• autoimmune diseases
• autoimmunity
• treatment

We are pleased that our article on the role of linoleic acid (LA) in autoimmune disorders is of interest to readers. However, regarding the methodological issues raised by Lee,1 several points need to be considered and clarified.

First, Mendelian randomisation (MR) requires stringent assumptions, that is, the genetic instruments are associated with the exposure, are not linked with the outcomes other than via effects on the exposure and no confounders of the associations of the genetic instruments with the outcome exist.2 We agree that weak instruments which violate these assumptions would lead to biased associations. As such, we are very cautious in the selection of genetic instruments. Specifically, we used the most significant three uncorrelated (r²<0.01) single-nucleotide polymorphisms (SNPs) from a genome-wide association study (GWAS),3 as previously,4 and replicated using uncorrelated SNPs in genes relevant to the metabolism of n−6 PUFA, that is, FADS1, FADS2 and NTAN1.5 To ensure the SNPs predicting LA were not confounded, we assessed their Bonferroni corrected associations with key confounders, that is, socioeconomic position (job and Townsend Index) and lifestyle factors (alcohol and smoking), in the UK Biobank. To ensure the selected SNPs were solely linked with autoimmune disorders via effects on LA (no pleiotropy), we checked using three comprehensive curated genetic cross-reference systems, Ensembl (http://www.ensembl.org/index.html), the GWAS catalogue (https://www.ebi.ac.uk/gwas/) and PhenoScanner (www.phenoscanner.medschl.cam.ac.uk), which provide all well-established known associations of SNPs with their phenotypes, including subgenome-wide associations. We also used MR-PRESSO (MR Egger, Mendelian Randomization Pleiotropy RESidual Sum and Outlier) and multivariable MR to identify and correct for unknown potential pleiotropy. Using these genetic instruments, we validated that the effects on lipid profile were consistent with the well-established cholesterol-lowering effect of LA.6

Second, in the letter Lee makes a link between “limited numbers of IVs” and “bias from weak instruments”1; however, they are not equivalent. Instead, there is a “bias-variance trade-off for the number of instruments used in IV estimation”.7 Specifically, at a fixed mean F-statistic, increasing the number of instruments will lower the variance of the estimate (increase the precision) but at the same time may increase the possibility of bias from weak instruments.7 The validity of the instrument is mainly based on the compliance with the MR assumptions rather than the number of instruments available. A single SNP, if validated, can also be used as an instrument in an MR study,8 as has been the case in previous influential MR studies.9 10 Lee did not provide any information about checking the instruments for associations with potential confounders, such as socioeconomic position, smoking and alcohol use, or checking for pleiotropic associations, in addition to sensitivity analysis using different analytic methods.1

We agree that using more valid instruments could increase the power of an MR study. However, we are unclear as to the validity of the use of 75 SNPs for LA as mentioned by Lee.1 The 173 SNPs associated with LA at the genome-wide significance are highly correlated.3 We cannot identify 75 independent SNPs meeting the selection criteria given by Lee (“linkage disequilibrium R² of 0.001, clumping distance of 10 000 kb, and a p-value threshold of 5.00E−08”)1; those criteria only give the three SNPs providing the same information as what we used. However, if we apply a method suitable for correlated SNPs11 and use all 167 SNPs available at genome-wide significance, we get an estimate very similar to that in our original letter (OR 0.97, 95% CI 0.95 to 0.98, p<0.001).