Introduction

Obesity is a major public health concern with well-established risk-increasing effects oncardiometabolic diseases1. Given its high prevalence worldwide1, investigating if obesity influences additional diseases is relevant forunderstanding the range of its health consequences.

Psychiatric disorders are one of the main causes of years lived with disabilityglobally2. There is considerable evidence suggesting an associationbetween obesity and psychiatric disorders, including depression3,4,bipolar disorder5,6 and schizophrenia7,8. Reversecausality could be one of the explanations for this association because increase in bodyweight is a side effects of some anti-psychotic medications6,9. Besidestreatment, biological, psychological, and sociodemographic variables related topsychiatric disorders may affect lifestyle factors such as physical activity and dietand thus lead to obesity10,11.

Cohort studies provide support that obesity both predicts and can be predicted bydepression3,12,13 and bipolar disorder14. Moreover,higher frequencies of obesity measures were reported in first episode and/ormedication-naive schizophrenia patients15,16, although notuniversally17,18. A recent instrumental variable analysis supportedthe hypothesis that obesity influences depression19.

Most of the evidence regarding the association of obesity with psychiatric disorderscomes from observational studies, which present several limitations for causalinference, including residual confounding, measurement error and reverse causation20,21. Using genetic variants as instrumental variables for modifiabledisease risk factors or exposures (ie, Mendelian randomization) contributes to overcomesuch limitations given Mendel’s laws, the fact that germline genetic variantsare determined at conception and the general lack of association between geneticvariants and common confounders of observational associations21,22,23.

Mendelian randomization relies on assuming that any association between the geneticinstrument(s) and the health outcome is entirely mediated by the exposure (ie, verticalpleiotropy)21,22,23. However, the polygenic nature of complextraits increases the probability of existing biological links betweenexposure-associated variants and the outcome not mediated by the exposure itself (ie,horizontal pleiotropy). Indeed, the largest genome-wide association study (GWAS) of bodymass index (BMI) to date identified variants implicated in biological pathways relatedto the central nervous system24, thus potentially complicating Mendelianrandomization involving BMI and psychiatric disorders.

Previous Mendelian studies on this topic yielded inconsistent findings. However, suchstudies have some limitations, including using only FTO and MC4R variantsas genetic instruments25,26, both of which are pleiotropic loci27,28 that possibly violate Mendelian randomization assumptions25,29,30. Another limitation is that the studies were performed in thesingle-sample context25,26,29,31,32, which renders the results proneto bias towards the observational (and possibly confounded) estimate if the geneticinstrument is weakly associated with BMI33,34.

Currently, many GWAS consortia make summary-level results freely available. Such data canbe used to obtain causal effect estimates based on multiple single nucleotidepolymorphisms (SNPs) using the inverse-variance weighting (IVW) method35.This is likely to improve statistical power because SNP-exposure and SNP-outcomeassociations are typically estimated in large samples. Moreover, the recently proposedMR-Egger regression36 and weighted median37 methods can beused in summary data Mendelian randomization investigations as sensitivity analyses todetect and (at least partially) account for violations of instrumental variableassumptions. MR-Egger causal effect estimates are consistent even if all instruments areinvalid, as long as SNP-exposure and direct (ie, not solely mediated by the exposure)SNP-outcome associations are independent. The weighted median requires that at least 50%of the information come from valid instruments; if this is satisfied, its causal effectestimate is consistent regardless of the type of horizontal pleiotropy in the invalidinstruments (see Materials and Methods section for details). We aimed at estimating thecausal effect of BMI on three psychiatric traits using these three Mendelianrandomization methods in a two-sample framework.

Results

Estimation of causal effects of BMI on schizophrenia using Mendelianrandomization

A flowchart depicting the selection process of the genetic variants used inMendelian randomization analysis is shown in Fig. 1.Table 1 describes each psychiatric dataset. SNP-BMIF-statistics in the Genetic Investigation of Anthropometric Traits (GIANT)consortium dataset were similar across the variants available in eachpsychiatric dataset, with mean and median values about 56 and 34, respectively.However, approximate SNP-BMI F-statistics (ie, instrument strength) inpsychiatric datasets were considerably different: mean and median values were~3 and ~2, respectively, for bipolar and major depressivedisorders, and 14.4 and 9.0 for schizophrenia. Tetrachoric correlations betweenGIANT and each PGC datasets were very close to zero, suggesting that there was,at most, little sample overlap (see Materials and Methods for details).

