Establishing causal relationships between sleep and adiposity traits using Mendelian randomisation

Objective To systematically evaluate the direction of any potential causal effect between sleep and adiposity traits. Methods Two-sample Mendelian randomization (MR) was used to assess the association of genetically predicted sleep traits on adiposity and vice versa. Using data from UK Biobank and 23andme, the sleep traits explored were morning-preference (chronotype) (N=697,828), insomnia (N=1,331,010), sleep duration (N=446, 118), napping (N=452,633) and daytime-sleepiness (N=452,071). Using data from the GIANT and EGG consortia, the adiposity traits explored were adult BMI, hip circumference (HC), waist circumference (WC), waist-to-hip ratio (WHR) (N=322,154) and child-BMI (N=35,668). Results We found evidence that insomnia symptoms increased mean WC, BMI and WHR (difference in means WC=0.39 SD (95% CI=0.13, 0.64), BMI=0.47 SD (0.22, 0.73) and WHR=0.34 SD (0.16, 0.52)). Napping increased mean WHR (0.23 SD (0.08, 0.39). Higher HC, WC, and adult-BMI increased odds of daytime-sleepiness (HC=0.02 SD (0.01, 0.04), WC=0.04 SD (0.01, 0.06) and BMI 0.02 SD (0.00, 0.04), respectively). We also found that higher mean child-BMI resulted in lower odds of napping (-0.01 SD (0.02, 0.00). Conclusions The effects of insomnia on adiposity, and adiposity on daytime-sleepiness, suggest that poor sleep and weight gain may contribute to a feedback loop that could be detrimental to overall health.


Introduction
Poor sleep is common, with up to 67% of UK adults reporting disturbed sleep, 26 -36% experiencing insomnia and 23% sleeping for < 5 hrs per night [1]. Sleep traits, such as chronotype (i.e. morning-or evening-preference), insomnia and sleep duration, have previously been studied in relation to both being overweight and obesity. Sleep disorders and obesity have been linked to almost every aspect of health, from mental health [2][3][4] to overall physical health [4][5][6][7][8][9]. Therefore, establishing the extent to which they relate to each other is important for identifying modifiable targets for interventions that could have beneficial effects on healthy sleep and weight and hence other health outcomes.
Conventional multivariable regression analyses show reported evening preference, insomnia, shortand long-sleep duration to associate with increased odds of obesity (Body Mass Index (BMI) ≥30 kg/m 2 )[10] [11]. However, it is difficult to determine whether these associations are causal or explained by residual confounding or reverse causality. These studies have predominantly explored whether sleep has an impact on adiposity, with few investigating whether there is a reverse relationship -a potential effect of adiposity on sleep traits.
Mendelian randomisation (MR) is a causal inference approach that utilizes germline genetic variants associated with potentially modifiable risk factors as instruments to estimate causal effects on outcomes. MR is less vulnerable to biases incurred by conventional observational analyses, such as reverse causation and confounding, though there are a set of assumptions that can produce biased estimates when violated [12][13][14].
We have identified three existing MR studies that have explored potential causal effects between adiposity and sleep traits [15][16][17] (Table 1). Together these suggest that higher adult BMI potentially increases daytime napping and sleepiness and morning preference, greater waist circumference and waist-to-hip ratio increase daytime napping, longer sleep duration reduces child BMI, and more frequent napping may increase waist circumference and waist-to-hip-ratio. None of these systematically explore a range of sleep traits with a range of adiposity traits within the same study, making it difficult to establish potential bidirectional effects from these separate studies, and most did not undertake sensitivity analyses to explore bias due to assumption violations.
Our aim was to systematically evaluate the potential causal direction of effect between sleep and adiposity traits.
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Methods
We used two-sample MR analyses in which the associations of the germline genetic instrumental variants with both the exposure (sample 1) and the outcome (sample 2) were derived from two independent (i.e. non-overlapping) samples. Sleep traits explored in this study were: morningpreference, insomnia, sleep duration, napping during the day and daytime-sleepiness. Adiposity traits explored in this study included adult body mass index (adult-BMI), childhood body mass index (child-BMI), waist circumference (WC), hip circumference (HC), and waist-to-hip ratio (WHR).
For further information regarding study design see

Genetic instruments for sleep traits
Genetic instruments for sleep duration, napping and daytime dozing traits used in two-sample MR were generated from GWAS conducted in UK Biobank (UKB) [18,19], and instruments for morningpreference and insomnia were generated from GWAS conducted in a meta-analysis of UKB and 23andme. For this, a linear mixed model association method was used to account for relatedness and population stratification, with BOLT-LMM software (v2.3) [20]. At baseline, participants completed a touchscreen questionnaire, which included questions about their sleep behaviours.

