Homogeneity in the association of body mass index with type 2 diabetes across the UK Biobank: A Mendelian randomization study.

BACKGROUND: Lifestyle interventions to reduce body mass index (BMI) are critical public health strategies for type 2 diabetes prevention. While weight loss interventions have shown demonstrable benefit for high-risk and prediabetic individuals, we aimed to determine whether the same benefits apply to those at lower risk. METHODS AND
FINDINGS: We performed a multi-stratum Mendelian randomization study of the effect size of BMI on diabetes odds in 287,394 unrelated individuals of self-reported white British ancestry in the UK Biobank, who were recruited from across the United Kingdom from 2006 to 2010 when they were between the ages of 40 and 69 years. Individuals were stratified on the following diabetes risk factors: BMI, diabetes family history, and genome-wide diabetes polygenic risk score. The main outcome measure was the odds ratio of diabetes per 1-kg/m2 BMI reduction, in the full cohort and in each stratum. Diabetes prevalence increased sharply with BMI, family history of diabetes, and genetic risk. Conversely, predicted risk reduction from weight loss was strikingly similar across BMI and genetic risk categories. Weight loss was predicted to substantially reduce diabetes odds even among lower-risk individuals: for instance, a 1-kg/m2 BMI reduction was associated with a 1.37-fold reduction (95% CI 1.12-1.68) in diabetes odds among non-overweight individuals (BMI < 25 kg/m2) without a family history of diabetes, similar to that in obese individuals (BMI ≥ 30 kg/m2) with a family history (1.21-fold reduction, 95% CI 1.13-1.29). A key limitation of this analysis is that the BMI-altering DNA sequence polymorphisms it studies represent cumulative predisposition over an individual's entire lifetime, and may consequently incorrectly estimate the risk modification potential of weight loss interventions later in life.
CONCLUSIONS: In a population-scale cohort, lower BMI was consistently associated with reduced diabetes risk across BMI, family history, and genetic risk categories, suggesting all individuals can substantially reduce their diabetes risk through weight loss. Our results support the broad deployment of weight loss interventions to individuals at all levels of diabetes risk.

Introduction

Type 2 diabetes is a chronic metabolic condition characterized by insulin resistance and impaired insulin secretion [1], and is a leading cause of disability and death globally, partly due to cardiovascular complications [2]. Obesity is a primary risk factor for type 2 diabetes [3,4], and lifestyle interventions including weight loss and exercise reduced diabetes risk by 58% in a randomized clinical trial among overweight, prediabetic individuals with elevated post-load and fasting plasma glucose levels [5]; similar results have been observed in earlier studies [6,7]. Observational studies have also provided evidence that individuals overweight during childhood but not adulthood have reduced incidence of diabetes compared to persistently overweight individuals [8], and that overweight and obese individuals who actively participate in weight loss lifestyle change programs experience lower subsequent incidence of diabetes [9]. Interventions to reduce obesity will become increasingly relevant to public health as obesity rates worldwide continue to rise [10].

Despite the clear benefit of weight loss interventions in reducing diabetes among high-risk individuals, it is unclear whether these results generalize to lower-risk individuals. For instance, it is unclear whether weight loss causes individuals who have a normal weight to begin with, and lack genetic or familial risk factors, to reduce their diabetes risk even further. There might be a “plateau” beyond which additional weight loss has only a minor effect on diabetes risk.

More generally, other factors such as genetics and family history could modulate the effectiveness of weight loss on risk reduction. Genetics is a known driver of response to pharmaceutical interventions in general [11] and to metformin, the most commonly prescribed diabetes therapeutic, in particular [12]; it stands to reason that the same may be true for non-pharmaceutical interventions such as weight loss. On the other hand, genetic risk does not appear to modulate the risk-reducing effects of healthy lifestyle factors on coronary artery disease (CAD), with favorable genetics and lifestyle appearing to act independently of each other to reduce risk [13]. Understanding the dynamics of this process—which factors do and do not influence how weight loss translates into reduced diabetes risk—could provide insights into disease pathophysiology and inform personalized medicine.

In this study, we consider 3 factors that could plausibly modulate the risk reduction effectiveness of weight loss: initial body mass index (BMI, defined as weight in kilograms divided by squared height in meters), family history (whether a mother, father, or sibling has diabetes), and genetic risk according to a polygenic risk score constructed from over 100,000 DNA sequence polymorphisms based on their association with type 2 diabetes in a recent genome-wide association study [14]. We explore how these factors may influence the effectiveness of weight loss interventions on diabetes risk reduction in a population-scale cohort, the UK Biobank [15], encompassing over 280,000 individuals of self-reported white British ancestry with medical histories and genome-wide DNA sequence polymorphism data.

Methods

Study population

The UK Biobank is a prospective cohort comprising over 500,000 British individuals recruited in 2006–2010 at age between 40 and 69 years. Our analysis was restricted to 287,394 unrelated individuals of self-reported white British ancestry with anthropometrically measured BMI, type 2 diabetes diagnosis status, and self-reported ascertainment of family history of diabetes. Self-reported white British ancestry was provided as the “in_white_British_ancestry_subset” column of the UK Biobank sample quality control file (ukb_sqc_v2.txt). For quality control, we also excluded individuals not used to compute genotype principal components (“used_in_pca_calculation” column of ukb_sqc_v2.txt), individuals flagged as outliers in heterozygosity or missingness (“het_missing_outliers” column), individuals displaying putative sex chromosome aneuploidy (“putative_sex_chromosome_aneuploidy” column), and individuals with more than 10 putative third-degree relatives (“excess_relatives” column).

Of these 287,394 individuals, 13,982 (4.9%) were considered type 2 diabetes cases and 273,412 (95.1%) controls. Type 2 diabetes was defined based on Eastwood et al. [16] using “probable type 2 diabetes” and “possible type 2 diabetes” as cases and “type 2 diabetes unlikely” as controls; we excluded individuals with “probable type 1 diabetes” or “possible type 1 diabetes” or “possible gestational diabetes” and controls with HbA1C ≥ 39 mmol/mol, as this is indicative of undiagnosed diabetes or prediabetes [17]. Except where noted, “diabetes” refers to type 2 diabetes throughout the text.

