ACE or ADE (p-value or AIC)

Twin & family modeling
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I am running univariate analyses (ADE/ACE) on twin data and have a few queries.

  1. Should I run either the ACE or ADE model based on the correlation coefficient among Mz and Dz twins (if rMz > 2rDz - ADE model; else ACE model), or run both models and select the best-fitting?

  2. When selecting the best-fitting model (if I intend to report only one model), should I use the p-value or AIC?

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Hi jamal.giri! Responses to your questions:
1- It is possible to not feel confident about whether you should run or an ACE or ADE model when just reviewing the correlations. It is fine to run both and compare model fits against the saturated model and compare. Also, it would be helpful to look at parameter estimates from both models to ensure one produces estimates that are reasonable (e.g., no negative variance components).

2- I think it is useful to report both model fit comparison p-values and AIC. This will allow your reader to decide if they agree with your conclusions and provide more transparency to your process on how you chose your best fitting model.

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Thanks, Elizabeth. It was helpful.

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Plus 1 for checking model fit! In practice, I prefer to simply fit the ACE model without looking at the MZ DZ correlations first. Also, I prefer to fit the variance component model to interpret the C component of the model. If the C-squared estimate is negative it implies that dominance or other non-additivity has overwhelmed any common environment influences that would make rDZ > .5 rMZ. If it is positive, it implies that whatever non-additivity there is has been overwhelmed by the common environment so that rDZ is > .5 rMZ. In both cases, I would still want to compare the model to a saturated one, since this comparison can identify other issues with model fit - commonly due to non-normality of the measures, or possibly due to unequal MZ and DZ means or total phenotypic variances. Such effects can cause the model to be rejected against the saturated model. I have concern that inspection of correlations followed by selection of ADE vs ACE model has an adverse effect on the Type I error rate. One would expect the number of times ACE models fail when fitted following rMZ and rDZ inspection and finding rMZ < 2rDZ is less than when such pre-inspection was not done.

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Thank you for the clarification, Michael. A quick follow-up: is there a minimum sample size requirement to run these models (univariate ACE/ADE)? Will a sample size of 200 twin pairs (Mz+Dz+DzOS) have sufficient power to detect dominance for a continuous trait?

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We used to have a rule-of-thumb sample size for continuous traits: 400 pairs for ACE, 4000 pairs for ADE. Obviously this is only a rough guide, but there are things that work against the ADE model. One is that the A and D parameters are fairly highly correlated, because the coefficients in the design matrix are MZ: 1 and 1, DZ 1 and .25. Second, notice that it takes a lot of dominance variance to overwhelm any C that may also exist for the trait. Essentially, 4 times as much D variance is needed to wipe out the C. Higher order interactions across loci could further cut the DZ expectation to almost zero - a phenomenon that David Lykken referred to as emergenesis, which you could read about here: The mechanism of emergenesis - PubMed.

The above was a long way of saying, no, the standard error on even a big dose of D would still be so large with 200 pairs you’d have practically no chance of finding it significantly greater than zero.

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