Table 1 Characteristics of each psychiatric disorder dataset.
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Figure 1
figure 1

Flowchart depicting the selection process of the genetic instruments for bodymass index.

BMI: Body mass index. SNP: Single nucleotide polymorphism. GIANT: GeneticInvestigation of Anthropometric Traits consortium. PGC: Psychiatric GenomicsConsortium.

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Mendelian randomization results for each psychiatric disorder are shown in Table 2. For bipolar disorder, odds ratio of 0.90 (95% CI:0.69; 1.16) and 0.88 (95% CI: 0.62; 1.25) per 1-standard deviation (SD)increment in BMI were obtained using the IVW and weighted median methods. Theseestimates were directionally inconsistent with regular and SimulationExtrapolation (SIMEX)-corrected MR-Egger estimates of 1.23 (95% CI: 0.65; 2.31)and 1.26 (95% CI: 0.63; 2.52), respectively. Schizophrenia presented a similarpattern, with IVW and weighted median odds ratio of 0.98 (0.80; 1.19) and 0.93(0.78; 1.11), respectively, while regular and SIMEX-corrected MR-Egger estimateswere 1.41 (0.87; 2.27) and 1.46 (0.86; 2.47), respectively. Regarding majordepressive disorder, all methods yielded directionally consistent estimates:IVW, weighted median, regular and SIMEX-corrected MR regression odds ratio were(respectively) 1.15 (95% CI: 0.92; 1.44), 1.40 (95% CI: 1.03; 1.90), 1.28 (95%CI: 0.74; 2.24) and 1.33 (95% CI: 0.72; 2.47). (which measures regression dilution bias in MR-Egger regression)38 was 88.6%, 88.2% and 87.9% for bipolar disorder, major depressive disorderand schizophrenia, respectively, suggesting an attenuation of the causal effectestimates of about 12% due to regression dilution bias (which can be seencomparing regular and SIMEX-corrected MR-Egger results). All MR-Egger interceptswere close to 1.00 and none achieved conventional statistical significancelevels, suggesting that there was no strong directional horizontal pleiotropyunder the InSIDE assumption.

Table 2 Odds ratio (OR) estimates of bipolar disorder, major depressive disorder(MDD) and schizophrenia per 1-standard deviation increment in BMI based on IVW,MR-Egger and weighted median approaches.
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Sensitivity analyses removing influential instruments and within subgroupsof biological categories

SNPs were classified as influential using statistical tests based on studentizedresiduals and Cook’s distance (see Materials and Methods for details).The following SNPs – rs number (gene locus) – were classified asinfluential: rs4256980 (TRIM66), rs12401738 (FUBP1), rs9925964(KAT8), rs11191560 (NT5C2), rs11057405 (CLIP1) inbipolar disorder; rs13107325 (SLC39A8), rs11191560 (NT5C2),rs9400239 (FOXO3) and rs4787491 (INO80E) in schizophrenia; andrs571312 (MC4R), rs1462433 (HNF4G), rs6785875 (FHIT) andrs11191560 (NT5C2) in major depressive disorder (Fig.2). Removing influential SNPs made virtually no difference in bipolardisorder results. Regarding schizophrenia, removing influential SNPs attenuated(and increased precision) regular and SIMEX-corrected (respectively) MR-Eggerregression odds ratio to 1.22 (95% CI: 0.83; 1.81) and 1.25 (95% CI: 0.81; 1.92)per 1-SD increment in BMI. The magnitude of all major depressive disorderestimates increased, ranging from 1.25 (95% CI: 1.02; 1.52) to 1.60 (95% CI:0.93; 2.75) using IVW and SIMEX-correct MR-Egger, respectively.

Figure 2
figure 2

SNP-BMI and SNP-psychiatric associations for up to 97 BMI-associated SNPsidentified by the GIANT consortium.

Influential SNPs were marked with an “X” and labelled usingthe correspondent gene locus. SNPs were classified as influential usingstatistical tests based on studentized residuals and Cook’s distance(see Materials and Methods for details). Left column: scatter plots ofassociations between SNPs and (a) bipolar disorder (b,d,c)schizophrenia and (e) major depressive disorder (MDD) against SNP-BMIassociations. IVW, MR-Egger and weighted median estimates are indicated insolid, dashed and grey lines, respectively. Right column: funnel plots ofthe absolute value of the t-statistic of SNP-BMI association (ie,instrument strength) against individual-SNP ratio estimates in log oddsratio of (b) bipolar disorder, (d) major depressive disorderand (f) schizophrenia. IVW, MR-Egger and weighted median estimatesare indicated in solid, dashed and grey lines, respectively.

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When dividing SNPs into neuronal-related vs. non-neuronal-related subgroups, theresults were generally similar between subgroups (Table3). Regarding bipolar disorder, in all cases the IVW and weightedmedian estimates were directionally inconsistent with MR-Egger results. Regularand SIMXEX-corrected MR-Egger odds ratio estimates were weaker in theneuronal-related (1.19 [95% CI: 0.54; 2.60] and 1.19 [0.51; 2.75] per 1-SDincrement in BMI, respectively) than in the remaining SNPs (1.33 [95% CI: 0.38;4.68] and 1.42 [95% CI: 0.32; 6.34], respectively). This difference was moreevident after excluding influential SNPs, but in both cases confidence intervalsof one subgroup largely included the point estimate of the other subgroup. Inschizophrenia, the odds ratio estimates were also inconsistent, especially inthe non-neuronal subgroup. Again, MR-Egger estimates were stronger in thenon-neuronal subgroup, although such difference was attenuated after excludinginfluential SNPs and confidence intervals were wide. All major depressivedisorder estimates were directionally consistent and similar betweenneuronal-related and non-neuronal subgroups. Excluding influential SNPsincreased the estimates (especially IVW and MR-Egger ones).

Table 3 Odds ratio (OR) estimates of bipolar disorder, major depressive disorder andschizophrenia per 1- standard deviation increment in BMI based on IVW, MR-Eggerand weighted median approaches, within independent subgroups of SNPs definedusing biological criteria.
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IVW estimates for each outcome when SNPs belonging to a given biological categorywere removed are shown in Table 4. Regarding bipolardisorder, all but one of the IVW odds ratio estimates were directionallyconsistent, ranging from 0.75 (95% CI: 0.55; 1.03) to 0.98 (95% CI: 0.75; 1.28)per 1-SD increment in BMI. The exception was an estimate of 1.06 (95% CI: 0.81;1.41), obtained after excluding SNPs prioritized by annotation tools, but thatdo not belong to a well-defined biological category (referred to as an“unspecified” biological category). Schizophrenia estimates weremore heterogeneous, with 10 being smaller than 1 (ranging from 0.92 to 0.99) andsix being larger than or equal to 1 (ranging from 1.00 to 1.04). Conversely, allmajor depressive disorder odds ratio estimates were directionally consistent andranged from 1.06 (95% CI: 0.81; 1.39) to 1.29 (95% CI: 1.01; 1.64).

Table 4 Odds ratio (OR) estimates of bipolar disorder, major depressive disorder(MDD) and schizophrenia per 1- standard deviation increment in BMI based on theIVW approach, within subgroups of SNPs excluding one biological category at atime.
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Sensitivity analyses based on random effects meta-regression

Values of the meta-analytical measures of heterogeneityτ2 and I2(not ) in the individual-SNP ratio estimates were0.45 and 29.1% (P = 0.005) for bipolar disorder, 0.49 and68.8%(P = 9.9 × 10−24)for schizophrenia, and 0.20 and 18.4% (P = 0.073) formajor depressive disorder. In a random effects meta-regression model, includingan indicator variable of influentiality status reducedτ2 and I2values of major depressive disorder ratio estimates to 0.14 and 13.4%,respectively, with an adjusted-R2 value (which indicates theamount of heterogeneity explained by the moderators) of 29.3%(P = 0.028), and the test of residual between-instrumentsheterogeneity yielded P = 0.152. Regarding bipolardisorder and schizophrenia, the same procedure had a substantially smallerinfluence, with adjusted-R2 values of 1.1%(P = 0.015; test of residual between-study heterogeneityP = 2.4 × 10−23)and 2.4% (P = 0.193; test of residual between-studyheterogeneity P = 0.006), respectively. When an indicatorof belonging to a neuronal-related biological category was used instead ofinfluentiality status, all adjusted-R2 values were 0%.

The results of the forward selection process of biological moderators ofindividual-SNP ratio estimates using random effects meta-regression are shown inSupplementary Table S1. Adoptinga P ≥ 0.05 stopping criterion resulted in the selectionof two moderators for each outcome: unspecified and endocytosis/exocytosiscategories for bipolar disorder; neurotransmission and lipid-related forschizophrenia; and lipid-related and glucose homeostasis/diabetes for majordepressive disorder. Adjusted-R2 and residualI2 values for the selected moderators togetherwere 32.9% and 21.5% for bipolar disorder, 8.3% and 66.7% for schizophrenia and68.8% and 6.5% for major depressive disorder. Mendelian randomization odds ratioestimates excluding each and both of the selected biological categories areshown in Supplementary Table S2.Again, only major depressive disorder presented directionally consistentestimates in all Mendelian randomization methods and SNP subgroups.

Discussion

In the present study, we evaluated the association between BMI-associated SNPs andthree psychiatric disorders by Mendelian randomization using summary-level data.Only major depressive disorder presented consistent causal effect estimates usingthe three Mendelian randomization methods and in all sensitivity analyses. The factthat removing influential variants increased, rather than attenuated, the odds ratioestimates is also reassuring because it suggests that the true causal effect mightbe greater than that estimated using all variants simultaneously. However, theoverall statistical evidence for any meaningful associations was weak.

Our findings suggest that the commonly positive association between obesity andpsychiatric disorders reported in observational studies3,4,5,6,7,8 may not correspond to a causal risk-increasing effect (especially for bipolardisorder and schizophrenia). Such associations may have been driven by phenomenasuch as residual confounding, due to common causes imperfectly accounted for atstudy design and/or analysis; or reverse causation, due to, for example, sideeffects of anti-psychotic medication. Even though associations of obesity with laterdepression and bipolar disorder have been reported in cohort studies3,12,13,14, it is still possible that reverse causation occurred dueto effects (not related to medication usage) of pre-clinical psychiatric disorderson weight gain if such effects exist. Effects of pre-clinical psychiatric diseaseshave been recently detected in a longitudinal study where genetic predisposition toschizophrenia was associated with non-participation over time39.

Mendelian randomization studies on the association between obesity and psychiatricdisorders are scarce, with no studies for bipolar disorders and schizophrenia. Apositive association between BMI instrumented using the FTO variant rs1421085and common mental disorders was detected in the British Whitehall II study25. However, adiposity measures instrumented by FTO andMC4R variants were inversely associated with psychological distress in amuch larger Danish cohort26. These findings must be interpretedcautiously since there is evidence that FTO27 andMC4R28 are pleiotropic, in accordance with suggestionsthat FTO might not be a valid instrument for BMI when mental disorders arethe outcome25,29. In our study, the MC4R variant rs571312(and others, but not FTO) was identified as an influential (and potentiallyinvalid) instrument in major depressive disorder analysis, but not in the remainingoutcomes. In the Young Finns cohort, BMI instrumented by a 31-SNP allele score waspositively associated with depressive symptoms31. However, two otherstudies using a similar genetic instrument failed to detect any association withdepression-related outcomes, with risk-decreasing point estimates29,32. Our study extends Mendelian randomization analysis of the causal effects of BMIon psychiatric outcomes by using the more recently described set of 97BMI-associated variants.

Obesity and psychiatric disorders may share several dysregulated physiologicalpathways, including inflammation40. Elevated inflammation is apotential cause of psychiatric disorders41 since positiveassociations between inflammatory markers and later psychiatric-related outcomeshave been reported13,41. Given the well-defined role of obesity ininflammation, the later could be a mediator between obesity and psychiatricdisorders. Indeed, a study among older English adults reported that C-reactiveprotein mediated about 20% of the longitudinal association between obesity anddepressive symptoms13. However, there are only a few longitudinalstudies evaluating this association41 and a large Mendelianrandomization study did not suggest a causal association between C-reactive proteinand depression42. The latter (assuming that higher BMI raisesC-reactive protein levels) is in accordance with our inconsistent findings regardingthe association of genetically elevated BMI with bipolar disorder and schizophreniaand the weak statistical evidence regarding the association with depression.Nevertheless, further studies are required to understand the role of inflammationand other biological pathways shared by obesity and psychiatric disorders in thelatter.

European ancestry was predominant in all datasets, which increases the plausibilityof the assumption that the two datasets are samples from the same or comparablepopulations. Regarding power, two-sample Mendelian randomization power depends moreon the precision of SNP-outcome than SNP-exposure associations35.SNP-outcome associations used in this study were estimated in relatively smallsamples, except for schizophrenia. Sample size differences resulted in considerablydifferent approximate SNP-BMI F-statistics across psychiatric datasets. AlthoughSNP-BMI associations used in the analyses were obtained from GIANT, this differencesuggests that, for bipolar and major depressive disorders, SNP-outcome associationswere too imprecise, which is likely to decrease power. Indeed, in spite of theconsistency across Mendelian randomization methods and sensitivity analyses, causaleffect estimates for major depressive disorder – especially when usingMR-Egger – had wide confidence intervals and in some cases failed to achieveconventional statistical significance levels. On the other hand, given theaforementioned consistency and the fact that sensitivity analyses suggested evenstronger causal effect estimates, it is possible that there will be adequatestatistical power to detect causal effects once more precise SNP-major depressivedisorder estimates are available.

It is impossible to prove empirically whether Mendelian randomization results mostlyreflect causal effects of the exposure or violations of instrumental variableassumptions. In the present study, three Mendelian randomization methods –each with different assumptions regarding horizontal pleiotropy – were used,and all of them were consistent regarding major depressive disorder, but not whenanalyzing bipolar disorder and shcizophrenia. Moreover, both MR-Egger regression andthe weighted median approach (which are more robust against bias due to horizontalpleiotropy than IVW) point estimates were stronger than the IVW one. It was alsoreassuring that major depressive disorder presented the smallest heterogeneity inindividual-SNP ratio estimates measured using the conventionalI2 statistic, and that excluding four influential SNPsincreased the magnitude of the causal effect estimates and further attenuated theI2 statistic.

In general, our findings do not corroborate the notion that BMI has a causal effecton bipolar disorder or schizophrenia. Regarding major depressive disorder, althoughthe point estimates were consistent across a range of analyses, the overallstatistical evidence was weak. Re-addressing this research question onceSNP-depression associations from larger GWAS become available would be warranted toobtain more precise Mendelian randomization estimates (especially with respect toMR-Egger regression). Given the high prevalence of both obesity and depressionworldwide, understanding the mechanisms underlying associations between BMI anddepression, with identification and quantification of causal effects, is of publichealth relevance. Analyses involving schizophrenia were less prone to power issuesbecause SNP-schizophrenia associations were estimated in a relatively large sample.Bipolar disorder, similarly to major depressive disorder, require furtherinvestigation once more precise SNP-outcome associations are available.

Materials and Methods

Data sources

The final datasets were provided in Supplementary Tables S3–S6.

Body mass index

Locke and colleagues’, under the GIANT consortium, identified 97BMI-associated single nucleotide polymorphisms (SNPs)24.SNP-BMI linear regression coefficients and standard error estimates wereobtained from an analysis of up to 322,154 European ancestry individualsassuming additive genetic effects (https://www.broadinstitute.org/collaboration/giant/index.php/GIANT_consortium_data_files).

The outcome was obtained by applying an inverse normal transformation to BMIresiduals on age and age2 (in addition to relevantstudy-specific covariates such as ancestry-informative principalcomponents). In studies of unrelated individuals, residuals were calculatedwithin sex and (when relevant) case/control strata. In family studies,residuals were sex-adjusted rather than sex-specific.

