Update Meeting: 25-10-2021
jennysjaarda
2021-10-20
Last updated: 2021-10-26
Checks: 7 0
Knit directory: proxyMR/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 48b6256 | Jenny Sjaarda | 2021-10-26 | wflow_rename("analysis/update_meeting_28_10_2021.Rmd", "analysis/update_meeting_25_10_2021.Rmd") |
1 Progress update.
1.1 Impact of geography.
Wanted to assess impact of geography on couple trait correlation. Investigated this by using both genetic PCs and birth coordinates.
1.1.1 PC impact.
Tested the following:
- cor(PC_i,PC_p) for each PC (i.e. within couple PC correlation).
- cor(X,PC) for all PCs.
Next, I calculated the correlation due to counfounding as cor(X,PC)^2*cor(PC_i,PC_p) values, and plotted them against the raw cor(X_i,X_p) values.
The table below gives the data in the plot above:
outcome_descriptioncorresponds to the trait.trait_couple_corris the correlation ofoutcome_descriptionin couples.corr_due_to_confounding_allcorresponds to the formula:cor(X,PC)^2*cor(PC_i,PC_p), summed across all PCs.
1.1.2 Coordiante impact.
Performed the same analysis as above but replacing PCs with North and East birth co-ordinates (data field 129 and 130, respectively).
The table below gives the data in the plot above:
outcome_descriptioncorresponds to the trait.trait_couple_corris the correlation ofoutcome_descriptionin couples.corr_due_to_confounding_allcorresponds to the formula:cor(X,PC)^2*cor(PC_i,PC_p), summed across both coorindates.
1.2 Compairing paths from \(X_i \rightarrow Y_p\).
We performed two analyses to compare \(\rho\), \(\gamma\) and \(\omega\):
- No adjustment in \(Y_i \rightarrow Y_p\) MR.
- Adjustment for effects on \(X_i\) in \(Y_i \rightarrow Y_p\) MR, MVMR model as follows: \(Y_p \sim Y_i + X_i\) (IVs were a combination of all \(X\) and \(Y\) IVs, pruned at standard parameters using 1000G European data).
| Version | Author | Date |
|---|---|---|
| 529020f | jennysjaarda | 2021-09-24 |
Broad overview of results are shown in the figure below.
- Without adjustment.
- With adjustment.
Going forward, we will just use the adjusted results.
1.2.1 Exploring the difference between \(\rho\) and \(\gamma\).
In general, \(\rho\) is significantly larger that \(\gamma\), meaning that \(X_i \rightarrow Y_p\) favors paths where assortative mating is through \(X\) rather than \(Y\). This makes a lot of biological and intuitive sense. In other words, exposures are passed from index to partner, rather than outcomes.
A summary of the linear model of \(\rho\) vs \(\gamma\), forced through the intercept, is below.
Call:
lm(formula = y ~ x + 0, data = fig_data)
Residuals:
Min 1Q Median 3Q Max
-0.38531 -0.02515 0.00292 0.03829 0.54599
Coefficients:
Estimate Std. Error t value Pr(>|t|)
x 0.60512 0.01442 41.96 <0.0000000000000002 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.07834 on 987 degrees of freedom
Multiple R-squared: 0.6408, Adjusted R-squared: 0.6404
F-statistic: 1761 on 1 and 987 DF, p-value: < 0.00000000000000022The corresponding figure is below. The blue line includes only BF-significant \(\rho\) and \(\gamma\), where the green line includes all points (analagous to the linear model above).
1.2.2 Exploring the difference between \(\omega\) and [\(\rho\) and \(\gamma\)].
A few observations:
- In general, \(\omega\) is significantly larger than both \(\rho\) and \(\gamma\), as shown in the figures below.
- On the other hand, when we sum \(\rho\) and \(\gamma\), \(\omega\) is in general lower than the sum.
- There are a number of instances where \(\omega\) is significantly smaller than the sum &rightarrow not as interesting? But what does this mean? That we didn't have power in the \(\omega\) (i.e diagonal) MR to capture the relationship that is likely only going through the either \(\rho\) or \(\gamma\) (or a sum of the two)?
- There are a few cases where \(\omega\) is significantly larger than the sum. See below for details.
Call:
lm(formula = y ~ x + 0, data = fig_data)
Residuals:
Min 1Q Median 3Q Max
-0.65813 -0.03940 -0.00337 0.03210 1.99081
Coefficients:
Estimate Std. Error t value Pr(>|t|)
x 0.64639 0.01175 55.03 <0.0000000000000002 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1064 on 987 degrees of freedom
Multiple R-squared: 0.7542, Adjusted R-squared: 0.754
F-statistic: 3029 on 1 and 987 DF, p-value: < 0.00000000000000022A summary of the cases where \(\omega\) is significantly larger or smaller than the sum of \(\rho\) and \(\gamma\) are shown in the two tables below (taking absolute values of each).
1.3 Next steps.
- In the \(Y_i \rightarrow Y_p\) MR, rather than performing a MVMR (\(Y_p \sim Y_i + X_i\)), try in a two step process as follows:
- Calculate the effect of \(Y_p\) without effects of \(X_i\) on \(Y_p\) as: \(Y_{resid} = Y_p - \omega*X_I\).
- Run MR with the residualized \(Y\) as: \(Y_{resid} \sim Y_i\)
Question: What is the corresponding SEs on \(Y_{resid}\)?
- Check for cases of reverse causation in the same-person MR.
- Remove SNPs were the effect is significantly larger on the outcome than the exposure.
- In the results including both sexes, meta-analyze at the SNP-level rather than the MR level (note that right now the two horizontal, same person MRs in the DAG above are different because they are sex specific. I then meta-analyze \(\omega\), \(\gamma\) and \(\rho\) as the final step).
- Calculate the variance of \(\rho + \gamma\) as: \(2 * cor(\rho, \gamma) * SE_{\gamma} * SE{\rho}\), i.e. include the extra-term of 2*correlation.
2 PolyMR.
- Finished discussion points.
- Waiting on Jonathan to add bibtex file before adding my references.
- Haven't done a summary on CATE - who was going to do that?
- Question: Why is there often an inflection point around the (0,0) point? Is this an effect of standardization?
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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