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1 A few notes (for myself).

  • The number of effective tests can be found at the target num_tests_by_PCs.
  • The number of effective tests among those significant in the MR can be found at the target num_tests_by_PCs_AM_sig.

2 Relationship between causal effects and raw phenotypic correlation in couples.

Sought to compare the raw correlation amongst couples vs. the standardized MR effects. There are many traits where the correlation > MR effects including some traits of interest such as standing height, place of birth, among many others. A plot comparing the two and a summary table of the significant effects is shown below.

Version Author Date
e3cbe36 Jenny Sjaarda 2022-02-03

2.1 Summary of cases where correlation > MR estimate.

The table below displays the 41 traits that have correlation significantly > MR-estimate.

2.2 Search for potential confounders to explain cases where correlation > MR estimate.

  1. Restrict to only traits that have correlation significantly > MR-estimate (41 traits have correlation > MR_estimate).
  2. For each of these traits, find the traits which have a causal effect on this trait (MR p-val < 0.05/[number of effective tests]).
  3. Calculate the correlation due to confounding as: \(C = (\alpha_{z\rightarrow x})^2 * \alpha_{z_i\rightarrow z_p}\).
  4. Calculate the ratio of this correlation (\(C\)) and the correlation of \(X\) in partners (\(C/r_x\)).

A summary of the these results can be seen below:

3 Effect of sex, age and time together on causal effects in couples.

  • For each trait in the pipeline, we tested the causal effect within couples (i.e. the number of analyses corresponds to the number of traits (110)).
  • The significant results after adjusting for multiple hypothesis testing are shown below.
  • IVW_meta_beta and IVW_meta_pval corresponds to the beta and p-value of the meta-analyzed MR across sexes, respectively (i.e. MR estimates were computed in each sex-seperately using sex-specific SNP-exposure and SNP-outcome results and then meta-analyzed).
  • After adjusting for multiple tests (p < 0.05/62), identified 60 significant assortative mating (same-trait) MR results (corresponding to the table below)..

3.1 Sex heterogeneity.

  • For each AM MR (\(X_{p} \sim X_i\)), analyses were run in each sex separately.
  • Of the significant results shown above, we tested to see if there was any difference in AM MR estimates between sexes.
  • A similar adjustment for multiple hypothesis testing was applied as above, resulting in 28 number of effective tests.
  • After adjusting for multiple hypothesis testing (p < 0.05/28), 4 traits showed significant differences amongst sexes (this changed from before).
  • The table below shows the nominally significant results at p < 0.05.

3.2 Binned results (exploring effect of age and time-together).

  • For each AM MR (\(X_{p} \sim X_i\)), analyses were run in the full sample as well as in 5 roughly equal sized bins according to time couple had been together (time_together_even_bins) estimated using time at household variable, and median age (age_even_bins).
  • Of the 60 significant results shown above, we tested to see if there was any significant difference in AM MR estimates amongst the two grouping variables.
  • Specifically, the outcome data set was split into 5 bins, and the SNP-outcome effect was estimated in each bin separately (and each sex seperately).
  • These outcome-SNP effects were then used to generate bin-specific MR estimates, using the same SNP-exposure effects from Neale.
  • To estimate the difference among bins, we used two approaches:
    1. The Cochran's Q test to test for heterogeneity in meta-analyses (of which we obtained no significant results, so not presenting in paper).
    2. Tested the significance of the slope of linear model of median bin (either age or time together) versus the bin-specific MR estimate.

Slopes were calculated by estimating the beta-coefficient of a linear regression between MR estimate within each bin (dependent variable) and median bin (independent variable, either age or time at same household). Linear models were run both unweighted and weighted for the by the inverse of the SE of the MR estimate.

The number of significant trends (\(\beta\) estimates from the model: \(\alpha_{bin} \sim median_{bin}\)) significant after multiple hypothesis testing (p < 0.05/28 = 0.0017857) in each group was:

  • Binned by median age of couples, number of significant results after adjusting for number of tests:
    • \(\beta\) unweighted, meta-anlayzed across sexes: 0
    • \(\beta\) weighted by inverse of the SE, meta-anlayzed across sexes: 0
    • \(\beta\) unweighted, significantly different between sexes: 0
    • \(\beta\) weighted by inverse of the SE, significantly different between sexes: 0
  • Binned by time couple had been together, number of significant results after adjusting for number of tests:
    • \(\beta\) unweighted, meta-anlayzed across sexes: 0
    • \(\beta\) weighted by inverse of the SE, meta-anlayzed across sexes: 0
    • \(\beta\) unweighted, significantly different between sexes: 0.
    • \(\beta\) weighted by inverse of the SE, significantly different between sexes: 0

Given that we have no significant results, how should we report these analyses?

A few potential figures we could include for a given trait are shown below.

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4 Heterogeneity stats.

  • In the single trait analysis, we also decided to investigate Cochran’s heterogeneity Q-stat to identify traits with high heterogeneity.
  • This would indicate that associations between the index genotype and partner’s phenotype may not only act indirectly through causal relationship between the traits, but some direct effect is present.
  • Ideally, for the majority of the traits, the heterogeneity would be low, confirming that (despite what Tenesa suggests) there are no direct index genome to partner phenome effects.
  • We tested heterogeneity statistics using the function mr_heterogeneity from the TwoSampleMR package.

The number of traits with significant heterogeneity in the MR is: 0.

5 Impact of confounders on couple correlation.

We tested the impact of confounding on genetic PCs, N/E coordinates and the following 4 traits:

Average total household income before tax
Age completed full time education
Townsend deprivation index at recruitment
Fluid intelligence score

5.1 Ratio of confounding to correlation.

We tested the ratio of confounding to correlation for each confounder trait tested.

trait_interest mean_ratio median_ratio sd_ratio number_of_traits
Age completed full time education 0.0212381 0.0084649 0.0316105 105
Average total household income before tax 0.1034712 0.0398425 0.1327846 105
Fluid intelligence score 0.0185683 0.0035172 0.0659349 105
household_coords 0.0059082 0.0034912 0.0080903 106
PCs 0.0032632 0.0020719 0.0031792 106
Townsend deprivation index at recruitment 0.0244587 0.0102159 0.0351698 106

A note on the number of traits:

We tested the impact of trait_interest on couple correlation amongst all traits in our couple MR framework (number of traits = 110) with the exception of home location and birth place coordinates (2 each [N and E] * 2), we also removed the trait itself from the confounder analysis where applicable (in the case of traits 20016_irnt, 738 and 845). [Trait 189_irnt was not included in our final couple MR analysis but could still be evaluated here because no MR-estimates were used.]

5.2 Plots.

The figure below shows the 4 trait which showed the greatest impact on couple correlation (mean confounding ratio > 0.01).

Version Author Date
e3cbe36 Jenny Sjaarda 2022-02-03

6 Comparison of paths from index to partner.

As a recap, the model is below.

Version Author Date
529020f jennysjaarda 2021-09-24

We sought to compare the different paths from \(X_i\) to \(Y_p\) using the estimates computed as \(\omega\), \(\rho\) and \(\gamma\).

Version Author Date
e3cbe36 Jenny Sjaarda 2022-02-03

We considered the regression of the following estimates vs \(\omega\) with an intercept passing through the origin (i.e. \(estimate \sim \omega + 0\):

  1. \(\rho\)
  2. \(\gamma\)
  3. \(\rho\) + \(\gamma\)
  4. \(\rho_{resid} + \gamma\), where \(\rho\) is residualized for \(\gamma\) (i.e. \(\rho_{resid} = resid(lm(\rho \sim \gamma))\))

The results are summarized below:

outcome term estimate std.error statistic p.value r.squared
rho omega 0.5876223 0.0142951 41.10651 0 0.6452499
gam omega 0.6159675 0.0110146 55.92270 0 0.7709763
gam_rho omega 1.2035898 0.0169569 70.97924 0 0.8443117
gam_rho_resid omega 0.7722464 0.0143026 53.99350 0 0.7583434

To further explore these estimates, performed paired t-tests to find the significant differences between pairs of estimates. We first removed all instances where the sign did not match between any two pairings. In total, of the 930 trait pairs under consideration, 11 were removed.


    Pairwise comparisons using t tests with pooled SD 

data:  data_boxplot$beta and data_boxplot$data 

                Gamma      Gamma_Rho  Gamma_Rho_resid Omega  
Gamma_Rho       0.00007441 -          -               -      
Gamma_Rho_resid 0.83533    0.00017    -               -      
Omega           0.94622    0.00009843 0.88834         -      
Rho             0.09790    0.00000002 0.06248         0.08497

P value adjustment method: none

Version Author Date
e3cbe36 Jenny Sjaarda 2022-02-03

6.1 Paths summary.

A summary of the \(\omega\), \(\rho\), \(\gamma\) and \(\rho_{resid} + \gamma\) estimates are summarized in the table below. Those with BF-significant differences between the estimates (according to a Z-test, p < 0.05/930) are given as T/F in the last three columns.


sessionInfo()
R version 4.1.0 (2021-05-18)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)

Matrix products: default
BLAS:   /data/sgg2/jenny/bin/R-4.1.0/lib64/R/lib/libRblas.so
LAPACK: /data/sgg2/jenny/bin/R-4.1.0/lib64/R/lib/libRlapack.so

locale:
[1] en_CA.UTF-8

attached base packages:
[1] stats     graphics  grDevices datasets  utils     methods   base     

other attached packages:
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[21] tidyverse_1.3.1    targets_0.5.0.9001 workflowr_1.6.2   

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