All individuals had medical history data, as well as DNA sequence polymorphism data for approximately 800,000 markers ascertained using the UK Biobank Axiom or UK BiLEVE genotyping array and imputed using a combination of the UK10K, 1000 Genomes, and Haplotype Reference Consortium reference panels [18]. We used the following types of data from each of these individuals: the aforementioned polymorphism data, age, sex, genotyping array used (Axiom or BiLEVE), type 2 diabetes diagnosis, self-reported family history of diabetes (mother, father, and/or sibling), BMI calculated from measured height and weight, medication status for insulin and metformin, and, to correct for residual population stratification, UK Biobank assessment center and the top 40 principal components of the DNA sequence polymorphism matrix across individuals [19].

Polygenic risk score

We calculated the polygenic risk score for each of the individuals in our cohort using the 136,795-polymorphism score from a recent diabetes genome-wide association study [20]. The polygenic risk score was imperfectly predictive of disease status (area under the receiver operating characteristic curve [AUC] 0.66), owing both to type 2 diabetes having a strong environmental component, rather than being purely genetic, and to the substantial missing heritability [21] not yet accounted for by genome-wide association studies.

Mendelian randomization

We stratified individuals on BMI (non-overweight, BMI < 25 kg/m2, N = 100,294; overweight, 25 ≤ BMI < 30 kg/m2, N = 123,820; obese, BMI ≥ 30 kg/m2, N = 63,280), family history (mother, father, or any sibling with diabetes, N = 48,238), and polygenic risk score for type 2 diabetes derived from genome-wide summary statistics with and without BMI adjustment (low, medium, or high tertile, N = 95,798). We also stratified diabetes cases based on metformin (N = 7,923 of 13,982) or insulin (N = 2,094 of 13,982) prescription, while using the full set of control individuals. Within each subset of individuals, as well as in the full cohort, we performed inverse-variance-weighted Mendelian randomization (MR) and MR–Egger regression [22] and used the MR–Egger intercept test to assess the impact of horizontal pleiotropy. We refer the reader to Emdin et al. [23] for a comprehensive introduction to MR and its applications to medicine.

First, we performed genome-wide association studies for BMI and diabetes in UK Biobank with linear and logistic regression, respectively, using the PLINK software package [24] (version 2.0), restricted to only the individuals in each respective subset. We included as covariates age, sex, genotyping array, UK Biobank assessment center, and the top 40 global principal components of the DNA sequence polymorphism matrix. To mitigate bias in MR effect sizes due to participant overlap [25], we restricted the BMI genome-wide association study to only type 2 diabetes controls.

We then performed MR using genome-wide-significant BMI-associated polymorphisms from the GIANT consortium [26] curated by a previous MR study [27] as instrumental variables. Although a recent study [28] meta-analyzed this GIANT consortium GWAS with the UK Biobank and found over 500 independent BMI-associated polymorphisms, we chose not to use this GWAS for instrument selection because MR instruments should be chosen from an external GWAS (in this case, one that does not include UK Biobank data) to avoid winner’s curse.

For quality control [29], we required polymorphisms to be missing in fewer than 10% of individuals (“--geno 0.1”) and to have a Hardy–Weinberg equilibrium p-value of greater than 1 × 10−20 (“--hwe 1e-20 midp”) [30]. Overall, 57 of 69 instruments passed these thresholds: rs7899106, rs17094222, rs11191560, rs4256980, rs2176598, rs3817334, rs12286929, rs7138803, rs11057405, rs9581854, rs12429545, rs10132280, rs12885454, rs7141420, rs3736485, rs758747, rs12446632, rs2650492, rs1558902, rs1000940, rs12940622, rs1808579, rs7243357, rs6567160, rs17724992, rs29941, rs2287019, rs657452, rs3101336, rs17024393, rs543874, rs2820292, rs13021737, rs11126666, rs1016287, rs11688816, rs2121279, rs1528435, rs7599312, rs6804842, rs3849570, rs13078960, rs16851483, rs1516725, rs10938397, rs11727676, rs2112347, rs2207139, rs13191362, rs1167827, rs17405819, rs2033732, rs4740619, rs10968576, rs6477694, rs1928295, and rs10733682. These 57 polymorphisms are conceptually different from the variants in the polygenic risk score, since they were chosen based on their association with BMI, whereas the polymorphisms in the polygenic risk score were chosen based on their association with diabetes. Furthermore, the polygenic risk score used thousands of polymorphisms to capture as much trait variance as possible, while these 57 polymorphisms were selected to have individually measurable effects on BMI.

We tested for non-linearity in the relationship between diabetes odds ratio and BMI using the method of Staley and Burgess [31]. We constructed an “allele score” as a sum of the 57 instruments, weighted by their effect sizes in Locke et al.’s smoking-adjusted European BMI summary statistics (BMI.SNPadjSMK.CombinedSexes.EuropeanOnly.txt; 1 instrument, rs9581854, did not appear in this file and was consequently excluded from the allele score). We input this allele score into Staley and Burgess’s method to estimate diabetes odds ratios within 50 BMI quantiles while accounting for collider bias. We then calculated a Cochran Q p-value to test for heterogeneity across the 50 quantiles. We also calculated Cochran Q and trend test p-values (as described in [31]) for whether the association of the allele score with BMI varied across the 50 quantiles; an assumption of the method is that it does not.

Mitigating collider bias

To mitigate collider bias [32], we ensured that all variables stratified on (BMI, family history, and polygenic risk score) were independent of the 57 instruments, using a combination of 2 strategies. For BMI and the polygenic risk score, we simply regressed out the 57 instruments (i.e., by predicting BMI from the instruments using multilinear regression, then mean-centering the predictions and subtracting them from BMI to create an adjusted BMI; and similarly for the polygenic risk score). Throughout the text, “BMI” and “polygenic risk score” refer to individuals’ BMIs and polygenic risk scores after regressing out the 57 instruments. Note that since these 57 instruments collectively explain only a small proportion of variance in BMI (r2 = 0.013) and polygenic risk (r2 = 0.003), the magnitude of this adjustment is minimal, and the adjusted BMIs and polygenic risk scores are approximately equal to the unadjusted values.

For family history, which unlike BMI and polygenic risk is binary, we instead corrected for collider bias by predicting family history from the instruments using multivariate logistic regression, then matching individuals between the family history and no family history groups on the logistic regression predictions in a 4.5:1 ratio. Specifically, we binned individuals into 10 deciles based on the predictions and, within each decile, randomly subsampled the no family history group to 4.5 times the size of the family history group (rounded to the nearest integer number of individuals). This subsampling led to the inclusion of a total of 48,238 individuals with family history and 217,071 without in the family history analysis; 22,085 individuals were excluded.

Results

Prevalence of diabetes in UK Biobank

One simple way to estimate the effectiveness of weight loss in reducing diabetes risk is to tabulate how diabetes prevalence differs between subsets of individuals with different diabetes risk factors. To this end, we stratified individuals within our self-reported white British UK Biobank cohort based on BMI, and further based on family history or polygenic risk score tertile, then tabulated diabetes prevalence within each stratum (Table 1; Fig 1 and S1 Fig).

Table 1

Prevalence of diagnosed type 2 diabetes in the self-reported white British UK Biobank cohort, stratified by BMI, family history, and polygenic risk score.

Group	Non-overweight (BMI < 25 kg/m2)	Overweight (25 ≤ BMI < 30 kg/m2)	Obese (BMI ≥ 30 kg/m2)
Overall	1.3%	3.7% (2.8×)	12.8% (9.8×)
Family history of diabetes
No	1.0%	2.8% (2.8×)	10.2% (10.2×)
Yes	3.1% (3.1×)	8.4% (8.4×)	22.2% (22.2×)
Polygenic risk score
Low	0.7%	1.8% (2.6×)	7.1% (10.1×)
Medium	1.1% (1.6×)	3.2% (4.6×)	11.6% (16.6×)
High	2.1% (3.0×)	6.2% (8.9×)	18.0% (25.7×)

Relative risks with respect to the lowest-risk (top left) category in each stratification are shown in parentheses. Because prevalences within our cohort are by definition exact, we do not report confidence intervals.

Fig 1

Variation of type 2 diabetes prevalence with BMI, family history, and polygenic risk.

Within each category, 50 bins of equal numbers of individuals with consecutive BMI values were selected, and the average BMI and percent of individuals diagnosed with type 2 diabetes are shown. Curves were fit using LOESS regression [33]. Individuals were stratified by (A) family history of diabetes or (B) polygenic risk score (PRS) tertile.

The diabetes prevalence of 1.3% among non-overweight individuals (BMI < 25 kg/m2) increased to 3.7% among overweight individuals (25 ≤ BMI < 30 kg/m2) and 12.8% among obese individuals (BMI > 30 kg/m2), which, as UK Biobank is not a fully representative sample of the UK population, differs somewhat from 2014 Public Health England prevalence estimates of 2.4% among healthy-weight individuals, 5.2% among overweight individuals, and 12.4% among obese individuals [34]. Family history of diabetes was associated with between doubled and tripled diabetes prevalence across all BMI categories (though this increase could be overestimated due to within-category correlations between family history and BMI; see Discussion and S2 Fig).

Polygenic risk was also associated with increased prevalence: across all BMI categories, prevalence doubled to tripled from the lowest to the highest tertile of polygenic risk, similar to the doubling to tripling observed with family history. Hence, BMI, family history, and genetics all showed association with diabetes risk, as expected, likely in part due to these 3 risk factors being correlated with each other [35].

What do these results imply for weight loss interventions? Table 1 and Fig 1 show that elevated BMI is associated with increased diabetes prevalence across all categories of individuals. However, we should not interpret this to suggest that all individuals can reduce their diabetes risk through weight loss, because observational studies are highly prone to confounding. One example of potential confounding in Table 1 and Fig 1 is the correlation of socioeconomic status with both BMI [36] and type 2 diabetes prevalence [37]; complicating the problem, the degree of correlation depends on how socioeconomic status is measured [36].

MR effect size of BMI modification on diabetes risk

To mitigate some of the limitations of observational studies, we used MR [22,23], a powerful technique that aims to assess causality between traits by using DNA sequence polymorphisms as instrumental variables. MR has been likened to a quasi-randomized control trial, where individuals are randomized based on their unique set of inherited genetic polymorphisms [38], and is therefore less vulnerable to confounders than other types of observational data analysis. For instance, MR is able to rule out high-density lipoprotein cholesterol as a causal risk factor for CAD [39]. We build on a rich body of medical literature using MR in the UK Biobank dataset to interrogate epidemiological relationships [27,40-43].

Rather than reporting mere prevalences, MR is able to estimate the odds ratio of diabetes per kg/m2 decrease (or increase) in BMI within each subset of individuals (Table 2 and S1 Table; S3 Fig), a critical quantity when considering weight loss interventions. Non-overweight individuals were estimated to have a 1.31-fold (95% CI 1.11–1.53) reduced odds of diabetes per unit decrease in BMI according to inverse-variance-weighted MR. This is broadly concordant with previous MR estimates of 1.26-fold, using the GIANT and DIAGRAM studies [44], and 1.19-fold, using the GIANT and Genetic Epidemiology Research on Adult Health studies and a subset of the UK Biobank cohort [45]. Overweight and obese individuals had roughly the same odds ratios as non-overweight individuals, though the odds ratio for obese individuals (1.25-fold, 95% CI 1.20–1.31) was slightly but significantly lower than that for overweight individuals (1.36-fold, 95% CI 1.28–1.45; p = 0.03). There also appeared to be some heterogeneity within BMI categories (S2 Table), particularly between obese individuals with BMI < 35 kg/m2 (1.38-fold, 95% CI 1.29–1.47) versus ≥35 kg/m2 (1.13-fold, 95% CI 1.05–1.21; p = 6 × 10−5); however, using the method of Staley and Burgess [31], we did not find significant evidence of heterogeneity across 50 BMI quantiles (Cochran Q heterogeneity p = 0.6; S4 Fig). Polygenic risk score and family history also appeared to have minimal influence on odds ratio, with no significant differences based on family history or between PRS groups for any BMI category (S1 Table). Results were broadly concordant using MR–Egger regression instead of inverse-variance-weighted MR (S3 and S4 Tables).

Table 2

Diabetes odds ratio per kg/m2 increase in BMI within various subsets of individuals, according to inverse-variance-weighted Mendelian randomization.

	Non-overweight (BMI < 25 kg/m2)	Overweight (25 ≤ BMI < 30 kg/m2)	Obese (BMI ≥ 30 kg/m2)
Overall	1.31 (1.11, 1.53)	1.36 (1.28, 1.45)	1.25 (1.20, 1.31)
Family history of diabetes
No	1.37 (1.12, 1.68)	1.34 (1.24, 1.44)	1.24 (1.18, 1.32)
Yes	1.09 (0.87, 1.36)	1.34 (1.21, 1.49)	1.21 (1.13, 1.29)
Polygenic risk score
Low	1.17 (0.82, 1.65)	1.29 (1.11, 1.48)	1.22 (1.12, 1.34)
Medium	1.59 (1.21, 2.10)	1.35 (1.19, 1.53)	1.28 (1.19, 1.38)
High	1.16 (0.93, 1.45)	1.40 (1.29, 1.53)	1.25 (1.18, 1.32)
Diabetes medication
Insulin only	1.39 (0.98, 1.97)	1.32 (1.12, 1.55)	1.33 (1.22, 1.44)
Metformin only	1.44 (1.12, 1.85)	1.49 (1.37, 1.61)	1.30 (1.23, 1.38)

95% confidence intervals are indicated in parentheses.

We also considered the influence of diabetes medication on the results, to investigate the influence of confounding due to reverse causality of these medications on BMI [5] or differences in diabetes severity between medicated and non-medicated individuals. When we restricted our set of diabetes cases to individuals prescribed metformin (7,923 of 13,982 individuals) or insulin (2,094 of 13,982 individuals), while using the full set of control individuals, odds ratios were again similar (Table 2). On the whole, MR predicted that all individuals have a substantial ability to reduce their diabetes risk through weight loss, regardless of BMI, family history, or genetic risk.

Relative versus absolute risk reduction

While overweight and obese individuals are predicted to have similar relative risk reduction with weight loss, it is also worth considering how this translates into absolute risk reduction (i.e., reduction in population prevalence), which is arguably more important from a public health perspective. We predict that a hypothetical 1-kg/m2 BMI reduction among all the overweight individuals in our cohort would reduce diabetes prevalence from 5.2% to 3.8% (i.e., 5.2% divided by 1.36, making the approximation that relative risk is similar to odds ratio since prevalences are sufficiently low and odds ratios are sufficiently close to 1 [46]). This would result in a substantial absolute reduction in diabetes prevalence of 1.4 percentage points (95% CI 1.1–1.6) among these overweight individuals (Table 3). By a similar calculation, we predict that the same 1-kg/m2 BMI reduction among the obese individuals in our cohort would reduce prevalence by an even more substantial 2.5 percentage points (95% CI 2.1–2.9). The larger absolute risk reduction from weight loss among obese individuals suggests that existing public health efforts focused on this high-risk group have not been misplaced.

Table 3

Relative versus absolute risk reduction across BMI categories.

Measure	Non-overweight (BMI < 25 kg/m2)	Overweight (25 ≤ BMI < 30 kg/m2)	Obese (BMI ≥ 30 kg/m2)
Relative odds ratio, from Mendelian randomization (β)	1.31 (1.11, 1.53)	1.36 (1.28, 1.45)	1.25 (1.20, 1.31)
Diabetes prevalence (P), from Public Health England [34]	2.40%	5.20%	12.40%
Prevalence after 1-kg/m2 BMI reduction (P/β)	1.8% (1.6, 2.2)	3.8% (3.6, 4.1)	9.9% (9.5, 10.3)
Absolute risk reduction: Reduction in prevalence after 1-kg/m2 BMI reduction (~P − P/β)	0.6% (0.2, 0.8)	1.4% (1.1, 1.6)	2.5% (2.1, 2.9)

Absolute risk reduction for a 1-kg/m2 reduction in BMI is estimated from the baseline diabetes prevalence (P) and Mendelian randomization odds ratio (β) as P − P/β. 95% confidence intervals are indicated in parentheses.

Example: Risk reduction for a fixed amount of weight loss

Consider an individual of 1.7 meters (approximately 5 feet, 7 inches) in height. If the individual is overweight (72 kg [159 lbs] to 87 kg [192 lbs]) and loses 2.3 kg (5 lbs), MR predicts a 22% relative reduction in diabetes risk (95% CI 18%–25%), or a 0.8% absolute reduction (95% CI 0.7%–0.9%), according to the same type of calculation as in Table 3. (This analysis relies on the multiplicative nature of odds ratios, so that for instance a 2.5-kg/m2 BMI reduction at an odds ratio of 1.30 would result in a predicted relative risk reduction of 1 − 1/1.302.5, or about 48%.) On the other hand, for a 1.7-meter tall obese individual (87 kg [192 lbs] or greater), the same 2.3-kg (5-lb) weight loss would result in a 16% predicted relative risk reduction (95% CI 13%–19%) and a 2.1% absolute reduction (95% CI 1.7%–2.5%). The results of similar calculations for 4.5-kg (10-lb), 5.0-kg, 9.1-kg (20-lb), and 10.0-kg weight reductions are shown in Table 4.

Table 4

Predicted relative and absolute diabetes risk reduction resulting from various amounts of weight loss, for a 1.7-meter-tall individual.

Weight lost	Predicted relative percent reduced risk		Predicted absolute percent reduced risk
	Overweight (25 ≤ BMI < 30 kg/m2)	Obese (BMI ≥ 30 kg/m2)	Overweight (25 ≤ BMI < 30 kg/m2)	Obese (BMI ≥ 30 kg/m2)
2.3 kg (5 lbs)	22% (18, 25)	16% (13, 19)	0.8% (0.7, 0.9)	2.1% (1.7, 2.5)
4.5 kg (10 lbs)	39% (32, 44)	30% (25, 35)	1.4% (1.2, 1.6)	3.8% (3.1, 4.5)
5.0 kg (11 lbs)	42% (35, 47)	32% (27, 38)	1.5% (1.3, 1.8)	4.1% (3.4, 4.8)
9.1 kg (20 lbs)	62% (54, 69)	51% (43, 58)	2.3% (2.0, 2.6)	6.5% (5.5, 7.4)
10.0 kg (22 lbs)	66% (58, 72)	54% (46, 61)	2.5% (2.1, 2.7)	7.0% (5.9, 7.8)

95% confidence intervals are indicated in parentheses.

Example: Weight loss for a fixed amount of risk reduction

We can also invert the problem to predict how many pounds lost would result in a given amount of risk reduction, for the same 1.7-meter-tall individual. The results of this calculation, for a 25% or 50% relative or 1% or 2% absolute risk reduction, are shown in Table 5; we predict that losing 5 kg (11 lbs) would be sufficient to reduce relative risk by 25% and absolute risk by 1% in both overweight and obese individuals, and that losing 11 kg (about 25 lbs) would be sufficient to reduce relative risk by 50% and absolute risk by 2% in both groups.

Table 5

Predicted number of pounds/kilograms that would need to be lost to achieve various percent reductions in relative or absolute diabetes risk, for a 1.7-meter-tall individual.

Percent reduced diabetes risk	Predicted weight loss needed to achieve risk reduction
	Overweight (25 ≤ BMI < 30 kg/m2)	Obese (BMI ≥ 30 kg/m2)
25%, relative	6 lbs (5, 7)/3 kg (2, 3)	8 lbs (7, 10)/4 kg (3, 5)
50%, relative	14 lbs (12, 18)/6 kg (5, 8)	20 lbs (16, 25)/9 kg (7, 11)
1%, absolute	6 lbs (5, 8)/3 kg (2, 4)	2 lbs (2, 3)/1 kg (1, 1)
2%, absolute	16 lbs (13, 20)/7 kg (6, 9)	5 lbs (4, 6)/2 kg (2, 3)

95% confidence intervals are indicated in parentheses.

Discussion

In this study, we quantitatively examined the influence of BMI, family history of diabetes, and genetic risk on the association between BMI and diabetes in a population-scale cohort of over 280,000 individuals. We found that all groups, even those at low risk, show evidence of an association between reduced BMI and reduced diabetes risk, suggesting that all individuals have the ability to reduce their diabetes risk through weight loss. Crucially, neither family history nor genetic risk fundamentally alter the strength of this association, suggesting that despite some degree of genetic and environmental predisposition, all individuals can still take charge of their diabetes risk through lifestyle modifications. Our results support ongoing public health campaigns to encourage weight loss for all individuals. We note, however, that there is still substantial interindividual variation in treatment adherence [47], and personalized adherence strategies remain a fruitful area for further research.

There are several limitations to our study. Our use of discrete divisions for BMI, family history, and polygenic risk, though standard among epidemiological studies of this kind [13], opens up the possibility of heterogeneity in other variables within each division. For instance, although family history is associated with a large increase in risk even within each BMI category, some of this increase could be due to within-category correlations between family history and BMI. Our individuals’ self-reported family history of diabetes does not distinguish between type 1 and 2 diabetes (though type 2 diabetes accounts for 90% to 95% of cohort diabetes cases) and could also be subject to ascertainment bias, such as people only becoming aware of a family history of diabetes after being diagnosed themselves. Family history may be less informative in societies undergoing demographic transition, where the parental environment may be drastically different. BMI is an imperfect proxy for body adiposity [48], and other anthropometrics, such as waist circumference, might have overlapping effects on diabetes risk. In particular, it has been shown that waist circumference is associated with diabetes risk even after accounting for BMI [49]. In addition, our observations are of present BMI and are thus concurrently ascertained with diabetes status, not recorded at or before the time of diagnosis.

While MR is designed to account for confounding due to environmental factors, and age, sex, and population structure were explicitly corrected for, there could be residual confounding, particularly due to covariates with non-linear effects. MR is also known to be vulnerable to pleiotropy [50] (e.g., polymorphisms affecting BMI and diabetes through 2 independent biological mechanisms) and reverse causality, and stratifying on the exposure (BMI) could induce correlation between the outcome (diabetes) and instrumental variables (DNA sequence polymorphisms) [31,51], contrary to an assumption of MR. As noted previously [52], the analogy between MR and randomized control trials is imperfect because of (1) violations of non-exchangeability due to population structure, (2) study eligibility criteria being defined late in life, after conception (i.e., post-randomization), (3) potentially imperfect linkage between the instruments and the true causal genetic variants, and (4) an unclear definition of adherence to treatment.

Perhaps most importantly, the estimates reported by MR, being based on inherited DNA sequence polymorphisms, represent cumulative effects of the exposure over an individual’s entire lifetime, and may consequently incorrectly estimate the risk modification potential of interventions later in life, violating an implicit assumption of gene–environment interchangeability in MR [50]. Conceptually, although MR can determine that lower lifetime BMI is protective against diabetes, this does not necessarily imply that weight loss later in life, after carrying excessive weight for decades, would have the same result. We stress the need to validate the conclusions presented here via randomized controlled trial or prospective study evidence, since even MR is not fully immune to the limitations of observational cohorts. For instance, as the UK Biobank cohort continues to age, new incidence of type 2 diabetes cases might be used in a prospective fashion to estimate age-related effects.

In conclusion, by analyzing a cohort of over 280,000 individuals, we found that across BMI, family history, and genetic risk categories, genetically predicted lower BMI is consistently associated with reduced diabetes risk. This suggests that individuals still have substantial ability to reduce diabetes risk through weight loss, regardless of genetics or family history.

Variation of type 2 diabetes prevalence with BMI, stratified by sex and polygenic risk.

Within each category, 50 bins of equal numbers of individuals with consecutive BMI were selected, and the average BMI and percent of individuals diagnosed with type 2 diabetes are shown. Curves were fit using LOESS regression [33]. Individuals were stratified by (A) sex or (B) polygenic risk score quantile (0%–5%, 47.5%–52.5%, 95%–100%).

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Difference in BMI in individuals with versus without family history of diabetes.

Individuals were stratified into controls (left) and type 2 diabetes cases (right) and further stratified by the presence (brown) or absence (green) of a family history of diabetes. There was a significant difference in mean BMI between individuals with a family history of diabetes in controls (0.8 kg/m2, t test p < 0.001) but not in cases (0.2 kg/m2, t test p = 0.1).

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Diabetes odds ratio per kg/m2 increase in BMI within various subsets of individuals, according to inverse-variance-weighted MR.

Error bars indicate 95% confidence intervals.

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Click here for additional data file.

Diabetes odds ratios across 50 BMI quantiles, using the method of Staley and Burgess.

The average of the 50 odds ratios is shown as a gray line. We found no significant evidence of heterogeneity across the 50 quantiles (Cochran Q heterogeneity p = 0.6). However, the association of the allele score with BMI appeared to vary slightly across the 50 quantiles (Cochran Q heterogeneity p = 0.01, trend test p = 0.7), limiting the conclusions that can be drawn from this analysis.

(PNG)

Click here for additional data file.

p-Values between all adjacent groups in Table 2, calculated via a difference-of-odds-ratios test.

(DOC)

Click here for additional data file.

Diabetes prevalence and odds ratio per kg/m2 increase in BMI computed via MR, as in Table 2, but with more fine-grained stratifications for overweight and obese individuals.

(DOC)

Click here for additional data file.

The results of Table 2 using MR–Egger regression instead of inverse-variance-weighted MR.

(DOC)

Click here for additional data file.

MR–Egger intercept test p-values.

(DOC)

Click here for additional data file.

2 Sep 2019

Dear Dr. Rivas,

Thank you very much for submitting your manuscript "Homogeneity in the Effect of Body Mass Index on Type 2 Diabetes across the UK Biobank: A Mendelian Randomization Study" (PMEDICINE-D-19-02124) for consideration at PLOS Medicine.

Your paper was evaluated by a senior editor and discussed among all the editors here. It was also discussed with an academic editor (who has some comments below) with relevant expertise, and sent to independent reviewers, including a statistical reviewer. The reviews are appended at the bottom of this email and any accompanying reviewer attachments can be seen via the link below:

[LINK]

In light of these reviews, I am afraid that we will not be able to accept the manuscript for publication in the journal in its current form, but we would like to consider a revised version that addresses the reviewers' and editors' comments. Obviously we cannot make any decision about publication until we have seen the revised manuscript and your response, and we plan to seek re-review by one or more of the reviewers.

In revising the manuscript for further consideration, your revisions should address the specific points made by each reviewer and the editors. Please also check the guidelines for revised papers at http://journals.plos.org/plosmedicine/s/revising-your-manuscript for any that apply to your paper. In your rebuttal letter you should indicate your response to the reviewers' and editors' comments, the changes you have made in the manuscript, and include either an excerpt of the revised text or the location (eg: page and line number) where each change can be found. Please submit a clean version of the paper as the main article file; a version with changes marked should be uploaded as a marked up manuscript.

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We expect to receive your revised manuscript by Sep 23 2019 11:59PM. Please email us (plosmedicine@plos.org) if you have any questions or concerns.

***Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.***

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Please use the following link to submit the revised manuscript:

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Your article can be found in the "Submissions Needing Revision" folder.

To enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. For instructions see http://journals.plos.org/plosmedicine/s/submission-guidelines#loc-methods.

Please ensure that the paper adheres to the PLOS Data Availability Policy (see http://journals.plos.org/plosmedicine/s/data-availability), which requires that all data underlying the study's findings be provided in a repository or as Supporting Information. For data residing with a third party, authors are required to provide instructions with contact information for obtaining the data. PLOS journals do not allow statements supported by "data not shown" or "unpublished results." For such statements, authors must provide supporting data or cite public sources that include it.

We look forward to receiving your revised manuscript.

Sincerely,

Adya Misra PhD

Senior Editor

PLOS Medicine

plosmedicine.org

-----------------------------------------------------------

Requests from the editors:

Please avoid causal language as this study is not a trial – please remove the word ‘effect’ from the title and any other incidences in the manuscript.

Similar line 1 of the Methods and Findings section of the abstract (causal - Mendelian Randomization (MR) study of the causal effect size of BMI on diabetes odds in 287,399 unrelated individuals of white British ancestry in the UK Biobank) and causal appears multiple times in the main text.

Please provide p values in the abstract and elsewhere where any data is quantified with 95%Cis.

Please add a sentence as the final sentence of the Methods and Findings section of the abstract on the study’s limitations.

Please provide some summary demographic data to go into an abstract from the cohort you use in your study.

At this stage, we ask that you include a short, non-technical Author Summary of your research to make findings accessible to a wide audience that includes both scientists and non-scientists. The Author Summary should immediately follow the Abstract in your revised manuscript. This text is subject to editorial change and should be distinct from the scientific abstract. Please see our author guidelines for more information: https://journals.plos.org/plosmedicine/s/revising-your-manuscript#loc-author-summary

Academic Editor comments:

My only query/concern is on the 57 variants that were used to define the instrument. This is based on a 2015 GWAS, and variants curated from a previous MR analysis from a different group. It's good to have consistency between publications, but there have been many more variants associated now.