To investigate the biological function of the 97 BMI-associated variants,Locke and colleagues assigned, for each SNP, all genes within 500 kband r2 > 0.2. For variants withoutgenes mapping to this interval, the nearest gene was used. This resulted in405 genes, which were annotated based on a manual literature review usingseveral venues. Through this process, those 405 genes were manually curatedinto 25 biological categories containing at least three genes, to which eachof the 97 BMI-associated variants were assigned (see Locke andcolleagues24 for details). We only considered the 16categories that contained at least nine (~10%) SNPs (Supplementary Table 5S). Those categoriessubstantially overlapped: four of them (“neuronal developmentalprocesses”, “neurotransmission”,“hypothalamic expression and regulatory function” and“neuronal expression”) were neuronal-related and 62 SNPswere present in two or more categories. It is also noteworthy that thosecategories were aimed at providing insights into the biological processesimplicated in obesity based on genetic associations rather than a detailedbiological description of each SNP. Such biological categorizations are ofapproximate and provisional nature, changing over time as new dataemerges43. The biological categories were used in thepresent work for sensitivity analyses purposes only (as described in the“Statistical analyses” section).

Psychiatric disorders

Log odds ratio and standard error estimates of SNPs-psychiatric disordersassociations were obtained from the Psychiatric Genomics Consortium (PGC)(http://www.med.unc.edu/pgc/downloads), which performedlogistic regression adjusting for ancestry-informative principal componentsand assuming an additive effect.

Bipolar disorder

Sklar and colleagues’ – under the PGC Bipolar DisorderWorking Group – performed SNP-bipolar disorder associations on7,481 cases and 9,250 controls of European descent44. All97 BMI-associated SNPs were available. After harmonizing effect andnon-effect alleles between SNP-bipolar disorder and SNP-BMI datasets,the Pearson correlation coefficient between effect allele frequencieswas > 0.999.

Major depressive disorder

SNP-major depressive disorder associations correspond to the discoverystage analysis of Ripke and colleagues under the PGC Major DepressiveDisorder Working Group in 9,240 cases and 9,519 controls of Europeanancestry45.

Only 62 BMI-associated SNPs were available. Proxies for missing variantswere identified using the SNP Annotation and Proxy Search tool (http://www.broadinstitute.org/mpg/snap/ldsearch.php). Aproxy was defined as a genetic variant within 500 kb of the index SNPand in high linkage disequilibrium(r2 > 0.8) with it. If therewas more than one proxy available for the same index SNP, the variantwith the higher r2 was selected. Using 1000Genomes Pilot 1 (CEU population) as the reference panel, 26 proxiesavailable in both SNP-BMI and SNP-major depressive disorder datasetswere identified. An additional search using HapMap release 22 (CEUpopulation) as the reference panel yielded two additional proxies, thustotalizing 28 proxy variants and 90 BMI-associated SNPs. Afterharmonization, the correlation between effect allele frequencies was0.989.

Schizophrenia

Ripke and colleagues performed SNP-schizophrenia associations under thePGC Schizophrenia Working Group in 34,241 cases and 45,604ancestry-matched controls (most of European ancestry), and threefamily-based studies comprising 1,235 parent affected-offspring Europeanancestry trios46. 96 BMI-associated SNPs were available(effect allele frequencies were unavailable).

Statistical analysis

In Mendelian randomization analyses, all BMI-associated SNPs available for eachpsychiatric disorder were used (Table 1 and Supplementary Tables S3–S6).The following methods were used:

  1. 1

    IVW method, consisting of a linear regression of SNP-outcome (dependentvariable) on SNP-exposure coefficients (independent variable), weightingby the inverse of the squared SNP-outcome standard errors. The interceptis constrained at zero, which follows from the assumption thatSNP-outcome associations are entirely mediated by the exposure35. This corresponds to a fixed effects meta-analysis ofthe ratio estimates from each genetic variant.

  2. 2

    MR-Egger regression, which differs from the IVW method because theintercept is not constrained. This yields a causal effect estimaterobust against horizontal pleiotropy under the InSIDE (InstrumentStrength Independent on Direct Effect) assumption, which requires thatthe SNP-exposure and direct SNP-outcome associations are independent.The intercept provides a test for directional horizontal pleiotropy36.

