After realizing that it is almost impossible for me to maintain a bibliography on complex diseases- the topic is too broad - I rescale my plan to this simple page with a few summaries.
What is a complex disease? Here is a simple answer: complex diseases are any genetic diseases which do not obey the single-gene dominant or single-gene recessive Mendelian law. The term complex traits is also used for phenotypes that may not be considered as diseases. What are more complicated answers? Well, these definitions basically exclude cases when the causes of the non-Mendelianness are trivial. But what causes are "trivial" and what are not is a whole discussion by itself!
Reduced penetrance: nearly Mendelian. Since this cause of the violation of Mendelianness is so obvious, let me list it separately. Reduced penetrance is when there is a small deviation from the dominant (the penetrance, i.e., the probabilities of being affected when the genotype is normal homozygote, mutant heterozygote, and mutant homozygote, (f0, f1, f2), is (0,1,1) ) and the recessive (the penetrance is (0,0,1)). For an example of the reduced penetrance: (f0, f1, f2)= (0, 0.2, 0.9).
This is a description of the meeting session, "Molecular basis of reduced penetrance", in this year annual meeting of American Society of Human Genetics (Oct 1998): "A primary feature of most disease traits is the absence of clinical disease in individuals harboring a mutant genotype, that is, reduction in penetrance. For common, complex traits all three possible genotypes at a susceptibility locus (mutant homozygote, mutant heterozygote, wild-type homozygote) can lead to affection, albeit with different probabilities. Reduced penetrance can arise from stochastic (random) variation such as the genetic and epi-genetic changes seen in triplet-repeat diseases. More frequently, penetrance is reduced by the action of modifiers, or from the segregation of additional genes required for phenotypic expression. These genes frequently appear to belong to a common biochemical pathway. "
Defining the phenotype: is it one disease or a collection of several diseases? Another reason that a disease or a trait does not follow the Mendelian law is that the definition of being affected can be too broad that it is actually a collection of several diseases. Many psychiatric disorders, in particular, could be hard to diagnose unambiguously.
Locus heterogeneity: can the disease be caused by either one of the abnormal genes? Suppose two gene products are involved in a biochemical pathway. The first is made from the gene on chromosome 1, and the second from chromosome 7. The disruption of either one can cause the disease. Among the families collected, some are due to the defect of the first gene product, and some are due to the second. Once these families are separated, the disease appears as Mendelian with a linkage signal at either chromosome 1 or 7. But when these families are mixed, it appears to be "complex".
Gene-gene interactions. One can imagine a situation where the gene products from two genes interactively create an effect. For example, two proteins form a functional dimer complex; The binding of two transcription factors at the promoter initiates an action of transcription; two proteins participate the same biochemical pathway, etc. Due to this large number of possibilities, it is not clear which gene-gene interaction model should be considered. Even for the simplest two-gene (two-locus) interactions with binary states (gene is on and off) and binary outcome (the person is affected and unaffected), the number of possibilities is 51 (Li, "A complete listing and classification of two-locus two-allele fully-penetrant disease models" , Am J Human Genetics, supp. 61(4), A204 (1997)). What we hope for is that many models are not realistic, and/or remaining models can be further reduced to a fewer number of model clusters.
Gene-environment interaction . This part is even more vague and is usually mentioned in a hand-waving way. For some diseases, it is known what the environmental factors are. Take obesity for example, the environmental factor is is the food intake. For many other complex diseases, such as mental illness, we have the slightest idea what these environmental factors are. If the relevant environmental factors are identified, and measure for each person, the analysis shouldn't be difficult.
Analysis of complex traits: (family) allele-sharing methods : In the
simplest scenario, one collects sibs who are affected with a complex
disease, and determine the identical-by-descent (IBD) status at each
genetic marker. Such IBD status can either be on the markers inherited
from one parent (allelic IBD) or from both parents (genotypic IBD).
Allelic IBD can either be 0 or 1. Genotypic IBD can be 0, 1, or 2.
The IBD from different sib pairs are added together (actually,
it may not be a good idea to simply add!! but it is too complicated to
discuss it here). It is a common practice nowadays to look at this
averaged IBD proportion as a function of the marker location, and
identify "interesting" regions by those with the highest IBD proportions.
One might see that if the genotypic IBD is used, this method tends
to identity regions which contribute to the complex disease "recessively"
(two copies of the mutants are required). In some sense, although no
disease model is assumed, using genotypic IBD is more appropriate for
recessive diseases when there is little interaction among disease genes.
[ A bibliography on allele-sharing linkage methods ]
Analysis of complex traits: (population, family) association :
Let me refer to this new review paper: Terwilliger, "Linkage disequilibrium
mapping and complex disease: fantasy or reality?",
Current Opinion in Biotechnology, to appear (1998).
[ A bibliography on association studies ]
Summary: if we know in what sense a complex disease is "complex", we might consequently find a strategy to deal with it. On the other hand, if we know nothing about a complex disease, have no idea, guess, hypothesis, assumption on the inheritance mode, it is not clear whether a magical universal analysis tool can help you. This month's (October, 1998) American Journal of Human Genetics carries a few review articles on statistical genetics, which should be of interests to the complex diseases field: