Bidirectional Mendelian randomization analysis
The study design was shown in Figure 1. The bidirectional MR analysis was based on summary-level data from the hitherto largest Asian GWAS. Summarized data were available from two studies with a total of more than 150,000 participants in 5 Japanese cohorts [including the BioBank Japan (BBJ) Project, the Japan Public Health Center-based Prospective Study (JPHC), the Tohoku Medical Megabank Project (TMM), the Japan Multi-institutional Collaborative Cohort (J-MICC) Study, and the Kita-Nagoya Genomic Epidemiology (KING) Study] [10, 11]. Data were downloaded from the National Bioscience Database Center (NBDC) Human Database (https://humandbs.biosciencedbc.jp/en/).
Forward Mendelian randomization analysis
To test whether higher BMI is the cause of elevated serum UA, we first extracted the summary statistics for the BMI-related SNPs in the largest Asian GWAS among 173,430 Japanese participants (including 158,284 in the BBJ Project and 15,146 in the JPHC and the TMM Project) . This study used rank-based inverse-normal transformed BMI as the dependent variable and identified 83 independent SNPs which were significantly associated with BMI at P < 5 × 10-8. Then, the effect estimates [β and standard error (SE)] for the associations of these SNPs with UA were derived from a genome-wide meta-analysis based on 3 Japanese cohorts (n=121,745), including 10,621 participants in the J-MICC Study, 2,095 participants in the KING Study, and 109,029 participants in the BBJ Project . After excluding 7 SNPs with missing estimates in the UA GWAS dataset, the left 76 BMI-associated SNPs were included as the candidate IVs in the forward MR analysis (Table S1).
Reverse Mendelian randomization analysis
To test whether higher serum UA is the cause of elevated BMI, we extracted the summary statistics for the SNP-UA association from the genome-wide meta-analysis among 121,745 Japanese participants mentioned above . This study employed Z-score transformed serum UA as the dependent variable and identified 36 independent SNPs with genome-wide significant association with UA (P < 5 × 10-8). Then, the effect estimates [β and SE] for the associations between these 36 SNPs and BMI were extracted from the results among 158,284 participants in the BBJ project  and included in the reverse MR analysis (Table S3).
Prospective Dongfeng-Tongji (DFTJ) cohort study
The DFTJ cohort is an ongoing prospective study carried out in Shiyan, China. The general information of this cohort has been described previously . Briefly, we recruited 27,009 retired workers in the Dongfeng Motor Corporation (DMC) from September 2008 to June 2010. Additional 14,120 retired workers were recruited into this cohort from April to October 2013. Among the whole population (n=41,129), we excluded the males (n=18,533), females with previous histories of malignant tumors at baseline (n=690), females with regular menstrual cycles at enrollment (n=2,298), females who were younger than 50 years-old and had missing information of menopausal status (n=17) or stopped menstrual cycles following unknown disease reasons (n=73) at baseline. Finally, the left 19,518 postmenopausal women were included in the subsequent analyses. All individuals signed informed consents to participate in this study and this work was approved by the Ethics Committee of Tongji Medical College, Huazhong University of Science and Technology.
Assessment of covariates
Face-to-face questionnaire interviews were carried out to collect information of demographic characteristics (e.g., age, sex, and education levels), lifestyles (e.g., smoking and alcohol drinking status), female reproductive history (e.g., past records of menopause, pregnancy, delivery, abortion and contraception), and medication history [e.g., diuretics, antibiotics, and hormone replacement therapy (HRT) use]. Participants who smoked at least one cigarette per day for more than half a year were defined as current smokers; those who ever smoked and had quitted over half a year were defined as former smokers; otherwise, they were defined as never smokers. Similarly, those who had drunk alcohol more than once a week for at least half a year were defined as current alcohol drinkers; those who had ever drunk but quitted over half a year were defined as former alcohol drinkers; otherwise, they were defined as never drinkers. Both former and current smokers / alcohol drinkers were classified as ever smokers / alcohol drinkers. Marital status was collected as married, unmarried, separated, divorced, and widowed, then grouped into married or single status. Menopause was defined retrospectively as the cessation of menstrual cycles for 12 months occurring spontaneously, which was self-reported at baseline interview. Females with missing menopausal information and females who had stopped menstrual cycles due to disease reasons (all aged 50 years or older) were considered as postmenopausal in the present study. During the physical examination at enrollment, the anthropometric indicators (height, weight, and waist circumference) were measured with participants in light indoor clothing and without shoes or hats. BMI was calculated as weight (kilogram) divided by height (meter) squared (kg/m2).
For each participant, 5 mL peripheral venous blood was collected after overnight fasting into an ethylenediaminetetraacetic acid anticoagulant tube. The serum level of UA was determined by experienced technicians using ARCHITECT Ci8200 automatic analyzer (Abbott Laboratories. Abbott Park, Illinois, USA) in the laboratory of Sinopharm Dongfeng General Hospital.
