Perform Drug-Target MR

[davebridges]

Drug-Target MR: LDL-C / Total Cholesterol to Serum Calcium

Objective: To determine if genetic inhibition of specific lipid-lowering drug targets (HMGCR, PCSK9, NPC1L1) causally affects serum calcium levels, mimicking the effect of pharmaceutical interventions.

1. Define Target Gene Regions

Instead of extracting genome-wide significant SNPs from the entire genome, we will strictly limit extraction to the genomic coordinates of the primary lipid-lowering targets (plus a 100kb flanking region to capture regulatory variants).

• HMGCR (Statins target): Chromosome 5 (approx. 74.6 Mb)
• PCSK9 (Repatha/Praluent target): Chromosome 1 (approx. 55.5 Mb)
• NPC1L1 (Ezetimibe target): Chromosome 7 (approx. 44.5 Mb)

2. Exposure Instrument Selection

• Extract SNPs from the LDL-C and Total Cholesterol (TC) GWAS datasets located only within the defined gene regions above.
• Apply a genome-wide significance threshold (p < 5e-8).
• Clump the SNPs for independence (r2 < 0.001, 10,000 kb).
• Contingency: If clumping leaves 0 or 1 SNP per gene, relax the clumping threshold (e.g., r2 < 0.3) to retain more variants, noting that this will require accounting for LD correlation in the analysis phase.

3. Outcome Data Extraction

• Extract the retained drug-target SNPs from the Serum Calcium GWAS.
• Harmonize the exposure and outcome datasets.
• Carefully align effect alleles to ensure the beta values represent lowering LDL-C/TC, mimicking the direction of the drug effect.

4. Analytical Models

Because the number of instruments per gene will be very small, standard sensitivity models (MR-Egger, PRESSO) cannot be used due to a lack of degrees of freedom.

• Single SNP: Use the Wald Ratio.
• Multiple Independent SNPs: Use the standard Inverse Variance Weighted (IVW) fixed-effects model.
• Multiple Correlated SNPs: If relaxed clumping was used, apply Generalized Least Squares (GLS) or Principal Component Analysis (PCA) MR to account for the LD matrix.

5. Adjudication & Biological Interpretation

• Evaluate each drug target independently against Serum Calcium.
• Compare the Drug-Target causal estimates against the "Global" LDL-C MR estimates.
• If HMGCR variants lower calcium but PCSK9 variants do not, the effect is driven by the specific statin pathway, not by systemic LDL-C reduction.

[davebridges]

MR Analysis Summary — Cholesterol → Serum Calcium

Overview

Two complementary Mendelian Randomization approaches both support a causal
effect of circulating cholesterol on serum calcium levels, providing human
genetic evidence motivating experimental validation in pre-clinical models.

Genome-Wide MR (Cholesterol → Calcium)

Using hundreds of genome-wide significant SNPs as instruments:

• Total cholesterol → calcium: IVW b=0.065, p=0.0006; consistent across
  weighted median, weighted mode, MR-PRESSO, MR-RAPS
• LDL-C → calcium: IVW b=0.053, p=0.006; consistent across all methods
• Reverse direction (calcium → cholesterol, calcium → LDL-C) is null across
  all methods, supporting a unidirectional cholesterol → calcium relationship
• Bidirectional design rules out reverse causation as an explanation

Drug-Target MR — HMGCR (Statin Proxy)

Using cis-SNPs within ±500 kb of HMGCR as instruments for the specific effect
of statin-mediated cholesterol lowering (11 instruments, allele score at r²<0.30,
median F-statistic well above 10):

• LDL-C instruments: IVW-RE b=0.163 (95% CI 0.011–0.315), p=0.035
• Total cholesterol instruments: IVW-RE b=0.160 (95% CI −0.005–0.325), p=0.057
• Heterogeneity Q non-significant for both (p=0.85 and p=0.59), indicating
  consistent estimates across instruments
• MR-Egger intercept non-significant (p=0.18 and p=0.70), no evidence of
  directional pleiotropy
• Leave-one-out analysis: all 11 iterations produced positive estimates
  (range 0.139–0.218 for LDL-C), confirming no single SNP is driving the result

Interpretation

The convergence of genome-wide and HMGCR drug-target MR in the same positive
direction supports the hypothesis that cholesterol causally increases serum
calcium. The drug-target result is specific to the HMGCR locus, meaning the
effect is consistent with either:

1. LDL-C itself promoting bone demineralization and calcium release, or
2. The mevalonate pathway (blocked by statins) having direct effects on
   osteoclast function via isoprenoid/prenylation-dependent mechanisms
   (Rho GTPase prenylation regulates osteoclast cytoskeletal organization
   and survival independently of LDL-C lowering)

These two mechanisms cannot be distinguished by HMGCR instruments alone, but
both are testable in mouse models. The effect sizes are consistent across
both exposures (LDL-C and total cholesterol), suggesting the signal is not
specific to one lipid fraction.

Motivation for LDLR/APOE Null Mouse Experiment with Statins

The human genetic evidence supports the following experimental logic:

• Genetically proxied elevation of cholesterol (via HMGCR instruments)
  increases serum calcium — therefore pharmacological reduction of
  cholesterol via statin treatment should reduce serum calcium
• The Ldlr⁻/⁻ model provides constitutive hypercholesterolemia, allowing
  a clean test of whether elevated LDL-C is sufficient to increase serum
  calcium and reduce bone density
• Statin treatment in Ldlr⁻/⁻ mice tests whether the calcium/bone phenotype
  is reversible by cholesterol lowering, directly mirroring the genetic
  instrument logic of the MR analysis
• If statin treatment normalises serum calcium and bone density in
  Ldlr⁻/⁻ mice, this confirms LDL-C (or the mevalonate pathway) as the
  causal intermediate and validates the human genetic finding experimentally
• The Apoe⁻/⁻ model provides a complementary hypercholesterolemia context
  with different lipoprotein distribution, allowing assessment of whether
  the effect is specific to LDL-C or broader hypercholesterolemia

Limitations of the MR Evidence

• HMGCR instruments cannot distinguish LDL-C from mevalonate pathway mechanisms
  — the mouse experiment with statins is needed to test reversibility and
  begin to separate these
• The calcium GWAS (MGI PheWeb) had insufficient variant coverage at the
  PCSK9 and NPC1L1 loci, precluding drug-target MR for those targets with
  the current dataset; this will be addressed in future analyses with
  higher-resolution outcome GWAS data
• Effect sizes from drug-target MR (b0.16) are larger than genome-wide MR
  (b0.06), consistent with cis-restriction capturing a more specific
  mechanistic signal but should be interpreted on their respective scales

[davebridges]

Need to update figures and tables for drug target MR

• add instruments to SNP lists (Supplementary Table 1)
• add instrument statistics to Table 2 (in summary-tables.qmd)
• create Table 3
• create SNP filtering schematic for UKBB Drug Target GWAS