Causal Relationship between Obesity and Vitamin D Status: Bi-Directional Mendelian Randomization Analysis of Multiple Cohorts

A mendelian randomization study based on data from multiple cohorts conducted by Karani Santhanakrishnan Vimaleswaran and colleagues re-examines the causal nature of the relationship between vitamin D levels and obesity.


Introduction
The prevalence of obesity has increased in the last two decades and it is presently the most common and costly nutritional problem [1][2][3][4]. In the United States, one-third of the population is affected by obesity, according to the National Health and Nutrition Examination Survey [5]. Despite a known genetic contribution, the increase in obesity prevalence has been largely attributed to lifestyle changes, which means that it is amenable to modification through public health and other interventions [6].
Vitamin D deficiency is another increasingly prevalent public health concern in developed countries [7][8][9], and there is evidence that vitamin D metabolism, storage, and action both influence and are influenced by adiposity. Observational studies have reported an increased risk of vitamin D deficiency in those who are obese; however, the underlying explanations and direction of causality are unclear [10]. Active vitamin D (1,25-dihydroxyvitamin D) may influence the mobilisation of free fatty acids from the adipose tissue [11]. In vitro experiments in rats have also shown that large doses of vitamin D 2 lead to increases in energy expenditure due to uncoupling of oxidative phosphorylation in adipose tissues [12]. However, randomized controlled trials (RCTs) testing the effect of vitamin D supplementation on weight loss in obese or overweight individuals have provided inconsistent findings [13][14][15]. It has also been suggested that obesity could result from an excessive adaptive winter response, and that the decline in vitamin D skin synthesis due to reduced sunlight exposure contributes to the tendency to increase fat mass during the colder periods of the year [16,17]. However, vitamin D is stored in the adipose tissue and, hence, perhaps the most likely explanation for the association is that the larger storage capacity for vitamin D in obese individuals leads to lower circulating 25-hydroxyvitamin D [25(OH)D] concentrations, a marker for nutritional status [18].
In the Mendelian randomization (MR) approach, causality is inferred from associations between genetic variants that mimic the influence of a modifiable environmental exposure and the outcome of interest [19]. If lower vitamin D intake/status is causally related to obesity, a genetic variant associated with lower 25(OH)D concentrations should be associated with higher body mass index (BMI) (in proportion to the effect on 25(OH)D). Conversely, if obesity leads to lower vitamin D status, then genetic variants associated with higher BMI should be related to lower 25(OH)D concentrations. The genetic associations, unlike the directly observed associations for vitamin D intake/status, should be less prone to confounding by lifestyle and socio-economic factors and be free from reverse causation as genotypes are invariant and assigned at random before conception [20]. The use of multiple SNPs to index the intermediate exposure of interest increases power and reduces the risk of alternative biological pathways (pleiotropy) affecting the observed associations between the genotype and the outcome [21,22].
In the present study, we investigated the relationship between BMI, a commonly used measure for monitoring the prevalence of obesity at the population level, and vitamin D status and we inferred causality by using genetic variants as instruments in bidirectional MR analyses. Meta-analysis included data from 21 studies comprising up to 42,024 individuals.

Ethics Statement
All participants provided written, informed consent, and ethical permission was granted by the local research ethics committees for all participating studies.

Participants
The collaboration investigating the association of vitamin D and the risk of cardiovascular disease and related traits (D-CarDia) consists of European ancestry cohorts from the United Kingdom (UK), United States (US), Canada, Finland, Germany, and Sweden. This study comprised a meta-analysis of directly genotyped and imputed SNPs from 21 cohorts totalling 42,024 individuals (Table 1). An expanded description of the participating studies is provided in the Text S2.
To replicate our findings on the association between the vitamin D-related SNPs and allele scores with BMI, we used the data from the genome-wide meta-analyses on BMI conducted as part of the Genetic Investigation of Anthropometric Traits (GIANT) consortium [23]. The GIANT meta-analyses consisted of 46 [24] and previously published genome-wide association studies for obesity-related traits [23,25,26]. The four vitamin D-related SNPs (DHCR7-rs12785878, CYP2R1-rs10741657, GC-rs2282679, and CYP24A1-rs6013897) were chosen on the basis of the recent genome-wide association study on 25(OH)D [27]. The studies that did not have genotyped data analysed imputed or proxy SNPs (r 2 = 1) as available (with a call threshold of 0.9 for the SNPs imputed with Impute; for those imputed with MACH, a call threshold of 0.8 was used) [28]. The genetic data for most studies were obtained from genome-wide association platforms, but for some studies, variants were genotyped de novo ( Table S1 shows the minor allele frequencies for the BMI and vitamin D SNPs that were included in the analysis. A detailed description of the genotyping methods is provided in Text S2.

