rg out of bounds in the presence of significant h2 for both traits

[Michel Nivard]

Hi,

I have run LDSC on a GWAS for 2 psychometric traits, one aggressive behavior related (N ~17k), one a meta analysis of externalizing (ADHD, ODD CD etc) related traits ( N ~ 40k).

Both h2 are significant (Z = 2.22 and Z = 3.3), yet the genetic correlation is out of bounds (rg =1.3). 

The sample overlap is considerable (as is evident from the large gcov_int: 0.176 

Hypothesis 1:

Perhaps I am really to close to "no significant h2". The large gcov_int might even result in the need for more accurate estimates of h2 to enable estimation of rg? 

Hypothesis 2: 

Perhaps gcov_int is underestimated ("luck"of the draw so to say), and the low intercept estimate leads to an overestimated slope (as slope and intercept are often  related).

Hypothesis 3:

Sample size is simply insufficient to estimate the rg given the h2.

My question is basically, in writing up these results, what further exploration within LDSC can I undertake to clarify and contextualize my findings? Is their any knowledge on the relationship between gcov_int and the ability to estimate rg?

Output below

Best,

Michel Nivard

Heritability of phenotype 1

---------------------------

Total Observed scale h2: 0.0547 (0.0246)

Lambda GC: 1.0165

Mean Chi^2: 1.013

Intercept: 0.9913 (0.0079)

Ratio < 0 (usually indicates GC correction).

Heritability of phenotype 2/2

-----------------------------

Total Observed scale h2: 0.0423 (0.0128)

Lambda GC: 1.0588

Mean Chi^2: 1.0617

Intercept: 1.0276 (0.0072)

Ratio: 0.4473 (0.1173)

Genetic Covariance

------------------

Total Observed scale gencov: 0.0626 (0.013)

Mean z1*z2: 0.2113

Intercept: 0.176 (0.0053)

Genetic Correlation

-------------------

Genetic Correlation: nan (nan) (rg out of bounds)

Z-score: nan (nan) (rg out of bounds)

P: nan (nan) (rg out of bounds)

WARNING: rg was out of bounds.

This often means that h2 is not significantly different from zero.

Summary of Genetic Correlation Results

                    p1                            p2   rg     se     z          p  h2_obs  h2_obs_se  h2_int  h2_int_se  gcov_int  gcov_int_se

 AGRESS.sumstats.gz  EXTER.sumstats.gz  1.3  0.353  3.68  2.330e-04   0.042      0.013   1.028      0.007     0.176        0.005

[Raymond Walters]

Hi Michel,

I think you’re entirely on target with your explanations for the results. I’d highlight the large SE (.35) for the rg estimate, which is consistent with the instability of estimation with small h2 values in the denominator, and since the ldsc estimator is unbounded it’s not entirely unreasonable to see out of bounds rg estimates if the true correlation is large.

Estimation with large sample overlap certain isn’t impossible (e.g. simulations with 100% overlap in the ldsc genetic correlation paper), but I’m not sure how much has been done to characterize that behavior once h2 is small. I suspect the relationship between gcov and gcov_int (e.g. something similar to the ratio reported with h2) may be more important to estimation than gcov_int itself, but that’s just a hunch.

As for further investigation, if you have access to the genotype data you may have better luck with a direct bivariate analysis of your substantial overlapping samples with e.g. GCTA or BOLT-REML. Depending on the structure of your externalizing traits analysis you might also look at subsetting that data by clinical outcomes in case phenotypic heterogeneity is driving down h2.

Cheers,

Raymond

------

Raymond K. Walters
Postdoctoral Research Fellow
Analytic & Translational Genetics Unit
Massachusetts General Hospital
rwal...@broadinsitute.org

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