Our model assumes that wi has a gamma distribution with mean = 1 and a variance of θ. Although θ is a variance component, it has two characteristics that make it a useful statistic for twin analysis. First, 1 + θ can be interpreted as the odds ratio for smoking initiation as a function of the twins smoking status (Clayton 1978). Second, the ratio of θ/(2 + θ) is equivalent to Kendall’s (1962) coefficient of intracluster rank correlation (Oakes 1982; Guo and Rodriguez 1992). Thus, by estimating θ for MZ pairs and DZ pairs separately, we can calculate pairwise correlation coefficients that take into account the duration of exposure and the subsequent onset of regular smoking. We estimate the heritability of regular smoking as twice the difference of the correlations between MZ and DZ pairs. These estimates are shown in Table 3.
