Table 2.

Summary of the multilevel regression models tested.

Model	Description	Parameters of interest	Explanation and interpretation
1	unconditional model	random effects	The proportion of variation in offspring AUD explained by each of the three levels.
2	phenotypic model	twin parent AUD and spouse parent AUD	A traditional analysis of the effect of parental AUD on offspring AUD, correctly accounting for the levels of clustering in the data.
3	phenotypic model with covariates	reductions in twin parent AUD and spouse parent AUD	The extent to which the relation between parental and offspring AUD is reduced when controlling for demographic characteristics, other substance use, and other psychopathology in the twins and spouses.
4	cotwin-control model	between-twin-family effect of twins' AUD	The effect of the mean AUD score for the twin pair on offspring AUD. (For a diagnosis, this would equal 0 for concordant unaffected twin pairs, 0.5 for discordant pairs, and 1 for concordant affected pairs.) This affects siblings and cousins equally.
		within-twin-family effect of twin's AUD	The difference between an individual twin parent AUD score and the mean AUD score for the twin pair. This affects siblings equally, but can differ for cousins. Twins who are concordant (or have the same number of symptoms) will both have scores of zero; in discordant pairs, the twin with an AUD (or with more AUD symptoms) will have a positive score, and the twin without an AUD (or with fewer symptoms) will have a negative score. This parameter estimates whether, among the offspring of discordant twin pairs, the offspring of the twin with an AUD (or with more AUD symptoms) have more AUD symptoms than their cousins. This provides a key test of a potential causal effect of parental AUD on offspring AUD.
5	within-zygosity cotwin-control model	MZ within-twin-family effect of twin's AUD	The within-twin-family effect from model 4, in the presence of a new interaction term, estimates whether, among the offspring of discordant MZ twin pairs, the offspring of the twin with an AUD (or more AUD symptoms) have more AUD symptoms than their cousins. This provides the most stringent test of a potential causal effect of parental AUD on offspring AUD.
		DZ-MZ within-twin-family effect of twin's AUD	The interaction of the within-twin-family effect from model 4 and twin zygosity (coded MZ=0 and DZ=1), in the presence of the within-twin-family effect from model 4, estimates whether the within-twin-family effect differs by zygosity. This provides a test of whether the familial confounds explaining the association between parental and offspring AUD are in part genetic.
6	within-zygosity cotwin-control model with covariates	reduction in the between-twin-family effect of twins' AUD	The extent to which the between-family association between parental and offspring AUD is reduced when controlling for demographic characteristics, other substance use, and other psychopathology in the twins and spouses.
		reduction in the MZ within-twin-family effect of twin's AUD	The extent to which the potential causal effect of parental AUD on offspring AUD is reduced when controlling for demographic characteristics, other substance use, and other psychopathology in the twins and spouses.

Note: AUD = alcohol use disorder, MZ = monozygotic, DZ = dizygotic