Methodological Framework Bias Necessity via Biology only Falsification

Methods Appendix: Temporal Falsification of Biology-Only Models via Negative Controls

1. Scientific Aim

This analysis does not estimate the causal effect of vaccination on mortality.

Instead, it addresses a logically prior question:

Are the observed mortality patterns compatible with any biologically plausible process in which vaccination affects mortality only after exposure?

If not, selection or another non-biological bias must exist, regardless of effect size.

This is a model falsification problem, not an estimation problem.
All claims are restricted to ruling out biology-only explanations, not quantifying effect sizes.

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2. Why This Is Possible with Limited Covariates

Although only age and sex are observed, the data contain strong temporal information:

• exact vaccination and death dates
• full population coverage
• pre-exposure mortality
• time-varying vaccination uptake

Temporal structure allows falsification of entire causal models without heavy covariate adjustment.
We are testing exchangeability assumptions necessary for causal inference, not estimating effects directly.

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3. Biology-Only Null Hypothesis

Under a biology-only data-generating process:

• Vaccination cannot affect mortality before it occurs
• Future vaccination is independent of past death, conditional on age and sex

Systematic pre-vaccination mortality differences violate this hypothesis.
Formally:

• Death before vaccination is independent of vaccination timing, given age and sex
• In symbols: D(t < V) ⟂ V | X, where X = (age, sex)

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4. Relation to Target Trial Logic

A target trial would randomize vaccination at time t and follow individuals forward.

This analysis does not emulate that trial to estimate a causal effect.
Instead, it tests whether the exchangeability required for such a trial is empirically plausible.

• If pre-vaccination mortality differs by future vaccination status, no target trial emulation can recover a causal effect without unverifiable assumptions.
• We explicitly highlight that this is a falsification test, not a causal estimate.

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5. Negative Control Reasoning

Two biologically guaranteed negative controls are used:

• Mortality before vaccination
• Placebo vaccination dates with no biological effect

Any association in these controls falsifies biology-only explanations.

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6. Causal Graphs

6.1 Biology-Only Model

graph TD
    Frailty --> Vaccination
    Frailty --> Death
    Age --> Vaccination
    Age --> Death
    Sex --> Vaccination
    Sex --> Death
    Vaccination --> Death

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7. Empirical Tests Implemented

Three independent falsification tests exploit temporal directionality and negative controls to probe the biology-only null hypothesis.

7.1 Pre-Vaccination Mortality (Temporal Falsification)

Objective:
Test whether mortality in a fixed window before vaccination differs systematically across groups defined by future vaccination timing.

Implementation details:

• Window: typically 30 days before the median vaccination date of each quantile
• Stratified by broad age groups
• Comparator: all individuals alive at the quantile date, or restricted to eventual vaccinators (configurable)
• Plots: separate figures per age group showing mortality rate vs. vaccination time quantile

Interpretation:
Any systematic pre-vaccination gradient falsifies the biology-only null.
Population-scale data make even small deviations detectable.

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7.2 Lagged Restricted Mean Survival Time (RMST)

Objective:
Compute RMST as a function of time since vaccination, including negative lags, to test temporal asymmetry.

Implementation details:

• RMST at time t = expected survival over next 30 days
• Conditional on survival to calendar day of each relative lag
• Kaplan–Meier estimator + influence-function variance; censoring >50% suppressed
• Lags: -30 to +60 days (configurable)

Logical implication:
Biology-only models require that RMST differences for negative lags equal zero.
Any deviation at negative lags directly falsifies the null.

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7.3 Placebo Vaccination Process (Selection Sufficiency Test)

Objective:
Assess whether selection on latent health alone can reproduce observed RMST patterns, using simulated placebo vaccination dates.

Implementation details:

• Uptake hazards estimated from real data (daily probability conditional on age, sex, calendar day)
• Placebo dates assigned only to never-vaccinated individuals
• Simulation: discrete-time Bernoulli hazard model
• Multiple simulations (default 3) → mean placebo curve + uncertainty bands
• Comparison: real RMST vs. placebo RMST, including negative lags

Interpretation:

• If placebo ≈ real, selection alone suffices to explain patterns
• Partial mismatch leaves ambiguity (selection + biology vs different frailty distribution)

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7.4 Triangulation Logic

• Pre-vaccination mortality: proves bias necessity
• Negative-lag RMST: confirms temporal directionality violation
• Placebo process: tests whether selection is sufficient

No single test is dispositive, but the joint pattern strongly supports the presence of non-biological selection.

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8. Structural Bias Considerations

The dominant non-biological bias pathway is selection on latent frailty, which affects both vaccination timing and mortality risk.

Conditioning on survival to vaccination time induces collider bias. Adjustment for age and sex alone is insufficient to block this pathway because frailty is multidimensional and unobserved.

This bias is a structural feature of the data-generating process, not a limitation of any particular estimator. Conventional regression adjustment, propensity scores, or machine-learning–based covariate balancing cannot eliminate this bias without strong and unverifiable assumptions.

This is precisely the kind of problem that C.S. Peirce warned about over a century ago: inference from non-random samples can produce fundamentally misleading conclusions.

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9. Interpretation

We can claim:

• Biology-only models appear highly inconsistent with the observed data patterns
• Selection on latent health is necessary
• Selection alone is often sufficient to reproduce observed patterns

We cannot claim:

• The true causal effect size
• Net benefit/harm of vaccination
• Exact decomposition of bias vs biology
• That selection is the only possible non-biological explanation

This is partial identification, ruling out a class of models rather than point-estimating parameters.

The evidence from temporal falsification, negative controls, and placebo simulations is sufficiently strong and convergent that maintaining a purely biological explanation as adequate would require substantially downplaying the foundational role of temporal precedence and negative control principles in causal inference.

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10. Summary

Temporal falsification, negative controls, and placebo simulations demonstrate that observed mortality patterns are extremely difficult to reconcile with a purely biological mechanism.

This is not a vaccine effectiveness study.
It is a demonstration of bias necessity and selection sufficiency, grounded in structural logic, temporal constraints, and negative controls.

References / Further Reading

• Hernán & Robins – Causal Inference: What If
• Robins – Structural nested models and g-estimation
• Pearl – The Book of Why (negative controls, backdoor paths)