Omitted familial extrinsic risk inflates inferred intrinsic lifespan heritability

This paper demonstrates that omitting heritable, mortality-relevant extrinsic risk factors from survival models causes the latent intrinsic frailty variance to absorb this omitted structure, thereby systematically inflating inferred intrinsic lifespan heritability estimates by approximately 9 percentage points.

The Gist

The Big Picture: A "Hidden Ingredient" in the Recipe

Imagine a famous chef (Shenhar) claims to have discovered a secret, pure ingredient called "Intrinsic Longevity" (the biological aging process inside our bodies). They say this ingredient is responsible for 50% of why some people live much longer than others.

To prove this, the chef baked a cake using a recipe based on old data from Danish twins born in the late 1800s. The chef's logic was: "If we remove all the external dangers of that time (like deadly infections, accidents, and bad sanitation) from the math, the remaining 'pure' cake must be 50% genetic."

Sergey Kornilov (the author of this paper) says: "Wait a minute. You didn't just remove the external dangers; you accidentally baked a hidden ingredient into your 'pure' cake. Because you didn't account for the fact that some families were genetically better at surviving those old infections, your math is tricking you. The 'Intrinsic Longevity' you measured isn't just biology; it's biology plus a hidden genetic advantage against old diseases."

The result? The chef's "50%" number is likely too high. The real number might be closer to 31% to 47%.

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The Core Problem: The "One-Size-Fits-All" Scale

To understand the mistake, let's look at how the chef measured the ingredients.

The Setup:
Imagine you have a scale that can only weigh one thing at a time.

• The Goal: You want to know how much "Genetic Aging" (the slow wear and tear of the body) weighs.
• The Problem: In the old days, there was also "Genetic Immunity" (the ability to survive infections). Both of these things made twins look similar to each other. If one twin survived a plague, the other likely did too, because they shared the same genes for both aging and immunity.

The Mistake:
The chef used a scale that could only measure "Genetic Aging." When the twins showed up looking very similar (because they shared genes for both aging and immunity), the scale had no other place to put that weight. So, it dumped all the weight onto "Genetic Aging."

• Analogy: Imagine you are trying to weigh a bag of apples (Aging) and a bag of oranges (Immunity) together, but your scale only has a label for "Apples." When you put both bags on, the scale reads "Apples: 10 lbs." You think you have 10 lbs of apples, but you actually have 5 lbs of apples and 5 lbs of oranges. You have overestimated the weight of the apples.

The Three Key Findings (The "Detective Work")

The author didn't just guess; they ran thousands of computer simulations to prove this "hidden ingredient" was the culprit.

1. The "Inflation" (The Scale is Broken)

The author found that because the model ignored the "Immunity" bag, the "Aging" bag got inflated by 22%.

• The Metaphor: It's like a balloon. If you pump air into a balloon but forget to account for the extra helium you accidentally added, the balloon looks 22% bigger than it really is.
• The Result: Because the "Aging" parameter was inflated, the final calculation of heritability jumped from the expected ~25% up to the claimed 50%.

2. The "Fingerprint" (The Cake Tastes Wrong)

If the chef's recipe were correct, the "cake" (the mathematical model) should taste exactly like the real world. But the author found a "fingerprint" of the mistake.

• The Metaphor: Imagine a tailor making a suit. If they get the measurements wrong, the suit might fit the waist perfectly but be too tight in the shoulders and too loose in the legs.
• The Evidence: The author showed that the chef's model predicted that twins would be too similar when they were very old (80+ years) and not similar enough when they were young. This "shape" of the error proved that the model was trying to force "Immunity" genes into the "Aging" category.

3. The "Negative Test" (Proving it wasn't just bad luck)

To be sure, the author ran "negative controls" (tests designed to fail if the theory was wrong).

• Test A: What if the "Immunity" genes weren't shared by twins? (Result: No inflation. The scale worked.)
• Test B: What if the "Immunity" genes didn't actually affect death? (Result: No inflation. The scale worked.)
• Test C: What if we added the "Immunity" ingredient back into the recipe? (Result: The "Aging" weight dropped back down to the correct level.)

This proved that the error wasn't a random glitch; it was specifically caused by ignoring heritable immunity.

Why Does This Matter?

You might ask, "So what? We live in modern times now. Infections aren't a big deal anymore."

The author argues that it's too late to fix the math.

