Twin Studies

The Basic Models

Suppose we're interested in how important genes or familial environment are in determining people's heights. For simplicity, suppose (1) each chromosome has a "height score" (2) person's height is a weighted sum of (a) all their chromosomes' "height scores", (b) their familial environment "height score", and (c) random noise. These are the assumptions that underlie the ACE model ACE model, which is, as far as I can tell, the most commonly used model in analyzing twin study data.

Computing the estimates of the amount of variance in height due to genes, common environment, and unshared environment is straightforward in this model if you have the correlation of monozygotic (identical) twins' heights and the correlation between dizygotic (fraternal) twins' heights.

To compute the genetic contribution, just take the difference between the two correlations and double it. To get the common environment contribution, just take the dizygotic twin correlation and subtract half the genetic contribution. The unshared environment is just whatever variance is left over, which includes things like measurement error and luck.

The other common model is the ADE model ADE model. The downside of the ADE model is that it requires the assumption that there is zero common environment. The upside is that it relaxes the assumption that all genetic effects are linear by allowing for dominance effects.

Because ACE ignores genetic dominance effects, its biased against genetic explanations and in favor of common environment ones. Because ADE ignores common environment, it's biased the other way. In my experience, ACE is far more common in the literature. There is a model that includes both common environment and genetic dominance effects: the ACDE model, but its typically not used because it is difficult/impossible to estimate all four parameters using a sample of only monozygotic and dizygotic twins.

Measurement Error

Suppose you're trying to estimate the heritability of height. Each person has some platonic height, but your dataset, sadly, only has measured height. Measured height can differ from platonic height due to a number of factors: rounding, human error, height's tendency to shrink throughout the day, etc.

Presumably, your genes affect your platonic height but not the sources of error that end up mediating measured height. That is, the only way genes affect your measured height is through your platonic height.

When we are computing the monozygotic and dizygotic correlations, we can adjust for this source of measurement error. Here's how we do so:

Let $r$ be the correlation between true height and measured height. Note, since true height is impossible to observed directly, we can't observe this correlation directly either.

To get around this issue, we can measure someone's height twice, the correlation between the two measured heights should be $r^2$. Hence, the square root of the "test-retest" correlation should be $r$.

If we want to get the true $r_{MZ}$, it turns out we can just divide it by $r^2$. Ditto for $r_{DZ}$. Hence, the heritability estimate becomes

Or just

The hawk-eyed reader will note that this just means our adjusted estimate of heritability is the naive estimate of heritability divided by $r^2$.

Lest you think I'm a crank, here's people with credentials talking about the same issue Frisell, and here is a study where this kind of thing played a major issue Riemann.

Assortative Mating

Assortative mating will cause naive twin studies to over-estimate the effects of shared environment and underestimate the effects of additive genes. Sadly, the vast majority of twin studies ignore this issue.

How strong is this effect?

Running this code with different parameters yields this table:

Note: Even though I used a sample of two million hypothetical twins, there is still some sampling error, which is why (for instance) the first row is close to zero but doesn't equal it precisely. This is likewise why the first column is close to the actual heritability but not exactly the same.

We can use this table to adjust twin studies for assortative mating. For instance, if a twin study finds a heritability of 72% but there is a correlation of 0.3 between fathers and mothers for that trait, the true heritability is probably a smidge above 80%.

Age

In general, the heritability of psychiatric traits increase with age Bergen and the common environment of traits decrease with age Meta-analysis of the heritability of human traits based on fifty years of twin studies . For this reason, estimates derived from studies of, say, young children should generally not be used to make conclusions about adults (and vice versa).

One place this shows up is educational attainment, where the years of education obtained has a large common environment component - probably because it is the result largely of events and decisions that occur in childhood, when parents still have large influence over their children. It notably contrasts with standardized high school test scores, which generally have approximately zero common environment component, and with IQ, which is probably the trait most famous for having a heritability that shifts with age.

As an aside, I am forced to wonder whether this has anything to do with the fadeout of educational interventions over time.

Other Methodological Shortcomings

In addition to the issues with using ACE or ADE, twin studies typically suffer from other methodological shortcomings

• Twin studies often use questionnaires, often not verifying the reported information including whether the pair of people in question are even twins . Misclassifying people a fraternal twin as identical (or vice-versa) biases estimates against genes and towards common environment. The unreliability of self-reported data is rando and is similar to the measurement error discussed above and will generally bias estimates of genes and shared environment downwards - the exception is if the unreliability is non-random (e.g. twins are likely to misreport in similar ways).
• Twin studies frequently draw on (non-random) convenience samples.
• When twin studies use siblings rather than (or in addition to) dizygotic twins, this causes birth-order effects to be interpreted as genetic effects, biasing heritability estimates upwards and common environment estimates downwards.
• If monozygotic twins are treated more similarly than dizygotic twins (or siblings if they're used), this biases common and unshared environment downwards while biasing genetic estimates upwards.
• Maybe twins make choices to be more (or less) similar. This would bias estimates of unshared environment upwards. Alternatively, maybe this force is stronger in identical twins than fraternal twins, which would bias estimates of heritability upwards. This hypothesis is difficult to evaluate, but here are some related studies Fortuna Mark.
• To the literature's credit, publication bias seems generally minor, with one major exception: the choice of ACE or ADE. Generally, studies start with an ACE model and, if this results in a negative estimate for common environment, change to an ADE model. This use of choice causes a positive bias for dominance genetic effects, a positive bias for common environment effects, and a negative bias for additive genetic effects - especially in small sample sizes Meta-analysis of the heritability of human traits based on fifty years of twin studies (see also the supplement).
• TODO: gene-environment interactions Kaprio Avinun
• TODO Grotzinger

Despite the widespread belief that smaller populations should have less additive genetic variance, the empirical evidence is scant Wood.

todo Røysamb

Appendix: Assortative Mating II

If a study is assuming zero common environment, then it is common to estimate heritability as just $h^2 = r_{MZ}$. In this case, assortative mating will bias heritability estimates upwards, and the corrections needed to account for it are different: