Authors’ response: Associations of obesity and circulating insulin and glucose with breast cancer risk

We thank Tan and colleagues for their careful reading of our manuscript.¹ As suggested, we performed two separate analyses for fasting insulin using betas from genome-wide association studies (GWAS) of fasting insulin, either with or without the adjustment of body mass index (BMI). Both analyses yielded consistent results for the association between genetically predicted fasting insulin and breast cancer risk, similar to our original results (Table 1).

BMI is usually adjusted in GWAS for waist- hip ratio (WHR).^2,3 Also, measured BMI is adjusted in most epidemiological studies in order to assess the association of WHR with health outcomes independent of BMI. Therefore, we used betas from GWAS for WHR with an adjustment for BMI as the weights in our Mendelian randomization (MR) analysis. This was described clearly in our original report. Our analysis showed that the inverse association between genetically predicted WHR and breast cancer risk is evident at specified BMI.

The possibility of horizontal pleiotropic effects is a major concern in MR analyses. To reduce their possible influence on our results, we performed analyses that excluded single nucleotide polymorphisms (SNPs) with clear evidence of pleiotropic effects. We understand that such pruning could possibly remove variants that are in the same causal pathway with the risk of breast cancer, affecting the strength and validity of study instruments. Therefore, we presented results from analyses using the instruments that either included or excluded pleiotropic SNPs in our original report. Results from both analyses were very similar for obesity-related traits, indicating that the potential bias raised by Tan and colleagues should not be a major concern. Furthermore, our analyses could provide additional insight into breast cancer aetiology and biology. For example, after removing SNPs associated with BMI and WHR, we showed that insulin-related traits might indeed be associated with breast cancer risk via pathways other than obesity.

We agree that for the two-sample MR analysis to be valid, the two samples should ideally be from the same underlying population. Therefore, we performed analyses only among European descendants in our original report, using instruments derived from GWAS conducted among European descendants or predominantly European descendants. Typically, sex differences are small for the large majority of non-sex-specific associations identified in GWAS. The estimated association effect size could be less accurate in sex-specific analyses because of a smaller sample size. As suggested, we present the results from analyses using instruments constructed with betas from GWAS of BMI and WHR_{adj BMI} conducted among women of European ancestry or predominantly European ancestry (Table 1). Because not all of the BMI- and WHR_{adj BMI}-associated SNPs achieved an association P-value of 5 × 10^–8 in female-specific GWAS, we conducted a separate MR analysis using significantly associated SNPs after Bonferroni correction. We observed consistent results, similar to those presented in our original report.

Table 1.

Associations of genetically predicted obesity and fasting insulin with breast cancer risk: updated results from Mendelian randomization analyses

		All SNPs					After exclusion of pleiotropic SNPs
Traits	nSNP	ORa	95% CI	P	Phet	nSNP	ORa	95% CI	P	Phet
Fasting insulin
Originally reported	18	1.16	0.96 − 1.41	0.128	0.939	10	1.71	1.26 − 2.31	5.09 × 10−4	0.442
No BMI adjustment	18	1.19	0.96 − 1.47	0.120	0.859	10	1.74	1.29 − 2.35	2.60 × 10−4	0.461
BMI-adjusted	18	1.24	0.99 − 1.54	0.059	0.974	10	1.76	1.27 − 2.45	7.30 × 10−4	0.493
BMI
Originally reported	166	0.76	0.72 − 0.80	5.25 × 10−22	0.042	162	0.77	0.73 − 0.82	5.05 × 10−19	0.086
Using female-specific βs	166	0.76	0.72 − 0.80	2.92 × 10−23	0.047	162	0.77	0.73 − 0.82	7.43 × 10−20	0.070
Using significant female-specific βs	146b	0.75	0.71 − 0.80	2.31 × 10−23	0.081	143b	0.77	0.73 − 0.81	7.46 × 10−20	0.120
WHRadj BMI
Originally reported	54	0.85	0.79 − 0.91	4.48 × 10−6	0.132	50	0.85	0.79 − 0.91	9.22 × 10−6	0.152
Using female-specific βs	54	0.88	0.83 − 0.93	1.66 × 10−5	0.102	50	0.87	0.82 − 0.93	1.29 × 10−5	0.125
Using significant female-specific βs	53b	0.88	0.83 − 0.93	1.82 × 10−5	0.109	49b	0.87	0.82 − 0.93	1.42 × 10−5	0.135

^aOdds ratios (ORs) were calculated with respect to one-SD change in exposure of interest.

^bExcluding SNPs showing an non-significant association with BMI or WHR_{adj BMI} after Bonferroni correction in GWAS among women.

We applaud Tan and colleagues for promoting rigorous methodology in MR analyses and, theoretically, the biases they discussed could be a concern in some MR analyses. However, these biases do not affect our study results; thus, what we reported initially remains valid.