    Both IVW and MR-Egger regression (as currently implemented) make theso-called NOME (No Measurement Error) assumption. That is, they assumethat the SNP-exposure (in this case BMI) association estimate is equalto the true association. NOME violations attenuate the causal effectestimate towards the null in two-sample MR studies, and MR-Eggerregression has been shown to be more prone to such attenuation than IVW.Moreover, NOME violations might either inflate or attenuate the MR-Eggerintercept (depending on presence of and directional consistency betweenthe intercept and the causal effect estimate). A modified version of theI2 statistic – – has been proposed to quantifyregression dilution in MR-Egger regression due to NOME violations, whichcan adjusted for using the SIMEX method38.

  3. 3

    Weighted median method, which provides a valid causal estimate if atleast 50% of the weights (ie, the “information” thateach genetic instrument contributes to the estimate, which depends onthe precision of individual estimates) come from valid instruments,regardless of whether or not horizontal pleiotropic effects of theremaining variants respect the InSIDE assumption37.

Point estimates and standard errors were calculated for the IVW, MR-Egger andweighted median methods using the code provided by Bowden et al.36,37. Since SNP-BMI associations were estimated usinginverse-transformed BMI, the Mendelian randomization estimates can beinterpreted as the odds ratio per 1-SD increment in BMI.

Sensitivity analyses

Sample overlap between GIANT and PGC datasets can bias causal effect estimatesfrom Mendelian randomization towards the observational (and possibly confounded)estimate33,34. We evaluated the issue of sample overlapindirectly using a method developed for meta-analysis of dependent“omic” datasets47. Briefly, assuming that thenull hypothesis is true for most of the genome, correlations between datasetsregarding Z-statistics of the SNP-phenotype associations would be expected to beclose to zero if there is no sample overlap. To improve robustness against“contamination” due to true signals (ie, common geneticeffects), tetrachoric correlations for each pair of BMI-PGC datasets werecomputed using Z-statistics truncated into two categories: 1 ifZ > 0 or 0 if Z ≤ 0.

Mendelian randomization analyses were also performed within SNP subgroups ofbiological function: neuronal-related (comprising the “neuronaldevelopmental processes”, “neurotransmission”,“hypothalamic expression and regulatory function” and“neuronal expression” categories); and non-neuronal (comprisingthe remaining categories). Consistency among different biological subgroupswould argue against the role of horizontal pleiotropy in the results.

To evaluate if the results were substantially driven by a few instruments, theanalyses were repeated excluding influential SNPs. A SNP was classified asinfluential if at least one of two tests of influence (based on studentizedresiduals and Cook’s distance) yielded aP-value < 0.05. These were calculated separately for IVW orMR-Egger regression, but the same SNPs were classified as influential usingeither Mendelian randomization method. The null distributions of these testswere: Student’s t-distribution with degrees of freedom equal to thenumber of SNPs minus 2, for studentized residuals; or the F-statistic with jointdegrees of freedom equal to (1, number of SNPs minus 1) (for IVW) or (1, numberof SNPs minus 2) (for MR-Egger regression), for Cook’s distance48.

In exploratory analysis aimed at identifying factors associated with horizontalpleiotropy, individual-SNP ratio estimates (in this study, per-allele log oddsof a psychiatric disorder divided by the correspondent per-allele change ininverse-transformed BMI residuals units) were used to calculatebetween-instrument heterogeneity, which corresponds to horizontal pleiotropy inthe Mendelian randomization context49. Standard errors wereobtained using the delta method50. Random effects meta-regressionwas used to evaluate how much of between-instrument heterogeneity (and,therefore, horizontal pleiotropy) can be explained by influentiality status andbiological categories. For the latter, an additional analysis using a forwardselection process was performed to identify categories that explainheterogeneity. Indicators of belonging to a given biological category were addedone at a time based on the largest reduction inτ2, until no additional covariates reachedP < 5%.

Two additional sensitivity analyses were performed: (i) IVW estimates withinsubgroups of SNPs excluding one biological category at a time; (ii) estimationof causal effects using the three Mendelian randomization methods after removingSNPs belonging to the biological categories identified in the forward selectionprocess described above.

Analyses were performed using R 3.2.4 (www.r-project.org).

Additional Information

How to cite this article: Hartwig, F. P. et al. Body mass index andpsychiatric disorders: a Mendelian randomization study. Sci. Rep.6, 32730; doi: 10.1038/srep32730 (2016).