Statistical Analysis
Analyses in each study were performed according to a standardized analysis plan. When used as outcome variables, 25(OH)D and BMI were natural log transformed to be more closely approximated by normal distributions. If multiplied by 100, coefficients from linear regression models with ln transformed outcomes can be interpreted as the percentage difference in the outcome [29]. Models with BMI as an outcome were adjusted for age, sex, geographical site, and/or principal components from population stratification analysis (depending on data available); models with 25(OH)D as the outcome were additionally adjusted for month of blood sample collection (as a categorical variable) to account for seasonal variation and laboratory batch, where relevant. To assess the BMI relationship with 25(OH)D and vice versa, each study ran linear regression models adjusting for the covariates listed for each outcome, and the models were repeated stratifying by sex.
For the BMI SNPs, the effect allele was the BMI raising allele as established by Speliotes et al. [23]. We created a weighted score in each study [30], by multiplying each SNP (coded as 0-2) by a weight based on its effect size with BMI in the meta-analysis by Speliotes et al. [23]. The weighted BMI allele score was rescaled over the sum of weights for the available SNPs in each study to facilitate interpretation [30]. For the vitamin D SNPs, the effect allele was the 25(OH)D lowering allele as established by the SUNLIGHT Consortium [27]. As external weights were not available and the use of internal weights could bias the instrumental variable (IV) results [31], we performed an unweighted allele score analysis for the vitamin D SNPs. Vitamin D SNPs were used to form two separate allele scores [32]: a ''synthesis'' allele score, created by summing the risk alleles in DHCR7 and CYP2R1, and a ''metabolism'' allele score, created by summing the risk alleles in GC and CYP24A1 ( Figure S1). Synthesis allele score was not created for the LURIC study (one missing SNP) and both synthesis and metabolism allele scores were not created for the MRC Ely study (two missing SNPs). The synthesis allele score included the SNPs that contribute directly to the production of 25(OH)D, and hence, for which the association with the outcome can be readily estimated based on the magnitude of the association between the score and 25(OH)D [32]. All analyses were done separately for the ''metabolism'' SNPs that are involved in the clearance or transport of 25(OH)D (with possible influences on bioavailability [33]) as the quantification of the association with the outcome based on the observed SNP-25(OH)D association is more difficult [32]. We also evaluated the joint contribution of synthesis and metabolism scores on BMI by including both vitamin D scores as separate variables in a multiple regression model. To examine the strength of the allele scores as instruments, the F-statistic was approximated from the proportion of variation in the respective phenotype (R 2 ) explained by the allele score, [Fstat = (R 2 6(n22))/(12R 2 )] [34].
To confirm our findings on the association between the vitamin D-related SNPs and allele scores with BMI in a larger sample, we used the summary statistics for the four vitamin D-related SNPs from the GIANT consortium. These SNPs were combined into synthesis and metabolism allele scores using an approximation method as previously described [35]. The individual SNP association with BMI is then weighted according to its predefined effect size and meta-analysed using the inverse-variance method with the other SNPs in the score [35]. The formal MR analyses to estimate the possible causal effect of BMI on 25(OH)D (and vice versa) were done using the IV ratio method [20,36]. To estimate the IV ratio for the BMI effect on 25(OH)D, the meta-analysed association of the BMI allele score with 25(OH)D was divided by the association of BMI allele score with BMI. The variance for the IV ratio was estimated using a Taylor expansion [36]. The corresponding calculation was done to establish the 25(OH)D effect on BMI, with the IV ratio method applied separately for the two vitamin D allele scores. The joint contribution of the two vitamin D scores on BMI was assessed by multivariate metaanalysis [37], which incorporated the covariance matrix as estimated by study specific analyses.
In the presence of heterogeneity of association between the studies, random effects meta-analyses [38] were run, otherwise fixed effects models were used. Univariate meta-regression models were run to assess differences in the observed associations by study level factors of sex, average BMI (BMI#25 kg/m 2 versus .25 kg/ m 2 ), the average age of participants (#40, 41-60, and $61 y old), continent (North America versus Europe), and vitamin D assay (radio-immunoassay, enzyme-linked radio-immunoassay, and mass spectrometry). Power calculations for IV regression were performed by simulation [32] on the basis of associations observed between the phenotypes and their genetic proxies. For comparability across instruments/outcomes, power was determined for 0.02 log unit increase/decrease by decile, approximately corresponding to the association observed between BMI and 25(OH)D. To evaluate the ability to detect weaker effects on BMI using the synthesis and metabolism scores, power was also calculated for a 50% weaker effect (0.01 log unit increase/decrease). All metaanalyses and power calculations were performed at the Institute of Child Health (University College London, London) using STATA version 12 [39].