Genetic instruments for adiposity traits
Genetic instruments for all adult adiposity traits used in two-sample MR were generated from the Genetic Investigation of ANthropometric Traits (GIANT) consortia, a meta-analysis of ~59 studies from across the UK and Europe [21], with those for child BMI generated from the Early Growth Genetics (EGG) consortia, a meta-analysis of ~20 studies from across the UK and Europe [22]. BMI was calculated from weight (kg) divided by the square of height in metres (m2). An adult is classified as overweight if their BMI is 25.0 -29.9, and obese if their BMI is >30. Measures of hip-and waist . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted July 8, 2022. ; https://doi.org/10.1101/2022.07.08.22277418 doi: medRxiv preprint circumference were both taken in centimetres, and waist-to-hip ratio was calculated from waist circumference divided by hip circumference.
Genetic instruments for child-BMI were obtained from EGG Consortium summary data (N = 35,668) [22], for which 6 SNPs reached genome-wide significance. Supplementary table 1 provides summary statistics of the IVs used to instrument each trait.

Statistical Analyses
The two-sample MR approach uses genome-wide significant IVs to obtain estimates for the causal effect of risk factors on our chosen outcomes. For the univariable MR analyses in this study, the TwoSampleMR R package was used to combine and harmonize genetic summary data for each of our sleep exposure traits to determine the causal effect on adiposity, and subsequently for each of our adiposity traits to determine the causal effect on sleep. For all main analyses, an inverse variance weighted (IVW) approach was used, whereby an estimate of the causal effect is obtained from the slope of a regression line through the weighted IV-mean exposure vs IV-mean outcome associations, with the line constrained to have an intercept of zero.

Sensitivity Analyses and Limiting Assumption Violation
Three key assumptions must be fulfilled to ensure the validity of an MR study for making causal inference: i) the relevance assumption, that genetic IVs are statistically robustly associated with the exposure of interest in the population to which inference is made; ii) the independence assumption, that there is no confounding between the genetic IVs and outcome; and iii) the exclusion restriction assumption, that genetic IVs only influence an outcome through the exposure of interest [28].
We explored instrument strength with the F-statistics of the association between the IVs and each exposure [29,30]. Population substructure can confound genetic instrument-outcome associations and therefore, it was minimised by restricting analyses to European ancestry participants and using GWAS data that had adjusted for principal components reflecting different ancestral subpopulations. To explore the potential for unbalanced horizontal pleiotropy we conducted sensitivity analyses using MR-Egger [31], weighted median [32] and weighted mode [33] MR, and also assessed between-SNP heterogeneity using Cochran's Q and leave one out analyses [13,34]. I 2 statistics were used to estimate the proportion of the variance between IV estimates that is due to heterogeneity [35]. Weighted and unweighted I 2 GX statistics were calculated to provide an indicator . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 8, 2022. ; https://doi.org/10.1101/2022.07.08.22277418 doi: medRxiv preprint 6 for the expected relative bias of the MR-Egger causal estimate [36], and SIMEX corrections were conducted to extrapolate bias-adjusted inference where necessary [37]. To identify IVs with the largest contribution towards heterogeneity, radial-MR was conducted (alpha = 0.05/nSNP) [38]. To identify instrumental SNPs more strongly associated with the outcome of interest than the exposure, Steiger-filtering was conducted [39]. Following both radial-MR and Steiger-filtering, MR was then repeated with any outliers removed to assess their impact.
Sample overlap between UKB and GIANT/EGG is negligible, therefore analyses between these consortia should not violate the independence assumption in two-sample MR.
Results from most sensitivity analyses for effects of different sleep traits on adiposity were consistent with the main analysis results. With the exception of sleep duration effect on child-BMI, where the results were attenuated following Steiger-filtering (beta=-1.77 SD, 95% CI=-7.24, 3.39), although they remained directionally consistent with those reported in the main analysis (Supp.  [29,40]. Between-IV heterogeneity for sleep trait instruments ranged from 0 -88% (Qstat = 19-1126; Qpval = 3.6x10 -153 -4.8x10 -1 ). Weighted and unweighted I 2 GX [36] was also calculated for each of the sleep traits on adiposity traits and found to be between 0 -74%. SIMEX corrections [37] were conducted for each analysis to account for this and found to be largely consistent with MR Egger results reported in the main analyses (Supp. Table   3).
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Table 5).
Results from most sensitivity analyses for effects of different adiposity traits on sleep were consistent with the main analysis results (Supp. Table 6). [29,40], and r 2 values suggest that instruments explain 0.98-2.00% of the variance of the exposures. Between-IV heterogeneity for adiposity trait instruments ranged from 0 -97% (Qstat = 3-399; Qpval = 3.8x10 -49 -3.6x10 -1 ). Weighted and unweighted I 2 GX [36] was also calculated for each of the adiposity traits on sleep traits and found to be between 0 -91%. SIMEX corrections [37] were conducted for each analysis to account for this and found to be largely consistent with MR Egger results reported in the main analyses (Supp. Table   5).

