Peircean Evidence‑Weighted RMST ‐ Simple Explanation

Peircean Evidence‑Weighted RMST

A simplified overview of a new survival analysis method

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The problem

Comparing groups like vaccinated versus unvaccinated is difficult because people get vaccinated at different times. This creates an unfair head start known as Immortal Time Bias.

The Peircean method fixes this by comparing two fair what‑if worlds:

• World A: What if this person never got vaccinated?
• World B: What if this person got vaccinated on their actual date?

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The innovation

Most methods use mathematical models to smooth data, which can hide or create patterns. This method is different:

1. It uses Brute Facts

It avoids complex formulas to guess risk. It looks only at exactly who lived and who died each day to ensure the results are grounded in reality.

2. It filters for Signal

It only fully counts days where the difference is supported by strong statistical evidence. It asks: Is this gap real, or just a random coincidence?

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Why Peircean?

Inspired by logician and mathematician Charles Sanders Peirce, the method defines evidence as Surprisal:
the degree of surprise felt when data contradicts what we expect by chance.

Strong evidence comes from gaps unlikely to happen randomly. If a gap is messy or small, the method treats it as noise and gives it less weight.

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How it works

1. Two Worlds: We follow each person in two parallel tracks (Never-Vax vs. Vax).
2. Daily Count: We record deaths each day to create Empirical Survival Curves.
3. Surprise Test: We test the gap daily. If it is unlikely to be a fluke, it is marked as Strong Evidence.
4. Weighing: Stronger evidence is given more weight, creating the Peircean Evidence Curve.
5. Results: We get two numbers: the Empirical Difference (what happened) and the Peircean Difference (what is proven).

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Summary

The Peircean method measures how much better a strategy performs and identifies how much of that difference is backed by non‑random evidence.