Phenotypic Association between BMI and 25(OH)D Concentrations
In the meta-analyses of 21 studies, each unit (kg/m 2 ) increase in BMI was associated with 1.15% (95% CI 0.94%-1.36%, p = 6.52610 227 ) lower concentrations of 25(OH)D after adjusting for age, sex, laboratory batch, month of measurement, and principal components. The inverse association between BMI and 25(OH)D was stronger among the studies from North America than those from Europe ( 29 ; p meta-regression = 4.10610 24 ) while no variation was seen by average age (p meta-regression = 0.78) or BMI (p meta-regression = 0.48) ( Figure 1A and 1B).

Evaluation of Causal Association Using MR Approach
The BMI allele score created from the 12 BMI-related SNPs In the analyses to establish the direction and causality of BMI-25(OH)D association by the use of the IV ratio, BMI was associated with 25(OH)D: each 10% increase in BMI lead to a 4.2% decrease in 25(OH)D concentrations (27.1% to 21.3%; p = 0.005). However, the IV ratio analyses provided little evidence for a causal effect of 25(OH)D on BMI (p$0.08 for both). We have summarised the coefficients for the MR analyses in Table 2.
The lack of association of the vitamin D allele scores with BMI was further confirmed using the GIANT consortium including 123,864 individuals in 46 studies [23]: neither the synthesis nor the metabolism allele score showed any evidence for an association with BMI (p$0.57 for both) ( Table 3).

Additional Analyses
Validation of the genetic instruments. The BMI SNPs and the vitamin D SNPs were all individually associated with BMI and 25(OH)D, respectively ( Figures S4 and S5). The exception was KCTD15 SNP, which despite previous evidence for an association [25], was not associated with BMI in our metaanalyses. Across the studies, the 12 BMI SNPs combined as the BMI allele score explained 0.97% of the variation in BMI (Fstatistic = 316; n = 32,391). The synthesis allele score explained 0.64% (F-statistic = 230; n = 35,873) and the metabolism allele score 1.26% (F statistic = 489; n = 38,191) of the variation in 25(OH)D. There was no evidence for variation in the BMI allele score-BMI association by continent (p meta-regression = 0.15) or BMI (p meta-regression = 0.83). However, the BMI allele score-BMI association was slightly weaker in studies with older compared to younger participants (20.03% [20.05% to 20.002%], p meta-regression = 0.03). The vitamin D allele score-25(OH)D association did not vary by age, BMI, continent, or assay (p meta-regression $0.09 for all comparisons).
Evaluation of the genetic outcome associations. Of the 12 individual BMI SNPs, the SNP for FTO was the only one that showed evidence of a univariate association with 25(OH)D (p = 0.050) ( Figure S6). None of the four 25(OH)D SNPs were individually associated with BMI (p$0.10) ( Figure S7). The lack of association of the four vitamin D SNPs with BMI was further confirmed using the summary data from the GIANT consortium (p.0.30 for all the SNPs) ( Table 3).
The association between BMI allele score and 25(OH)D did not vary by study level factors, including age (p meta-regression = 0.40), BMI (p meta-regression = 0.18), continent of study (p meta-regression = 0.78), or vitamin D assay (p meta-regression = 0.23). Similarly, there was no evidence for variation in the vitamin D allele score-BMI association by age (p meta-regression $0.25 for both scores), or continent (p meta-regression $0.50 for both scores). There was also no strong evidence for variation in the vitamin D allele score-BMI association by average BMI of the study (#25 kg/m 2 versus $25 kg/m 2 ), although for the synthesis score the meta-regression coefficient was of borderline significance (p meta-regression = 0.053, Figure S8; p meta-regression = 0.78 for metabolism score).
Power comparison. Illustrative power calculations are presented in Figure S9. In theory, we had greater power to detect an association between 25(OH)D and BMI using the metabolism score as an instrument, compared with an equal sized association between BMI and 25(OH)D using the BMI risk score. However, if the size of the association between 25(OH)D and BMI was only half that seen between BMI and 25(OH)D, our study would not have been adequately powered even with the inclusion of the GIANT results.