Ascertainment of incident breast cancer
During the follow-up period, the new incident cases of breast cancer and dates of cancer diagnosis were confirmed by reviewing their medical records or death certificates in DMC’s health care system, which includes five DMC-owned hospitals and the local Center for Disease Control and Prevention. International Classification of Diseases, 10th Revision (ICD-10) was used to classify the incident breast cancer cases (ICD codes C50.000-C50.900). Among the whole 19,518 postmenopausal women, 211 new incident breast cancer cases were identified by the end of 2018.
The bidirectional MR analysis used the summary-level data from two Japanese GWAS to infer the causal direction of association between BMI and serum UA. For forward MR analysis, we considered BMI as the exposure and serum UA as the outcome, and the BMI-related SNPs were used as IVs. In the reverse MR analysis, serum UA was considered as exposure and BMI was considered as the outcome, and the UA-related SNPs were used as IVs. MR analysis relies on 3 presuppositions: (1) the selected IVs are strongly associated with the exposure; (2) the IVs are not related to confounders for exposure-outcome association; (3) IVs only affect the outcome through its effect on exposure. To test the assumption (1), we calculated the F-statistic value for each SNP and excluded weak IVs with F-value < 10. For the assumptions (2) and (3), IVs with significant associations with diseases or traits other than the exposure of interest were excluded by searching PhenoScaner, a curated database of human genotype-phenotype associations . The MR analysis was mainly conducted by using inverse-variance weighted (IVW) method in a fixed effect meta-analysis model , and the sensitivity analyses by using weighted median method  and Mendelian Randomization Pleiotropy Residual Sum and Outlier (MR-PRESSO) method  were further conducted to test the robustness of associations. The MR analyses were performed by “MendelianRandomization” R package.
For the female participants in the DFTJ cohort, their follow-up time was calculated from the date of enrollment to the date of cancer diagnosis, death, loss to follow-up, or end of the follow-up (Dec 31, 2018), whichever came first. We used multivariable Cox proportional hazard models to estimate the hazard ratios (HRs) and 95% confidence intervals (CIs) of breast cancer incidence risk associated with per standard deviation (SD) increment of BMI and serum UA. The proportional hazard assumption was examined by creating a product term of survival time and exposure, and we found no significant deviation from the assumption. We used three models to test the above associations: model 1 was adjusted for age (continuous), smoking and drinking status (ever / never), education level (middle school and below / high school and above), marital status (married / single), and batch to enter the cohort (2008 / 2013); model 2 further included female reproductive histories [parity (continuous), mastitis history (ever / never), age at menopause (continuous)], and medication use [diuretics, antibiotics and HRT use (ever / never)] as the covariates; in model 3, the UA-breast cancer association was additionally adjusted for BMI and the BMI-breast cancer association was additionally adjusted for UA. Participants with missing information of exposure, outcome, or covariates were not included in the corresponding regression analyses. Besides, all participants were classified into four (Q1, Q2, Q3, and Q4) subgroups according to the quartiles of serum UA. When we used participants within the lowest UA quartile (Q1) as the reference group, the HRs and 95%CIs for the other three UA subgroups (Q2, Q3 and Q4) were calculated. To attenuate potential reverse causation, sensitivity analysis was performed by excluding participants diagnosed of breast cancer within the first year of follow-up. The association of waist circumference (another measurement of adiposity) with incident risk of postmenopausal breast cancer was also evaluated.
To further investigate the mediation effect of serum UA on the association between BMI and incident risk of postmenopausal breast cancer, causal mediation analysis was conducted for survival data within counterfactual framework by two statistical models (mediator model and outcome model) [24, 25]. The mediator model referred to generalized linear regression model for the association between BMI and serum level of UA (with adjustment for age, smoking and drinking status, education, batch to enter the cohort, marital status, parity, age at menopause, mastitis history, diuretics, antibiotics, and HRT use), and the outcome model referred to Cox proportional hazard model for the association of BMI and serum UA with breast cancer incidence risk (including BMI, serum UA, and the above covariates). Mediation analyses with and without the exposure-mediator multiplicative interaction term (BMI×UA) were both performed and the estimates of direct and indirect effects didn’t change substantially (data not shown), so we did not further include the interaction term of BMI×UA in the outcome model . The natural indirect effect (NIE) is the effect of BMI on breast cancer mediated by UA, and natural direct effect (NDE) is the effect of BMI on breast cancer independent of UA, which can be estimated on the log hazard ratio scale. On the log hazard ratio scale, total effect (TE) can be decomposed into NIE and NDE: TElog(HR) = NIElog(HR) + NDElog(HR), and the proportion mediated by UA can be calculated as NIElog(HR) / [NIElog(HR) + NDElog(HR)]. Similarly, we explored the mediation role of serum UA on the association between waist circumference and breast cancer incidence risk. The mediation analysis was performed by “%mediation” SAS macro.
The statistical analyses were performed with SAS program (version 9.4, SAS Institute, Carry, NC) and R software (version 3.6.3).