title: A unifying theory for genetic epidemiological analysis of binary disease data.
abstract: BACKGROUND
  Genetic selection for host resistance offers a desirable complement to chemical treatment to control infectious disease in livestock. Quantitative genetics disease data frequently originate from field studies and are often binary. However, current methods to analyse binary disease data fail to take infection dynamics into account. Moreover, genetic analyses tend to focus on host susceptibility, ignoring potential variation in infectiousness, i.e. the ability of a host to transmit the infection. This stands in contrast to epidemiological studies, which reveal that variation in infectiousness plays an important role in the progression and severity of epidemics. In this study, we aim at filling this gap by deriving an expression for the probability of becoming infected that incorporates infection dynamics and is an explicit function of both host susceptibility and infectiousness. We then validate this expression according to epidemiological theory and by simulating epidemiological scenarios, and explore implications of integrating this expression into genetic analyses.
  
  
  RESULTS
  Our simulations show that the derived expression is valid for a range of stochastic genetic-epidemiological scenarios. In the particular case of variation in susceptibility only, the expression can be incorporated into conventional quantitative genetic analyses using a complementary log-log link function (rather than probit or logit). Similarly, if there is moderate variation in both susceptibility and infectiousness, it is possible to use a logarithmic link function, combined with an indirect genetic effects model. However, in the presence of highly infectious individuals, i.e. super-spreaders, the use of any model that is linear in susceptibility and infectiousness causes biased estimates. Thus, in order to identify super-spreaders, novel analytical methods using our derived expression are required.
  
  
  CONCLUSIONS
  We have derived a genetic-epidemiological function for quantitative genetic analyses of binary infectious disease data, which, unlike current approaches, takes infection dynamics into account and allows for variation in host susceptibility and infectiousness.
authors.affiliation: The Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Easter Bush, Midlothian EH25 9RG, UK. debby.powell@roslin.ed.ac.uk.
authors.forename: Debby
authors.initials: D
authors.lastname: Lipschutz-Powell
authors.forename: John A
authors.initials: JA
authors.lastname: Woolliams
authors.forename: Andrea B
authors.initials: AB
authors.lastname: Doeschl-Wilson
mesh_terms: D000818:Animals; D004198:Disease Susceptibility / Q000662:veterinary*; D020022:Genetic Predisposition to Disease / Q000453:epidemiology; D058751:Livestock / Q000235:genetics*; D008954:Models, Biological; D011336:Probability; D012307:Risk Factors