, TDB and TDC.’

(ii) Table 3, first ‘Score’ line: ‘0.25tAB, 0.5tAC, 0.5tCB’ should read ‘0.5tAB, 0.5tAC, 0.5tCB.’

Since the paper was published the author has learned that the use of siblings as controls was proposed by L. S. Penrose, and a method of analysis devised by C. A. B. Smith, for application to studies of blood groups and duodenal ulcer (Clarke et al. 1956). The author is grateful to C. A. Clarke for making him aware of this previous work.

Clarke, C. A., Wyn Edwards, J., Haddock, D. R. W., Howel-Evans, A. W., McConnell, R. B. & Sheppard, P. M. ABO blood groups and secretor character in duodenal ulcer. Br. Med. J. (1956), 725–731.