Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology (1995)
Chapter: MAXIMUM LIKELIHOOD ESTIMATION
Page 34
· Phenocopy. Some diseases can be due to nongenetic causes. For example, colon cancer can be caused by mutations in the APC gene on human chromosome 5, but most cases of colon cancer are thought to be nongenetic in origin (and are often attributed to diet). As a result, one cannot conclude that an affected person has necessarily inherited the disease genotype.
· Genetic heterogeneity. Some diseases may be caused by mutations in any one of several different genes. Thus, a disease may show linkage to a genetic marker in some families but not in others.
· Polygenic inheritance. Some diseases may involve the interaction of mutations at several different genes simultaneously.
Due to the incomplete information on natural families and the uncertainties of complex genetic traits, a human geneticist often cannot reliably infer an individual's genotype based on his or her phenotype; inferences are probabilistic at best. As a result, genetic mapping requires more sophisticated analytical methods than simply counting recombinants between a disease gene and nearby markers.
Animal models of human diseases are slightly simpler, inasmuch as experimental crosses can be arranged. Still, interesting diseases typically show complex inheritance even in inbred animal strains. For example, mouse and rat models of diabetes involve incomplete penetrance, phenocopies, and polygenic inheritance. Sophisticated analytical tools are thus needed for such genetic mapping as well.
Maximum Likelihood Estimation
To handle the problem of incomplete information, geneticists have adopted the statistical approach of maximum likelihood estimation. Briefly sketched below is the basic formulation (see, e.g., Ott, 1991).
In most cases, a geneticist needs to estimate a parameter qfor example, the recombination frequency between a disease gene and a genetic marker or the mean increase in blood pressure attributable to a putative gene at a specific location along the chromosome. The geneticist would ideally like to have complete genotypic data Xfor example, the
