1. http://www.meb.ki.se/genestat/tl/genass_ldmap/index.htm (from Institutionen for Medicinsk Epidemiologi och Biostatistik, SWEDEN).
2. David Clayton's lecture slides: http://www-gene.cimr.cam.ac.uk/clayton/talks/ (advanced topics)
3. powerpoint slides by D. Altschuler (if you couldn't see PowerPoint, here is the PDF file)
4. a one-seminar class on association study at Simon-Fraser University: http://www.stat.sfu.ca/~jgraham/Teaching/S890_04/ (though not much material made available online)
5. A few HELP pages from Manchester University: http://slack.ser.man.ac.uk/theory/association.html (the more general "genetic analysis" page is at http://slack.ser.man.ac.uk/)
6. Terwilliger/Weiss' course on "logical reasoning in human genetics": http://www.genomeutwin.org/events/CR_GSTAT_19230904_HKI.html

• 1921
  1. W Alexander (1921), "", British Journal of Exprimental Pathology, 2:66
  2. JA Buchanan, ET Higley (1921) "The relationship of blood groups to disease", British Journal of Experimental Pathology 2:247-255.
• blood type - disease association
  1. Ronald Fisher set up a blood-grouping lab at Galton Laboratory in 1935. [to test ideas in population genetics, not on diseases]
  2. EB Ford of Oxford suggested a search for association between ABO and secretor polymorphisms and diseases in 1945: "Polymorphism", Biological Reviews, 20:73-88.
  3. Ian Aird, HH Bentall, JA Fraser-Roberts (1953), "A relationship between cancer of stomach and the ABO blood groups", British Medical Journal, 1:799-801.
  4. I Aird, HH Bentall, JA Mehigan, JAF Roberts (1954), "The blood groups in relation to peptic ulceratiuon and carcinoma of the colon, rectum, breast and bronchus: an association between the ABO groups and peptic ulceration", British Medical Journal, 2:315-321.
• HLA - disease association
  • JL Amiel (1967), "Study of the leukocyte phenotypes in Hodkin's disease", in Histocompatibility Testing 1967, eds. ES Curtoni, PL Mattiuz, RM Tosi (Munksgaard, Copenhagen), pp.79-81.
• "linkage disequilibrium" between two chromosome locations
  • a population genetic topic
• "modern time: disease-marker association for non-HLA markers
  • 1984 Genetic Analysis Workshop 2 on "methods for detecting and interpreting disease-marker associations and linkage" (GAW homepage: http://www.gaworkshop.org/ )
  • 1987 Falk and Rubinstein's family-based association: CT Falk, P Rubinstein (1987) "Haplotype relative risk: an easy way to construct a proper control sample for risk calculations", Annals of Human Genetics, 51:227-233.
  • 90s use of isolated population for linkage disequilibrium mapping
  • several extension of Falk and Rubinstein's idea: Ott (1990), Ott and Terwilliger (1992), "TDT" (1993)
  • 1996 Risch and Merikangas' paper to compare affected-sib-pair design (non-parametric linkage) to parents-affected-child design (TDT): N Risch, K Merikangas (1996), "The future of genetic studies of complex human diseases", Science, 273:1516-1517. [see Risch's account of this paper: PDF]
• current trends
  • use of the dense SNP markers instead of microsatellite markers
  • use of population sample design (case-control) instead of pedigree designs
  • determine the genome wide linkage disequilibrium pattern in human genome. HAPMAP project homepage: http://www.hapmap.org/
• a comprehensive bibliography http://www.nslij-genetics.org/ld/

• data collection: roughly equal number of people with the diseases ("cases") and people without the disease ("controls")
• genotyping each person to determine its genotype (there are only three possibilities: aa, aA, AA)
• count the number of case samples with each type of genotype, same thing for control samples:

1. testing Hardy-Weinberger equilibrium for both the control and the case group (especially the control group). For example, using the program FINETTI: http://ihg.gsf.de/cgi-bin/hw/hwa1.pl
   [COMMENTS: control group should follow H-W equilibrium, but for the case group, if the marker is indeed close to the disease gene, it may not obey H-W equilibrium. ]
2. At least two ways to construct a 2-by-2 table for statistical tests:
   1. allele a versus allele A

      	allele "a"	allele "A"
      case	210	1790
      control	106	1900

      [COMMENTS: this 2-by-2 table effectively doubles the sample size (the number of alleles is twice the number of persons). and it is "cheating". see: PD Sasieni (1997), "From genotypes to genes: doubling the sample size", Biometrics, 53:1253-1261. PDF ]
   2. either combining aa and aA as one columne (dominant model), or, combining aA and AA as one column (recessive model):

      	aa+aA	AA			aa	aA+AA
      case	200	800		case	10	990
      control	103	900		control	3	1000

      [COMMENTS: since we do not know which 2-by-2 table should be used, we should test both. then there is a "multi-testing" issue here. ]
3. Pearson's chi-square test (if you are not familiar with this topic, see any of the following pages: http://www.psychstat.smsu.edu/introbook/sbk28m.htm,
   http://www.answers.com/topic/pearson-s-chi-square-test,
   http://faculty.vassar.edu/lowry/tab2x2.html,
   and many many more).

   p-value=9.1 x 10^-10 (allele 2-by-2 table) (or 1.3 x 10^-9 if Yates' correction is used)
   p-value=1.2 x 10^-9 (genotype, recessive) (or, 1.8 x 10^-9 if Yates' correction is used)
   p-value= 0.051 (genotype, dominant) (or 0.094 if Yates' correction is used)
   min(p-value(rec), p-value(dom))= 1.2 x 10^-9

   [COMMENTS: an alternative to Pearson's chi-square test is the Fisher's exact test -- more accurate for smaller sample sizes. ]

4. Odd ratio and 95% confidence interbal of odd ratio: "odd" is the ratio of the number people who possess the "risk" (e.g. allele "a") over the number of people who do not contain the "risk". "odd ratio" (OR) is the ratio of two such ratios, one for the case group, another for the control group.

   for the three 2-by-2 tables:
   OR = (210/1790)/( 106/1900)= 2.10
   OR = (200/800)/( 103/900)= 2.18
   OR = (10/990)/( 3/1000)= 3.47

   [COMMENTS: Odd ratio is an approximation of "relative risk", defined as Prob(affected|risk)/Prob(normal|risk). but due to the case-control sample collection design, the relative risk can never be calculated exactly. ]

   OR value itself is not enough, we need to know the range of OR's (confidence interval). here is a R/SPLUS script for this calculation. This formula is due to: B Woolf (1955), "On estimating the relation between blood and disease", Annals of Human Genetics, 19:251-253. For the above three 2-by-2 tables:

   95%CI: (1.65, 2.68)
   95%CI: (1.69, 2.82)
   95%CI: (0.92, 12.27)
   [COMMENTS: when one bound is smaller than 1 and another larger than 1, the result is not significant at p-value=0.05. ]

1. If we know which gene is responsible for the disease and if we can "see" the gene, know whether it contains mutation or not, the association analysis is direct. However, the marker we examine may not have a one-to-one correspondence with the mutation status at the disease gene. It has a distance between the disease gene and the linkage disequilibrium may not be complete. The marker is typed in terms of genotype, and "phase" is usually unknown.

2. What we consider a homogeneous group of people from which the control samples are collected may not be homogeneous after all. Same for the case sample population. How do we deal with heterogeneity?