Discussion
Obesity, and perhaps vitamin D deficiency, are among the most important modifiable risk factors for a number of chronic diseases. Obesity and vitamin D status are known to be associated but the direction of the association and whether it is causal has been uncertain. We have presented genetic evidence that higher BMI leads to lower vitamin D status. Conversely, our analyses provided no evidence for a causal role of vitamin D in the development of obesity, although our study was not powered to detect very small effects. These results suggest that although increases in vitamin D status are not likely to help with weight regulation, increased risk of vitamin D deficiency could contribute to the adverse health effects associated with obesity.
The association between obesity and vitamin D status was remarkably consistent across the different populations included in our meta-analyses, being apparent both in men and in women, and in the young and older cohorts alike. Interestingly, the association between obesity and 25(OH)D concentrations appeared stronger for populations in North America compared to Europe, possibly reflecting differences in the distribution of BMI across the continents. Recent intervention studies have shown that obese individuals need higher vitamin D dosages than lean individuals to achieve the same 25(OH)D concentrations [40,41]. Given that North America has one of the highest rates of obesity in the world [42], our study highlights the importance of considering obesity as a risk factor for vitamin D deficiency with implications on the dosage requirements and possible targeting of relevant health promotion strategies.
The lack of any suggestion for an association between the vitamin D SNPs and BMI in the GIANT consortium (n = 123,864) alongside our own large meta-analyses provides a strong case against linear increases in 25(OH)D having a substantive influence on BMI. This conclusion is in accordance with a recent study on Chinese women (n = 7,000), which also failed to observe evidence for an association with BMI for genetic variants in the vitamin D pathway [43]. Although a recent RCT (n = 77) suggested greater loss in fat mass for women receiving vitamin D [15], previous trials have failed to show any evidence for an effect despite larger treatment groups (n = 200-445), use of higher vitamin D dosages, and equal duration of treatment (12 mo) [13,14]. Dilution related to the greater volume of distribution has been recently proposed as the most likely explanation for the lower 25(OH)D concentrations in obese individuals [44]. In that study, no evidence was found for reduced bioavailability through increased sequestration of vitamin D in the adipose tissue, which had previously been suggested to contribute to the low 25(OH)D concentrations in obesity [18]. In contrast, intact parathyroid hormone (iPTH) levels [45], which stimulate the 1-a-hydroxylase (CYP27B1) enzyme that converts 25(OH)D to 1,25-dihydroxyvitamin D (the active hormonal form), have been found to be elevated in obesity [46], which could to some extent also contribute to the lower 25(OH)D concentrations in obese individuals. It is also possible that differences in lifestyle could contribute to lower 25(OH)D concentrations in obese compared to normal weight individuals, although the association between obesity and low 25(OH)D concentrations has been found to only modestly attenuate after adjustment for vitamin D-related lifestyle and dietary factors [9].
The main strengths of this study are the large sample size and the individual level population-based data from North America and Europe. We used a bi-directional MR approach to investigate the causal directions between obesity and vitamin D deficiency, observing evidence for reductions in 25(OH)D by BMI but not vice versa. However, based on the biological pathways proposed, a possible effect of 25(OH)D on BMI could be expected to be weaker than the effect of BMI on 25(OH)D. Despite including data from the large GIANT consortium to narrow the range of effects compatible with the data, we are unable to exclude very small effects. Furthermore, while the MR approach enables the approximation of life-long differences in average concentrations, with genetic markers it is not possible to examine the influences arising from the extremes of non-linear distributions [20]. Consequently, we cannot discount a possible effect of severe vitamin D deficiency on BMI due to evidence of non-linearity seen in some studies [47]. In contrast, associations between BMI and 25(OH)D within levels in the obesity range were consistently linear in studies included in our analyses (unpublished data), hence the observed association between higher BMI and lower 25(OH)D is likely to be informative in the context of obesity.
One of the methodological challenges of the MR approach relates to the large sample size requirement, arising from the availability of relatively weak instruments for most exposures [22,31]. This aspect of the MR approach is also reflected in our study, notably in the relatively small amount of variation explained by all the instruments used. We used the IV ratio method on metaanalyzed coefficients since all studies were not able to share individual level participant data. This method assumes linear relationships and may have less power to detect an effect than other IV methods [48]. However, as shown by the clear outcome of these analyses, we were able to overcome these issues by combining several cohorts with comparable information, allowing us to achieve the large numbers required (maximum n = 42,024) [31]. To confirm the lack of association between vitamin D-related genetic variations and BMI, we were able to expand the analyses by using data from the large GIANT meta-analyses (n = 123,864) [23]. However, this cannot be considered an independent replication, as eight of the studies that were part of the D-CarDia Collaboration were also included in GIANT. The F-statistic is used to measure the strength of an instrument, and an instrument that has a value greater than 10 is considered strong enough to use in IV analyses [49]. In our analyses, the F-statistic was greater than 200 for all instruments used due to our large sample size.
Combining large population-based studies from North America and Europe could lead to confounding by population stratification;  however, we adjusted for geographical variation/principal components in all analyses, which appeared adequate, as there was no evidence for heterogeneity by continent for the allele score metaanalyses. An important benefit of the MR approach is that it helps to overcome problems of confounding and reverse causality, which limit the ability to draw causal inferences in non-genetic observational studies [19,20]. However, it could be argued that as the biological function for some of the BMI SNPs is yet to be established, there could be alternative biological pathways explaining their association with BMI. Using multiple SNPs to index BMI, we were able to minimise the risk of pleiotropic effects, as the effects of alternative pathways reflected by individual SNPs would be expected to be strongly diluted when combined in a multi marker score [21,22].
In conclusion, we demonstrated that the association between BMI and lower 25(OH)D concentrations in Caucasian populations from North America and Europe can be seen across different age groups and in both men and women. We also show that higher BMI leads to lower vitamin D status, providing evidence for the role of obesity as a causal risk factor for the development of vitamin D deficiency. Together with the suggested increases in vitamin D requirements in obese individuals [45,50], our study highlights the importance of monitoring and treating vitamin D deficiency as a means of alleviating the adverse influences of excess adiposity on health. Our findings suggest that population level interventions to reduce obesity would be expected to lead to a reduction in the prevalence of vitamin D deficiency.   Editors' Summary Background. Obesity-having an unhealthy amount of body fat-is increasing worldwide. In the US, for example, a third of the adult population is now obese. Obesity is defined as having a body mass index (BMI, an indicator of body fat calculated by dividing a person's weight in kilograms by their height in meters squared) of more than 30.0 kg/m 2 .

