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Potential source contribution to samples was also calculated from summarized read quantities of the bacterial and archaeal sub-trees (Supplementary Table S3) using SourceTracker version 0.9.834.
Sample code for estimating causal effects from summarized data for multiple variants associated with a risk factor in a single study and in multiple studies for R and WinBUGS is provided in the Supporting Information.
We compare the causal effect estimate (and its precision) obtained from summarized data to that obtained if individual-level data on the variants, risk factor and outcome were available on the whole study population.
However, if individual-level data are not available, then valid statistical inference can still be obtained from summarized data on the associations of genetic variants with the risk factor and the outcome.
Our methods for obtaining causal estimates from summarized data commonly presented in published reports facilitate causal assessment of risk factors in existing consortia without additional data collection or sharing.
Simulation results suggest that causal estimates obtained from summarized data using a likelihood-based model with independently distributed 'non-weak' variants are almost as precise as those obtained from individual-level data, with bias close to zero and coverage close to nominal levels.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com