# direct comparison between traits' heritability with no raw data

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lior abramson
Joined: 07/21/2017

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Dear forum

I am trying to conduct a meta-analysis on the heritability of two traits that are different, yet related (I found six studies in which the twins were measured in both traits).

I am trying to conduct a meta-analysis on the heritability of two traits that are different, yet related (I found six studies in which the twins were measured in both traits).

From what I know, in order to directly compare between the two traits heritability, I need to enter them in the same model, and for that, I need either the raw data or the full correlation matrix (and I have neither).

I would like to ask: Does anyone know a way to perform a direct statistical comparison between the heritability estimates of these traits, given that I only have information about the cross-twin-within-traits correlations, but not about the cross-twin-cross-trait correlations (e.g., the correlation between one twin 1 in trait 1 and the second twin in trait 2, separately for MZ and DZ twins)? Is a descriptive comparison between the heritability estimates of the traits the only option?

Thank you very much for your help,

Lior

## Given that you are just

So the difference in heritabilities would be 2*(rM1 - rM2 - rD1 +rD2). Be sure to read up on the limitations and assumptions of the Falconer formula.

Then to calculate the standard error for this value, that’s 2*sqrt(Var_rM1 + Var_rM2 -2*Cov_rM1rM2 + Var_rD1 + Var_rD2 -2*Cov_rD1rD2)

The issue, as you note, is that the covariance terms require estimates of not only the cross-twin within-trait correlations but also the within-twin within-trait and cross-twin cross-trait correlations. See Equations. 6: https://journals.sagepub.com/doi/pdf/10.1177/01466219922031239?casa_token=oACj12LtQeAAAAAA:SFVBEqelbBixTa1SC1_bqWn7GNzUJUziW75UCOuOKxSpqhZnKvDcLz-BNsuwsrTCnslrW-IaTTo

Given that this is only being used to calculate a standard error and not the point estimate, it may be reasonable to estimate a plausible value. For example rXtwinXtrait ≈ rWtwinXtrait * mean(rXtwinWtrait1, rXtwinWtrait2). You could also examine a few larger or smaller correlation estimates to illustrate potential implications of this assumption on SE width.

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