Summary of main findings
This study assessed the direction of effect between a series of adiposity and sleep traits using twosample MR analyses. Overall, we found consistent MR evidence, including from radial and Steiger filtering, of insomnia symptoms increasing mean WC, BMI and WHR, with little evidence for an effect in the opposing direction of adiposity on insomnia. There was evidence that napping increased mean WHR, but no effect was found in the other direction. Our results suggest higher mean child-BMI results in lower odds of napping, and that longer sleep duration may result in lower child-BMI, though for the latter Steiger-filtering, suggested the presence of shared causal variants more strongly associated with child-BMI, and there was no evidence for an effect in the opposing direction of adiposity on sleep duration.
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(which was not certified by peer review)
The copyright holder for this preprint this version posted July 8, 2022. ; https://doi.org/10.1101/2022.07.08.22277418 doi: medRxiv preprint 8 A bidirectional adverse effect was found between napping and WC, which was consistent across radial-MR and Steiger-filtered results. We found little evidence for an effect of daytime-sleepiness on adiposity in our main results; however, evidence for an adverse effect of daytime-sleepiness on HC, WC and BMI was found in radial-MR (and on WC and BMI in Steiger-filtered results). Reciprocal adverse effects were found in the opposing direction for the effect of HC, WC, and BMI on daytimesleepiness, which was consistent across radial-MR and Steiger-filtered results.

Public health and clinical implications
The public health and clinical implications of these results are potentially far-reaching. Our results show that experiencing more frequent insomnia symptoms increases BMI (Fig 2a). Therefore, someone who suffers from insomnia may struggle to lose weight without first dealing with their insomnia.
Overall, better understanding the complex relationship between sleep and adiposity traits may help individuals who struggle to maintain healthy sleep or healthy weight, improve overall health, and consequently reduce the economic burden to our healthcare system.

