A generalized estimating equations approach to fitting major gene models in segregation analysis of continuous phenotypes

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Abstract
This paper discusses the application of estimating equations methods based on a quadratic exponential model [Prentice and Zhao, 1991] as a potential competitor with full likelihood approaches to estimating the effect of major genes in a segregation analysis [Elston, 1981] of continuous phenotypes, in the single allele problem. We show that while the estimating equations methods based on the quadratic exponential family cannot be used by themselves to estimate all parameters of interest, an iterative two‐stage approach can be used, in which the population allele frequency is first considered to be a known parameter, which permits the estimating equations method to estimate the remaining parameters. At the second stage a “pseudo‐profile” loglikelihood based only on the founders is used to estimate the allele frequency. After each maximization of the pseudo‐profile loglikelihood at the second stage, the parameters in the first stage are reestimated using a new value of the allele frequency, and a new value of the second stage pseudo‐profile loglikelihood is obtained. We used simulated pedigree data for illustrations. © 1993 Wiley‐Liss. Inc.