Evidence of a causal relationship between body mass index and psoriasis: A mendelian randomization study

Background Psoriasis is a common inflammatory skin disease that has been reported to be associated with obesity. We aimed to investigate a possible causal relationship between body mass index (BMI) and psoriasis. Methods and findings Following a review of published epidemiological evidence of the association between obesity and psoriasis, mendelian randomization (MR) was used to test for a causal relationship with BMI. We used a genetic instrument comprising 97 single-nucleotide polymorphisms (SNPs) associated with BMI as a proxy for BMI (expected to be much less confounded than measured BMI). One-sample MR was conducted using individual-level data (396,495 individuals) from the UK Biobank and the Nord-Trøndelag Health Study (HUNT), Norway. Two-sample MR was performed with summary-level data (356,926 individuals) from published BMI and psoriasis genome-wide association studies (GWASs). The one-sample and two-sample MR estimates were meta-analysed using a fixed-effect model. To test for a potential reverse causal effect, MR analysis with genetic instruments comprising variants from recent genome-wide analyses for psoriasis were used to test whether genetic risk for this skin disease has a causal effect on BMI. Published observational data showed an association of higher BMI with psoriasis. A mean difference in BMI of 1.26 kg/m2 (95% CI 1.02–1.51) between psoriasis cases and controls was observed in adults, while a 1.55 kg/m2 mean difference (95% CI 1.13–1.98) was observed in children. The observational association was confirmed in UK Biobank and HUNT data sets. Overall, a 1 kg/m2 increase in BMI was associated with 4% higher odds of psoriasis (meta-analysis odds ratio [OR] = 1.04; 95% CI 1.03–1.04; P = 1.73 × 10−60). MR analyses provided evidence that higher BMI causally increases the odds of psoriasis (by 9% per 1 unit increase in BMI; OR = 1.09 (1.06–1.12) per 1 kg/m2; P = 4.67 × 10−9). In contrast, MR estimates gave little support to a possible causal effect of psoriasis genetic risk on BMI (0.004 kg/m2 change in BMI per doubling odds of psoriasis (−0.003 to 0.011). Limitations of our study include possible misreporting of psoriasis by patients, as well as potential misdiagnosis by clinicians. In addition, there is also limited ethnic variation in the cohorts studied. Conclusions Our study, using genetic variants as instrumental variables for BMI, provides evidence that higher BMI leads to a higher risk of psoriasis. This supports the prioritization of therapies and lifestyle interventions aimed at controlling weight for the prevention or treatment of this common skin disease. Mechanistic studies are required to improve understanding of this relationship.


Supporting Text A. Conversion of mean difference to odds ratios
As demonstrated by Perry et al [1], an effect estimate such as the standardised mean difference (SMD) can be converted to an odds ratio using the following formula: In support of this, Borenstein et al [2] stated that the SMD can be converted to the log odds ratio with the following formula:

= √
The method assumes continuous data to have a logistic distribution rather a normal distribution. As analyses of continuous outcomes are commonly performed assuming a normal distribution, the variance (V) of the log odds ratio is as follows:

=
The variance of the standard logistic distribution is π 2 /3, therefore the SMD can be converted to ln(odds) by multiplying by π/√3 or 1.81 to 2 decimal places [3].
This method was applied in the current study to obtain odds ratios for the association between BMI and psoriasis found during the meta-analysis of previously reported observational studies. In applying the first formula, SD denotes the standard deviation change in BMI per standard deviation change in the BMI genetic instrument. In individuals from the UK Biobank, we found this to be 0.135, using the BMI genetic risk score as the genetic instrument. SMD denotes the standardised mean difference in BMI estimated from the association studies that were meta-analysed. In adults this was found to be 0.360 (95% CI = 0.206, 0.515), and 0.363 in children (95% CI = 0.262, 0.465).

Supporting Text B. Reverse direction MR analysis: genetic liability as a linear variable
An additional one-sample MR analysis was performed where the genetic liability of psoriasis was considered as a linear variable with values from "0" to "1". This was performed in the UK Biobank and HUNT datasets using the two-staged least squares (TSLS) method with the "ivpack" R package [1] using individual SNPs for psoriasis as an instrument. This analysis involves two linear regression stages where psoriasis is first regressed upon the instrument (disease-associated SNPs), then the outcome (BMI) is regressed upon the fitted values from the first stage regression. The estimates from each genetic instrument were meta-analysed assuming a random effects model to give a single estimate for the effect of psoriasis genetic risk upon BMI within UK Biobank and HUNT. The estimates from each dataset were then meta-analysed assuming a fixed effect model to give an overall causal effect.     Results from MR analysis using rs1558902 as an instrumental variable. These are compared with final estimates obtained when using all BMI SNPs as a genetic instrument. One-sample MR was performed with individual-level data from UK Biobank and HUNT. Two-sample MR was performed with published GWAS summary-level data for BMI and psoriasis. Estimates are given per 1 unit increase in BMI (kg/m 2 ).

Fig I. Association of psoriasis SNPs with psoriasis and BMI within (a) UK Biobank and (b) HUNT.
IVW, MR-Egger, weighted median and simple median estimates are indicated by the red, green, purple and blue lines respectively.      * mean difference in BMI between psoriasis cases and controls ** change in BMI per doubling odds of psoriasis CI, confidence interval; IVW, inverse variance weighted analysis; MBE, mode-based estimate; TSLS, two-staged least squares.