paternal educational attainment, maternal smoking, and two-way interactions between parental alcohol problems and (i) maternal age at twins’ birth and (ii) paternal education. Although maternal education was examined as a covariate in Cox analyses, paternal education was more strongly predictive of separation (versus offspring substance involvement; data not shown), and thus for purposes of PSA, paternal rather than maternal educational attainment was modeled. Likewise, maternal history of smoking was modeled instead of either parent history of smoking. From resulting propensity scores, a 5-level categorical variable was computed with each level containing approximately 20% of the distribution, followed by within-quintile comparisons of family background risks and, conditional on successful matching, offspring substance involvement. In this way it was possible to examine whether effects of parental separation are consistent across the distribution of parental separation risk–in families with low prior probability of separation, in families at intermediate risk, and in families with high prior probability of separation–or whether there are discontinuities not captured by Cox analyses.