One reviewer commented:

"Is the opinion of this reviewer that the instrument should be updated accordingly", and another also raised concerns.

I would be interested in the statistical reviewer's opinion. I don't feel strongly either way, but it should probably be discussed in the paper.

Comments from the reviewers:

Reviewer #1: Review of: M. Wainberg et al. "Homogeneity in the Effect of Body Mass Index on Type 2 Diabetes across the UK Biobank: A Mendelian Randomization Study"

Submitted to PLOS Medicine

MS # MEDICINE-D-19-02124

In this manuscript, Michael Wainberg and colleagues investigated the effect of body mass index (BMI) on type 2 diabetes (T2D) using multi-stratum Mendelian randomisation (MR) analysis in the UK Biobank. Authors showed that genetically driven BMI reduction was consistently associated with reduced T2D odds across BMI, family history, and genetic risk categories. Findings suggest that all individuals can substantially reduce their T2D risk through weight loss.

The topic, as pointed out by the authors, is of high interest given evidence from large high-quality randomized clinical trials showing that lifestyle interventions can prevent or delay the progression to T2D by ~50% among high-risk individuals. The present study attempted to extend these observations in low-risk individuals using contemporary methodological approaches. The corroboration that body weight reduction strategies may work even among individuals at low T2D risk could offer a rational framework for practice and policy by supporting dietary or lifestyle interventions for T2D to be deployed across all gradients of the population. The manuscript is clear, concise, and very-well written.

This paper has the following strengths:

1. Focus on an interesting and relevant hypothesis

2. Well-powered study with appropriate genetic and outcome information

3. Robust statistical approach

4. Potential to inform practice and policy

5. Authors are top scientist in the field of obesity and T2D genetics

I would like to make the following suggestions in order to help improve the overall quality of the manuscript and strengthen the impact of main findings.

BMI is instrumented by the use of 57 BMI increasing-risk variants that passed the quality control threshold defined by the authors. Weights were based on Locke at al., data. There are now more than 530 independent loci associated with BMI (Yengo E, et al. Hum Mol Genet 2018) and some loci contain more than one causal SNP. Is the opinion of this reviewer that the instrument should be updated accordingly, otherwise they are building a genetic instrument based on a subset of variants that can be difficult to interpret. A potential solution to avoid the inclusion of poor quality variants is to identify proxies for loci in which the lead variant did not pass the quality control.

The relevance of these findings on T2D call for the need to investigate hard outcomes such as coronary artery disease.

Reviewer #2: The paper by Rivas and colleagues explores the causal effect of BMI reduction on risk of diabetes across the spectrum of diabetes risk using MR. This is an important question and I found the manuscript to be well-balanced in its methodological approach and discussion. I do have some questions and suggestions for the authors:

1. The authors constructed an allele score from the weighted sum of 57 alleles using GIANT results (Locke et al.). However, the authors also state "using correlation with BMI in UK Biobank to determine effect directions". Does this mean the direction of effect of (each of) the 57 polymorphisms determined in the UK Biobank for calculation of the allele score? This will certainly inflate the predictiveness of the instrument and bias results. Can the authors explain, and if this is not already the case, use the same direction of effect as in Locke et al.?

2. Why did the authors choose MR-Egger? Can the authors provide results using alternative method (IVW-MR and weighted median, for example)? Was horizontal pleiotropy a concern? If not, other methods are likely to be better powered.

3. A key assumption of the Staley and Burgess method (and all methods looking for non-linear relationships using MR in general) is that the effect of the IV on the exposure is linear and constant for all individuals across the entire of the exposure distribution. Have the authors checked this is the case?

4. It is unclear to me when and how the BMI genome-wide association study the authors have performed in each subset was used in results. If I understand correctly, 57 SNPs from the Locke paper were used as instruments, either with MR-Egger (and results of the diabetes GWAS in each subset) or as a weighted allele score for analysis of nonlinear relationships in 100 BMI quantiles. Can the authors clarify?

5. I suggest adding a column for non-overweight individuals (BMI<25) in Table 1. This would provide an estimate of baseline risk for individuals with a healthy BMI, as compared to "all BMI", which includes overweight and obese individuals.

6. The authors have used a log scale for the y-axis of Figure 1. I wonder if this might mask the rather spectacular effect of BMI on diabetes risk. If felt appropriate, I would suggest using a linear scale.

7. The authors state (page 12) that "However, individuals with a family history of diabetes were predicted to have reduced risk-modification ability through BMI compared to individuals without." This is not readily apparent to me from Table 2. In fact, ORs were consistently larger for individuals with a family history as compared to without. Also, is this difference significant?

8. Figure 2 and Table 2 provide the same information. Would it be possible to combine?

9. I find it difficult to interpret some of the comparisons for predicted weight loss because the "overweight" category includes both overweight and obese individuals. It would be more intuitive to restrict the overweight category to overweight participants (i.e. BMI from 25 to 29.9). To some extent, it is not surprising the two categories have similar risk reduction as they are largely overlapping as currently defined.

10. The labeling of Figure S2 does not match the figure legend.

11. Use of 100 BMI quantiles might obscure any non-linearity because of the large imprecision of estimates in each quantile (figure S3). Can the authors repeat using fewer quantiles?

Reviewer #3: This manuscript uses data from the UK Biobank to examine the causal impact of body mass (BMI)/obesity on type 2 diabetes. They look at prevalence of type 2 diabetes stratified by BMI categories, diabetes family history, and diabetes risk scores. Subsequently, they used Mendelian Randomization across BMI categories to test the reduced T2D risk per kg/m^2 reduction in BMI. Despite increases in T2D prevalence across BMI categories, predicted risk reduction per unit decrease in BMI is roughly comparable ~20-30% decrease across categories. These results are all broadly consistent with previous estimates of the impact of BMI on T2D risk and strongly suggest that weight loss is an effective intervention for diabetes prevention across all weight and genetic/environmental risk categories. The example showing risk reduction for a sample person in terms of weight reduction is useful.

