R/est_lambda.R
est_lambda.Rdest_lambda is a function which allows users to obtain an
unbiased estimate for lambda, a term used to describe the
correlation between the SNP-outcome and SNP-exposure effect sizes, using a conditional log-likelihood approach. This
correlation is affected by the number of overlapping samples between the two
GWASs and the correlation between the exposure and the outcome. Thus, when
using the function mr_simss, if the fraction of overlap and the
correlation between exposure and outcome are unknown, it is recommended to
employ est_lambda and use the value returned from est_lambda in
mr_simss.
Note: For greater accuracy in the estimation of
lambda, it is advisable to use summary statistics of the entire set of
unpruned SNPs from the exposure and outcome GWASs.
est_lambda(data, z.threshold = 0.5)A data frame to be inputted by the user containing summary
statistics from the exposure and outcome GWASs. It must have at least five
columns with column names SNP, beta.exposure,
beta.outcome, se.exposure, and se.outcome. Each row
must correspond to a unique SNP, identified by SNP.
A value which is used to obtain a subset of SNPs which have
absolute z-statistics for both exposure and outcome GWASs less than
this value. The method then assumes that both of the true SNP-outcome and
SNP-exposure effect sizes of each SNP in this subset are approximately 0.
The default setting is z.threshold=0.5.
A value which is an estimate of lambda, the correlation between the SNP-outcome and SNP-exposure effect sizes, using a conditional log-likelihood approach. Note that this estimate is unbiased but potentially has a high degree of variance.
https://amandaforde.github.io/mr.simss/articles/perform-MR-SimSS.html
for illustration of the use of est_lambda with a toy data set and
https://amandaforde.github.io/mr.simss/articles/derive-MR-SimSS.html for
the theoretical derivation of this method based on a conditional
log-likelihood approach for estimating lambda.