A note on the basis of regressive models for genetic analysis

✍ Scribed by George Ebow Bonney

• Publisher: John Wiley and Sons
• Year: 1986
• Tongue: English
• Weight: 232 KB
• Volume: 3
• Category: Article
• ISSN: 0741-0395
• DOI: 10.1002/gepi.1370030706

✦ Synopsis

Regressive models are constructed by conditioning a person's phenotype on those of his ancestors and antecedents. This note emphasizes the underlying probability structure and the many patterns of dependence within their scope. It is also shown that under certain conditions all likelihood calculations reduce to the same order of difficulty as for oligogenic models.

Consider a set of n relatives with trait values Y = (Yl, Y2, ..., Y , ) , and without loss of generality assume the value Xi of one covariate is associated with Yi. Write X = (X1,Xz, ..., Xn). We are interested in the probability (or density) of the vector Y as a function of the vector X. The regressive models are based on the decomposition Pr(Y1X) = Pr(Y1,Y2, ..., YnlX) = Pr (Y1 I X) Pr (Y2 1 Y1 ,X) . . .Pr (Yn I Y1, . . . ,Yndl ,X) . (1)

Consider the i-th factor

It is helpful to regard Y1,...,Yi-l, and X, as predicting Y.. Then for most family data, one or more of the following classes of models that define dependence of Yi on Y1, ..., Yi-l, X will be adequate. The first two classes of models do not utilize biologic relationships.