Using multivariable Mendelian randomization to estimate the causal effect of bone mineral density on osteoarthritis risk, independently of body mass index

Abstract

Objectives: Observational analyses suggest that high bone mineral density (BMD) is a risk factor for osteoarthritis (OA); it is unclear whether this represents a causal effect or shared aetiology and whether these relationships are body mass index (BMI)-independent. We performed bidirectional Mendelian randomization (MR) to uncover the causal pathways between BMD, BMI and OA.

Methods: One-sample (1S)MR estimates were generated by two-stage least-squares regression. Unweighted allele scores instrumented each exposure. Two-sample (2S)MR estimates were generated using inverse-variance weighted random-effects meta-analysis. Multivariable MR (MVMR), including BMD and BMI instruments in the same model, determined the BMI-independent causal pathway from BMD to OA. Latent causal variable (LCV) analysis, using weight-adjusted femoral neck (FN)-BMD and hip/knee OA summary statistics, determined whether genetic correlation explained the causal effect of BMD on OA.

Results: 1SMR provided strong evidence for a causal effect of BMD estimated from heel ultrasound (eBMD) on hip and knee OA {odds ratio [OR]hip = 1.28 [95% confidence interval (CI) = 1.05, 1.57], p = 0.02, ORknee = 1.40 [95% CI = 1.20, 1.63], p = 3 × 10-5, OR per standard deviation [SD] increase}. 2SMR effect sizes were consistent in direction. Results suggested that the causal pathways between eBMD and OA were bidirectional (βhip = 1.10 [95% CI = 0.36, 1.84], p = 0.003, βknee = 4.16 [95% CI = 2.74, 5.57], p = 8 × 10-9, β = SD increase per doubling in risk). MVMR identified a BMI-independent causal pathway between eBMD and hip/knee OA. LCV suggested that genetic correlation (i.e. shared genetic aetiology) did not fully explain the causal effects of BMD on hip/knee OA.

Conclusions: These results provide evidence for a BMI-independent causal effect of eBMD on OA. Despite evidence of bidirectional effects, the effect of BMD on OA did not appear to be fully explained by shared genetic aetiology, suggesting a direct action of bone on joint deterioration.

Keywords: Mendelian randomization; Osteoarthritis; UK Biobank; body mass index; bone mineral density.

Figure 1

Diagram summarizing hypothesized relationships between bone mineral density, body mass index and osteoarthritis Thicker arrows represent stronger hypothesized relationships. Diagram does not take account of temporality of relationships due to the uncertainty in the temporal sequence, e.g. OA may first cause an increase in BMI due to reduced PA, leading to further OA through greater joint loading; however, it is equally possible that BMI leading to an increase in joint loading is the initiating event. BMD, bone mineral density; BMI, body mass index; OA, osteoarthritis.

Figure 2

Assumptions of Mendelian randomization and how we tested these assumptions For a Mendelian randomization (MR) effect estimate to be valid, the instrument(s) must satisfy three key assumptions: IV1 [the instrument(s) must be robustly associated with the exposure], IV2 [the instrument(s) must not be associated with any confounders of the exposure–outcome relationship] and IV3 [the instruments(s) can only be associated with the outcome via the exposure and not via a different biological pathway independent of the exposure (i.e. horizontal pleiotropy)]. In one-sample analyses, IV1 was tested by calculating the F-statistic, which is a measure of instrument strength. A >10 threshold is used to determine sufficient instrument strength. IV2 was tested by determining the association between the instruments and potential confounders of the exposure–outcome relationship. In two-sample analyses, to satisfy IV1, we ensured that all instruments were robustly associated with the exposure by only including SNPs associated with the exposure at genome-wide significance. To address IV3, MR–Egger regression was performed to generate an estimate of horizontal pleiotropy (intercept) and a pleiotropy-robust estimate of the causal effect (slope). Weighted median regression was performed to determine the robustness of IVW estimates as weighted median estimates are valid even if ≤50% of the SNPs are not valid instruments. BMD, bone mineral density; BMI, body mass index; OA, osteoarthritis; SNP, single-nucleotide polymorphism.

Figure 3

Summary of results of one-sample, two-sample and multivariable Mendelian randomization analyses Effect estimates represent the SD increase in outcome per SD increase in exposure for BMD–BMI and BMI–BMD analyses, the odds ratio per SD increase in exposure for BMI–OA and BMD–OA analyses, and the SD increase in BMD or BMI per 1-unit increase in the log odds of OA. eBMD, estimated bone mineral density; BMI, body mass index; OA, osteoarthritis; MR, Mendelian randomization; SNPs, single-nucleotide polymorphisms.

Figure 4

Results of two-sample Mendelian randomization analyses eBMD, estimated bone mineral density; OA, osteoarthritis; BMI, body mass index; CI, confidence interval.