PhronesisThe question, and why it was stuck
Pooled across twelve studies and 752,899 participants, resting heart rate predicts cancer mortality at HR 1.13 (1.08–1.18) per 10 bpm. That association is large, replicated, and dose-responsive.
It is also completely ambiguous. A raised resting heart rate might drive worse outcomes — sympathetic tone as a displacing surround, in this site’s vocabulary. Or an undetected tumour might raise the heart rate, in which case the arrow runs backwards and the whole reading inverts. The meta-analysis cannot tell, and says so.
Every observational design has this problem. One design does not.
Why Mendelian randomisation settles it
Genetic variants that raise resting heart rate are allocated at conception, decades before any tumour, and a tumour cannot alter them. Using those variants as an instrument gives an estimate of the causal effect that reverse causation cannot contaminate by construction — not because the analysis controls for it, but because the arrow is structurally unavailable.
The instrument was already built. A genome-wide meta-analysis of resting heart rate covers up to 835,465 individuals and 493 independent variants. Two-sample MR from it has been run against dilated cardiomyopathy, atrial fibrillation and stroke. It had not been run against cancer.
Both halves are open. Checked by downloading them, not by reading a claim — this project spent a morning discovering that a preregistration’s “no permissions” was false, and does not make that assumption again.
What was run
Exposure: GCST007609, UK Biobank, 458,969 European individuals, resting heart rate mean.
Outcome: GCST004988, BCAC OncoArray, 76,192 breast cancer cases and 63,082 controls.
331 independent variants reached genome-wide significance, one lead kept per megabase, mean F-statistic 75 — far above the weak-instrument floor of 10. All 331 were present in the outcome. 53 palindromic variants were dropped because their strands cannot be aligned safely, leaving 278 instruments.
The result
| IVW (primary) | β +0.0109, se 0.0020 |
| Weighted median | β +0.0110 |
| MR-Egger slope | β +0.0109, se 0.0031 |
| Egger intercept | −0.00097, p 0.18 — no directional pleiotropy |
Three estimators that fail in different ways agree to three decimal places, and the pleiotropy test is null. The weighted median stays consistent if up to half the instruments are invalid; it moved by 0.0001.
Exposure effects are in beats per minute — median absolute single-variant effect 0.19 bpm, the scale of known resting-heart-rate loci and an order of magnitude too large for a standardised phenotype. That unit call carries every number here, so it is derived in the code rather than assumed. Per 10 bpm of genetically predicted resting heart rate:
OR 1.115 (1.072–1.160) for breast cancer — against an observational 1.13 (1.08–1.18) for cancer mortality.
The causal estimate lands almost exactly on the observational one. Whatever the meta-analysis authors feared they were seeing, the association survives the test built to break it.
Why the intervals are too narrow, and other reasons to be careful
The pruning is crude, and this is the real limitation. Instruments were separated by physical distance — one lead variant per megabase — rather than clumped against a linkage-disequilibrium reference panel, because no panel was available here. Distance pruning removes obvious neighbours and leaves long-range LD behind. Correlated instruments are counted as independent evidence, which narrows the confidence interval and shrinks the p-value. The stated interval is optimistic and 2.7×10−8 is smaller than it should be. What this run supports is the point estimate and the direction.
Balanced pleiotropy would not show up. The Egger intercept tests directional pleiotropy only. Resting heart rate is genetically correlated with body mass index and physical activity, both of which touch breast cancer through other routes; if those effects scatter in both directions the intercept stays null while the estimate is still contaminated. This is the most likely alternative explanation and this analysis does not exclude it.
Incidence is not mortality. BCAC measures whether breast cancer occurs. The observational 1.13 measures whether cancer kills. The two numbers agreeing is suggestive and is not the same quantity being estimated twice.
One cancer, one ancestry. European-ancestry breast cancer. Prostate and colorectal summary statistics are equally open and equally unrun.
What it changes
For the framework: the arrow points the way it assumed. Sympathetic displacement is not only a flag raised by an existing tumour — on this evidence some of it is upstream. The framework owns none of the biology and predicted nothing the cardiologists had not measured, but it read the literature the right way round, which was in genuine doubt this morning.
For Study 3: the hypothesis that β-blockade benefit varies with autonomic state is worth the trouble of a proper new-user design. The objection that could have killed it before it started — that high resting heart rate is merely a shadow cast by undiagnosed disease — is not supported here.
And the honest shape of the finding: the decisive test was free, open, and unrun. Both datasets sat on a public FTP server. The arithmetic is forty lines. Nobody had done it, and an afternoon was enough to get an answer worth checking properly.
Reproducing it
The code, the two download commands, and the raw output are in the repository at research/rhr_mr/. No R and no packages — the estimators are arithmetic. Anyone with 2 GB of disk can re-run this and disagree with it, which is the only property that makes it worth publishing at this stage.
References
Resting heart rate and cancer mortality, twelve studies and 752,899 participants, including the “marker or independent risk factor” question quoted above — full text.
The resting-heart-rate genetic instrument, 493 variants in 352 loci across up to 835,465 individuals, and its existing MR applications to cardiovascular outcomes — Nature Communications, 2023.
Exposure summary statistics: GWAS Catalog GCST007609. Outcome summary statistics: BCAC OncoArray, GWAS Catalog GCST004988.
The prior state of this question on this site, and the design problem this result rescues, are in Every Six Months Is Not a Series and the working note research/study-3-the-stratifier-moves.md.
Every hyperlink above was checked and returns 200.