Comparison with previous literature
The effects of insomnia on adult-BMI (1 SD = 5.1kg/m 2 ) and WHR (1 SD = 0.07) found in this study The effect of sleep duration on child-BMI found in this study (beta=-0.93 SD, 95% CI=-1.74, -0.11) is consistent, but less conservative, than the previous reported two-sample MR findings (1 SD = 4.65 kg/m 2 ) (beta=-0.27 SD, 95% CI=-0.51, -0.02) [17]. The same study by Wang et al also tested robustness of this effect in supplementary analyses by correction with MR-PRESSO and found consistent results (beta=-0.31, 95% CI=-0.53, -0.01), whereas our study reported some attenuation of effect following removal of SNPs more strongly associated with the outcome in Steiger-filtering (beta=-0.65 SD, 95% CI=-1.56, 0.25). We have also taken note of the imprecisely estimated MR-. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 8, 2022. ; https://doi.org/10.1101/2022.07.08.22277418 doi: medRxiv preprint Egger, median and mode results, and the weighted and unweighted I 2 gx result of 0% in our main analyses, suggesting a large amount of measurement error bias [36] (Supp Table 3).
The unidirectional effect we found for napping on WHR (beta=0.23 SD, 95% CI=0.08, 0.39) is also consistent with the previously reported results (beta=0.19 SD, 95% CI=0.04, 0.33), as to be expected given the same underlying data used for these analyses (UKB and GIANT summary statistics) [16].
Furthermore, our additional sensitivity analyses with radial-MR and Steiger-filtering found these associations to be robust.
To our knowledge, the unidirectional effect of child-BMI on napping found in this study (beta=0.28 SD, 95% CI=0.09, 0.46) has not previously been reported. No SNPs were flagged for removal in either radial-MR or Steiger-filtering for this analysis, but weighted and unweighted I 2 gx was found to be 0-14%, suggesting a large amount of measurement error bias [36] (Supp Table 4).
The unidirectional effect of adult-BMI on daytime-sleepiness reported in the main results of this study (beta=0.02 SD, 95% CI=0.00, 0.04) is consistent with that previously found by Dashti et al (beta=0.02 SD, 95% CI=0.01, 0.03) [15], furthermore this result persists after removal of outliers in radial-MR (beta=0.02 SD, 95% CI=0.01, 0.04). HC and WC were also found to increase daytimesleepiness (beta=0.02 SD, 95% CI=0.01, 0.04 and beta=0.04 SD, 95% CI=0.01, 0.06 respectively), both of which were robust to radial-MR and Steiger-filtering analyses. Whilst our main results in the opposing direction report little effect of daytime-sleepiness on adult-BMI, HC or WC, this may be attributed to the moderate to high heterogeneity between SNPs for this instrument (I 2 = 59-73%), leading to imprecise estimation. Following the removal of one outlier SNP (rs6741951) from the daytime-sleepiness instrument in radial-MR, heterogeneity between SNPs was reduced to 0-21%, and an adverse effect was then found for adult-BMI (beta=0.48 SD, 95% CI=0.13, 0.82), HC (beta=0.55 SD, 95% CI=0.12, 0.97) and WC (beta=0.51 SD, 95% CI=0.14, 0.88). Altogether, the evidence suggests that a bidirectional relationship may exist between daytime-sleepiness and adult-BMI, WC and HC.

Strengths and limitations
A key strength of this study is the use of two-sample MR to systematically appraise the causal effects of each of our sleep traits on adiposity and vice versa. Furthermore, MR assumptions were thoroughly tested with the use of additional sensitivity analyses, such as radial-MR and Steigerfiltering, the results of which provide evidence for the robustness of our results. The genetic . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 8, 2022. ; https://doi.org/10.1101/2022.07.08.22277418 doi: medRxiv preprint summary data used for all traits in this study were obtained from the largest available GWAS whilst still maintaining zero overlap between exposure and outcome datasets.
While we were thorough in our assessment of MR assumptions using various sensitivity analyses, we were not able to directly appraise independence of IVs from potential confounding factors. Given that MR uses germline IVs, it is largely understood that these will not be influenced by confounders.
Minimising population stratification may help to alleviate concerns of independence assumption violation [42], but this is difficult to test in a two-sample MR framework.
The use of overlapping sample populations between exposures and outcomes in a two-sample MR setting may be a potential source of bias [43]. Therefore, despite the availability of GWAS with larger sample sizes generated from meta-analysis of UKB and either GIANT or EGG data, we opted to use GWAS that utilised UKB-only sample populations for our sleep traits and GIANT-only or EGG-only sample populations for our adiposity traits to ensure zero sample overlap between exposure and outcomes for our analyses.

Further work
The analyses presented here demonstrate robust casual evidence for both uni-and bi-directional relationships between sleep and adiposity, therefore further investigation is required to inform clinical guidelines and policy. To improve the robustness of the findings in this study, it would be interesting to investigate the associations found using objective measures that correspond to selfreport sleep traits, such as accelerometer-derived sleep duration vs self-report sleep duration[44].
Furthermore, genetic epidemiological studies are disproportionately conducted in population samples of European ancestry. Therefore, future studies that include populations from a variety of ancestries will only serve to better our understanding of the genetics that underpin these associations.
In this study, directionality was explored between sleep and adiposity. Moving forward, it would be interesting to use these results to inform and conduct mediation analyses to look at effects on outcomes such as cancers and cardiovascular disorders.

Conclusion
This study has extended previous findings regarding the effect of sleep on adiposity and vice versa and provided robust evidence for these associations across a variety of methods. Collectively, the effect of insomnia on adiposity, and adiposity on daytime-sleepiness suggests that poor sleep and weight gain may contribute to a feedback loop that is detrimental to the overall health of the individual. Further understanding of these interactions and how, together, they might impact . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted July 8, 2022. ; https://doi.org/10.1101/2022.07.08.22277418 doi: medRxiv preprint association analyses of chronotype in 697,828 individuals provides insights into circadian rhythms. Nat Commun. 2019;10(1):343.
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