The paper is clearly written with a straightforward hypothesis. It provides clear examples of why this information is useful and indicates the similar utility of weight loss in T2D prevention for all strata. I have only a few questions/comments.

Comments:

1) My main question regarding the presentation of this analysis is why the results are presented with overlapping BMI categories? I can understand presenting the full distribution results (all BMIs), but it seems the analyses would be more logical if presenting discrete categories (such as typical BMI breakpoints <25, 25-30, >30) that are distinct from each other as opposed to categories that are nested within each other (>25, and >30).

2) Since many more than 69 SNPs have been associated with BMI, I assume the 69 SNPs used (subsequently pruned to 57) were chosen due to significant association in European-descent samples, correct? Some comment about this specific selection is warranted.

3) In so far as a noticeable signal of differences exists in these data, it is potentially between those with a family history and those without. Family history encompasses both a shared genetic component and a shared environmental component. Can we use these data to tease apart the two aspects as to which is contributing to the slightly declined value of weight loss in preventing T2D with a family history of T2D? It looks, in comparing odds ratios to T2D PRS to be rather complex.

4) I am confused by Figure S3. I assume that the lines extending from the point estimates are confidence intervals of some sort (not indicated). Can you explain why the confidence intervals are largest in the center of the BMI distribution where the bulk of the data lies and smaller at the tails? This seems counterintuitive.

Reviewer #4: I confine my remarks to statistical aspects of this paper. These were very well done and I have no problems recommending publication.

Any attachments provided with reviews can be seen via the following link:

[LINK]

18 Sep 2019

Submitted filename: Response to reviewers.pdf

Click here for additional data file.

23 Oct 2019

Dear Dr. Rivas,

Thank you very much for re-submitting your manuscript "Homogeneity in the Association of Body Mass Index with Type 2 Diabetes across the UK Biobank: A Mendelian Randomization Study" (PMEDICINE-D-19-02124R1) for review by PLOS Medicine.

I have discussed the paper with my colleagues and the academic editor and it was also seen again by reviewers. I am pleased to say that provided the remaining editorial and production issues are dealt with we are planning to accept the paper for publication in the journal.

The remaining issues that need to be addressed are listed at the end of this email. Any accompanying reviewer attachments can be seen via the link below. Please take these into account before resubmitting your manuscript:

[LINK]

Our publications team (plosmedicine@plos.org) will be in touch shortly about the production requirements for your paper, and the link and deadline for resubmission. DO NOT RESUBMIT BEFORE YOU'VE RECEIVED THE PRODUCTION REQUIREMENTS.

***Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.***

In revising the manuscript for further consideration here, please ensure you address the specific points made by each reviewer and the editors. In your rebuttal letter you should indicate your response to the reviewers' and editors' comments and the changes you have made in the manuscript. Please submit a clean version of the paper as the main article file. A version with changes marked must also be uploaded as a marked up manuscript file.

Please also check the guidelines for revised papers at http://journals.plos.org/plosmedicine/s/revising-your-manuscript for any that apply to your paper. If you haven't already, we ask that you provide a short, non-technical Author Summary of your research to make findings accessible to a wide audience that includes both scientists and non-scientists. The Author Summary should immediately follow the Abstract in your revised manuscript. This text is subject to editorial change and should be distinct from the scientific abstract.

We expect to receive your revised manuscript within 1 week. Please email us (plosmedicine@plos.org) if you have any questions or concerns.

We ask every co-author listed on the manuscript to fill in a contributing author statement. If any of the co-authors have not filled in the statement, we will remind them to do so when the paper is revised. If all statements are not completed in a timely fashion this could hold up the re-review process. Should there be a problem getting one of your co-authors to fill in a statement we will be in contact. YOU MUST NOT ADD OR REMOVE AUTHORS UNLESS YOU HAVE ALERTED THE EDITOR HANDLING THE MANUSCRIPT TO THE CHANGE AND THEY SPECIFICALLY HAVE AGREED TO IT.

Please ensure that the paper adheres to the PLOS Data Availability Policy (see http://journals.plos.org/plosmedicine/s/data-availability), which requires that all data underlying the study's findings be provided in a repository or as Supporting Information. For data residing with a third party, authors are required to provide instructions with contact information for obtaining the data. PLOS journals do not allow statements supported by "data not shown" or "unpublished results." For such statements, authors must provide supporting data or cite public sources that include it.

If you have any questions in the meantime, please contact me or the journal staff on plosmedicine@plos.org.

We look forward to receiving the revised manuscript by Oct 30 2019 11:59PM.

Sincerely,

Cathryn Lewis,

Division of Genetics and Development

PLOS Medicine

plosmedicine.org

------------------------------------------------------------

Requests from Editors:

Please add a space before square brackets for references

Introduction first sentence please consider metabolic condition instead of disease

Methods- we do not require a patient and public involvement section

Page 8 please rephrase “white British UK Biobank Cohort” and please clarify how the researchers know the participants are British. If this information is not available, please remove all references to Nationality.

Conclusion- please consider rephrasing “unfavourable genetics” to less stigmatising language

Page 10- please include a space between inverse-variance-weighted and Mendelian Randomization

Page 14 we suggest you edit the third sentence to include “our results show” or similar

Comments from Reviewers:

Reviewer #2: The authors have satisfactorily addressed all my concerns - thanks!

Any attachments provided with reviews can be seen via the following link:

[LINK]

31 Oct 2019

Submitted filename: Response to editors.pdf

Click here for additional data file.

1 Nov 2019

Dear Mr. Rivas,

On behalf of my colleagues and the academic editor, Dr. Cathryn Lewis, I am delighted to inform you that your manuscript entitled "Homogeneity in the Association of Body Mass Index with Type 2 Diabetes across the UK Biobank: A Mendelian Randomization Study" (PMEDICINE-D-19-02124R2) has been accepted for publication in PLOS Medicine.

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Thank you again for submitting the manuscript to PLOS Medicine. We look forward to publishing it.

Best wishes,

Adya Misra

Senior Editor

PLOS Medicine

plosmedicine.org