Likelihood and linkage: From fisher to the future

Abstract

Genetic epidemiology is almost unique among the sciences in that computation of a likelihood function is the accepted approach to statistical inference. In the context of genetic linkage analysis, in which genes are mapped by analysing the dependence in inheritance of different traits, the use of likelihood dates back to the early work of Fisher and Haldane, and has seldom been seriously challenged. After introducing the underlying genetic concepts, this paper reviews the history of the statistics of linkage analysis, from 1913 to 1980, and its dependence on the development of likelihood inference. With the sudden increase in genetic marker data deriving from new DNA technology, the potential for mapping the genes contributing to complex genetic traits is markedly increased, but the difficulties of likelihood analysis are also multiplied. With increasing complexity of models and the desire to make maximum use of available data on individuals not closely related, the likelihood approach to human linkage analysis faces new computational and methodological challenges. New methods are meeting some of these challenges; likelihood and linkage seem as closely interwoven as ever.