Supporting Information
Although there is a genetic contribution to obesity, people generally become obese by consuming food and drink that contains more energy than they need for their daily activities. Thus, obesity can be prevented by having a healthy diet and exercising regularly. Compared to people with a healthy weight, obese individuals have an increased risk of developing diabetes, heart disease and stroke, and tend to die younger. They also have a higher risk of vitamin D deficiency, another increasingly common public health concern. Vitamin D, which is essential for healthy bones as well as other functions, is made in the skin after exposure to sunlight but can also be obtained through the diet and through supplements. What Did the Researchers Do and Find? The researchers created a ''BMI allele score'' based on 12 BMI-related gene variants and two ''25(OH)D allele scores,'' which are based on gene variants that affect either 25(OH)D synthesis or breakdown. Using information on up to 42,024 participants from 21 studies, the researchers showed that the BMI allele score was associated with both BMI and with 25(OH)D levels among the study participants. Based on this information, they calculated that each 10% increase in BMI will lead to a 4.2% decrease in 25(OH)D concentrations. By contrast, although both 25(OH)D allele scores were strongly associated with 25(OH)D levels, neither score was associated with BMI. This lack of an association between 25(OH)D allele scores and obesity was confirmed using data from more than 100,000 individuals involved in 46 studies that has been collected by the GIANT (Genetic Investigation of Anthropometric Traits) consortium.
What Do These Findings Mean? These findings suggest that a higher BMI leads to a lower vitamin D status whereas any effects of low vitamin D status on BMI are likely to be small. That is, these findings provide evidence for obesity as a causal factor in the development of vitamin D deficiency but not for vitamin D deficiency as a causal factor in the development of obesity. These findings suggest that population-level interventions to reduce obesity should lead to a reduction in the prevalence of vitamin D deficiency and highlight the importance of monitoring and treating vitamin D deficiency as a means of alleviating the adverse influences of obesity on health.