• The Analogy: Imagine you are trying to figure out how much fuel a car uses by driving it in a heavy snowstorm. You calculate the fuel usage based on that storm. Then, you say, "Well, since we are driving on a sunny highway today, the fuel usage must be the same."
• The Reality: The car's engine was calibrated in the snow. The "fuel usage" number you got is contaminated by the snow. Even if you drive on a sunny highway today, your original calculation was still wrong because it was based on a stormy calibration.

The "Intrinsic Longevity" number (50%) was calculated using data from a time when infections were deadly. Because the model didn't separate "dying of old age" from "dying of infection," the number is contaminated.

The Bottom Line

The paper doesn't say that genetics doesn't matter for aging. It says that the 50% number is likely too high because it accidentally includes the genetic advantage of surviving old-fashioned diseases.

• The Chef's Claim: "50% of your lifespan is pure biological aging."
• The Author's Correction: "Actually, it's probably closer to 35%. The other 15% you counted was actually your family's genetic luck at surviving the plagues of the 1800s."

The study suggests that while we are getting better at living longer, our "biological aging" genes might not be as powerful as the headline number suggests. We need better recipes that separate the "aging" ingredients from the "immunity" ingredients to get the true measurement.

Technical Summary

1. Problem Statement

The paper critiques a recent study by Shenhar et al. (2026), which reported that the "intrinsic" heritability of human lifespan is approximately 50%, a significant increase from the commonly cited 20–25%. Shenhar's method involves a "calibrate-then-extrapolate" procedure:

1. Calibration: Fitting a one-component correlated-frailty survival model to historical twin data (where extrinsic mortality, $m_{ex}$, is non-zero) to match observed monozygotic (MZ) twin lifespan correlations.
2. Extrapolation: Setting the extrinsic hazard $m_{ex} = 0$ in the fitted model to estimate heritability in a counterfactual world free of external causes of death.

The Core Issue: Shenhar's model assumes that extrinsic mortality is a population-level constant with no individual heterogeneity. However, if heritable extrinsic susceptibility (e.g., genetic susceptibility to infections) exists but is omitted from the model, the calibration step cannot distinguish between intrinsic aging variance and extrinsic genetic variance. Consequently, the model absorbs the omitted extrinsic genetic structure into the intrinsic frailty parameter ($\sigma_\theta$), leading to an upwardly biased estimate of intrinsic heritability.

This paper distinguishes this omitted-variable bias (variance absorption during calibration) from collider bias (sample selection bias), which was previously identified by Hamilton (2026) as a separate threat.

2. Methodology

The author employs a rigorous simulation-based approach to isolate and quantify this bias mechanism.

• Data Generating Process (DGP):

  • A two-component model is used to simulate true lifespans:
    $$\mu_i(t) = m_{ex} \cdot \exp(\sigma_\gamma \gamma_i - \sigma_\gamma^2/2) + \exp(\theta_i) \cdot \exp(b \cdot t)$$
    • $\gamma_i$: Heritable extrinsic susceptibility (shared 100% by MZ, 50% by DZ).
    • $\theta_i$: Intrinsic aging parameter (shared 100% by MZ, 50% by DZ).
    • $\rho$: Genetic correlation (pleiotropy) between $\gamma$ and $\theta$.
  • Simulations use 50,000 twin pairs per zygosity, matching Danish cohorts born 1870–1900.
  • Three mortality model families are tested: Gompertz-Makeham (GM), Makeham-Gamma-Gompertz (MGG), and Saturating-Removal (SR).

• Experimental Design:

  • Misspecified Condition: The true DGP includes heritable extrinsic risk ($\sigma_\gamma > 0$), but Shenhar's one-component model (omitting $\gamma$) is fitted to the data.
  • Recovery Condition: A correctly specified two-component model is fitted to the same data to verify if the true intrinsic parameter can be recovered.
  • Negative Controls: Scenarios where extrinsic risk is non-familial, irrelevant to mortality, or vanishingly small to prove specificity.
  • Anchoring: Parameters $\sigma_\gamma$ and $\rho$ are anchored to empirical evidence (e.g., heritability of infection mortality, GWAS signals for HLA regions and longevity).

• Diagnostics:

  • Comparison of fitted $\sigma_\theta$ against true values.
  • Analysis of the bivariate twin survival surface $S(t_1, t_2)$ to detect structural misfit.
  • ACE Structural Equation Modeling to test if switching summary statistics resolves the bias.
  • Maximum Likelihood (ML) vs. Moment Calibration comparison to assess estimator dependence.

