Regression diagnostics for the class A regressive model with quantitative phenotypes

Regression diagnostic methods are developed and investigated under the Class A regressive model proposed by Bonney [(1984) Am J Med Genet 18:731-749]. We call a family whose phenotypic distribution does not conform to the same genetic model as the majority of the families an etiotic family. The exact case-deletion approach for identifying etiotic families, based on examining the changes in each model parameter estimate by excluding one family at a time, is very time-consuming. We proposed three alternative diagnostic methods: the empirical influence function (EIF), the one-step approximation, and the approximated one-step approach. These methods can be computed efficiently and were incorporated into the existing software package S.A.G.E. A thorough Monte-Carlo investigation of the performance of the diagnostic methods was conducted and generally supports the EIF approach as the recommended alternative. The phenotypic variance is the parameter whose associated regression diagnostic most frequently and correctly identified etiotic families in the models that were examined. An analysis of body mass index data from 402 individuals in 122 Muscatine, Iowa families is used to illustrate the methods. A Class A regressive model with a recessive major locus and equal mother-offspring and father-offspring correlations provided the best-fitting model. The proposed regression diagnostics identified up to 7.4% of the 122 families as etiotic. As a result of this investigation, case-deletion diagnostic assessment is now a practical component in the analysis of quantitative family data.