''Narrow sense heritability'' (Equation 5.4) is of interest mainly in connection with selective breeding of animals, and is not considered further here. ''Broad sense heritability'' addresses the relative partitioning of individual differences (say in drug response) into genetic and environmental components, and predicts genotypic values for individuals in a population at a given time.
More recently, Falconer proposed another relationship that approximates broad sense heritability. To give a sense of how Falconer's relationship is derived, some additional statistical concepts, i.e., for "covariance" and ''phenotypic correlation," are needed. Since identical (monozygotic, MZ) twins covary completely genetically and also share a familial environment, the covariance for identical twinships is defined as follows:
Fraternal twins have the same genetic components of covariance as full siblings (see Table 5.1), i.e., covdz = 1/2Va + 1/4Vd + VE(DZ)
Thus, the difference between the phenotypic covariances of identical and fraternal twins (assuming equivalent environments) is covmz - covdz = 1/2Va + 3/4Vd
Since a phenotypic correlation (r) is defined as a covariance divided by a variance, rDZ = [1/2Va + 1/4Vd + VE(DZ)]/Vp and rMZ = (Va + Vd + Ve(mz))/ Vp from which the difference between rMZ and rDZ is rMZ - rDZ = 0/2Va + 3/4Vd)/ Vp Doubling this difference gives
This formula (Equation 5.5) is called Falconer's estimate of broad sense heritability. Falconer's formula is an improvement over Holzinger's index for estimating broad sense heritability, but it still appears to be too simple a model for general application to estimate heritability from twin data. The shortcomings of this formula are beyond our present scope (other points may need amplification,17'19 but one point is easy to see—Falconer's formula overestimates broad sense heritability because it contains 1.5 times the dominance variance).
Table 5.2 represents a fairly complete summary of therapeutic agents that had been investigated by twinship study up to 1978. For several of the agents listed, the values for hB2 exceed unity—a result that is disturbing because heritability cannot exceed unity.
The acetylation polymorphism (see Appendix A) was one of the first pharma-cogenetic traits to be extensively investigated by twin study. In a small series of five identical and five fraternal twinships from a German population, the difference in elimination of isoniazid (as the percentage of dose) was taken as a measure of interindividual variability. Despite the rather small number of twin-ships studied, it is evident that the intrapair variation observed for identical twin-ships is consistently much less than for fraternal twinships; this finding suggests heredity is quite influential in isoniazid elimination.
Later, two additional twin studies of the acetylation polymorphism were performed. In the study performed in Japanese twins, a very high intrapair correlation (r = 0.95) between the isoniazid blood concentration of identical twinships compared to the correlation (r = 0.25) for fraternal twinships was observed—41 of 42 identical twin pairs were concordant, while 7 of 11 fraternal twin pairs were concordant and 4 were discordant. When the results of a third twin study consisting of five identical and four fraternal Caucasian twinships are combined with the German and Japanese studies, the concordance within identical twins is much greater than within fraternal twins (Table 5.3).20 The difference is highly significant (w2 = 21.1, p < 0.0001), and this finding provides additional support for the presence of important genetic factors in the control of isoniazid elimination.
Twin studies of antipyrine, dicumarol, and phenylbutazone as well as of several other therapeutic agents (Table 5.2)16 suggest the major mechanisms controlling variation in the rates of elimination of these drugs are also primarily of genetic origin. The relative importance of heredity and environment to more complicated pharmacological phenomena can also be better appreciated from twin studies (Table 5.4).21 For example, when two (or more) drugs are coad-
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