3. Key Contributions

1. Identification of Variance Absorption: The paper demonstrates that omitting heritable extrinsic frailty causes the calibration step to inflate the intrinsic frailty scale parameter ($\sigma_\theta$) to account for unmodeled twin concordance.
2. Quantification of Bias: The study provides precise estimates of the inflation under realistic parameter regimes, showing that the bias is not a minor artifact but a substantial distortion.
3. Structural Fingerprints: It identifies specific, observable signatures of this misspecification in the joint survival surface and age-specific conditional correlations, offering a way to falsify the one-component assumption in real data.
4. Model Generality: The bias is shown to be robust across different mortality model families (GM, MGG, SR) and different frailty distributions (log-normal, additive, gamma).
5. Falsifiability: The paper derives a testable prediction: if the genetic correlation between extrinsic susceptibility and intrinsic aging is negative ($\rho < 0$), the bias should reverse sign (deflating the estimate).

4. Key Results

A. Inflation of the Intrinsic Parameter

• Under the misspecified one-component model, the fitted intrinsic frailty parameter $\sigma_\theta$ is inflated by +22.1% (95% CI: 21.5–22.7%).
• This corresponds to a +49% inflation in variance ($\sigma_\theta^2$).
• Downstream Impact: This upstream distortion propagates to the Falconer heritability estimate ($h^2$), resulting in a net upward bias of +9.2 percentage points (pp) (95% CI: 8.7–9.7 pp).
  • Implication: If Shenhar's 50% estimate is corrected for this bias, the true intrinsic heritability would likely be in the range of 31–47%.

B. Structural Fingerprints

• Bivariate Surface Misfit: The misspecified model fails to reproduce the joint twin survival surface. The Integrated Squared Error (ISE) is 48 times larger than that of the correctly specified recovery model.
• Age-Specific Dependence: The misspecified model systematically overpredicts concordance at older ages (peaking at age 80, $\Delta r \approx 0.048$) and underpredicts it at younger ages. This reflects the model shifting extrinsic concordance into the intrinsic (Gompertz) component.

C. Specificity and Robustness

• Negative Controls: The bias disappears when extrinsic risk is non-familial, irrelevant to mortality, or negligible in magnitude, confirming the mechanism requires heritable, mortality-relevant, and familial extrinsic risk.
• ACE Decomposition: Switching from Falconer's formula to an ACE structural equation model does not resolve the bias. The heritable extrinsic component is absorbed into the additive genetic component ($A$) rather than shared environment ($C$), because it follows the same 1.0/0.5 sharing pattern as genetics.
• Estimator Dependence: While Maximum Likelihood (ML) estimation reduces the magnitude of inflation compared to moment matching (calibrating only $r_{MZ}$), ML still produces a structurally inflated pseudo-true parameter (+3% vs. +22% for moment matching). This confirms the bias is primarily a model-class issue, not just an estimator artifact.

D. Sensitivity and Falsifiability

• Dose-Response: Bias increases monotonically with the magnitude of extrinsic mortality and the heritable fraction of that mortality.
• Sign Reversal: In simulations where the genetic correlation $\rho$ is negative, the bias reverses direction (deflating the estimate), confirming the mechanism is driven by the interaction between intrinsic and extrinsic genetic pathways.

5. Significance and Conclusion

This paper fundamentally challenges the interpretation of Shenhar et al.'s 50% intrinsic heritability estimate. It argues that the estimate is not purely intrinsic but is contaminated by omitted heritable extrinsic susceptibility.

• Theoretical Impact: It highlights a critical limitation in "calibrate-then-extrapolate" survival models: if the model class is too restrictive (one-component), it cannot separate distinct sources of familial concordance, leading to pseudo-true parameters that absorb omitted variance.
• Practical Implication: The reported 50% heritability likely represents an upper bound. The true intrinsic heritability is likely lower (potentially 31–47%), though still higher than classical estimates.
• Future Directions: The paper suggests that resolving this identification problem requires:
  1. Bivariate diagnostics: Checking for the specific "early-deficit/late-excess" pattern in twin survival surfaces.
  2. Competing-risks models: Using cause-of-death data to separate intrinsic and extrinsic mortality events.
  3. Genomic anchoring: Incorporating polygenic scores to explicitly model the extrinsic frailty component.

In summary, the paper establishes that omitted familial extrinsic risk creates a structured, model-general upward bias in inferred intrinsic lifespan heritability, necessitating a re-evaluation of high heritability estimates derived from historical twin cohorts using single-component frailty models.