The Relative-Risk-of-2.0 Threshold

Definition

If an epidemiological study finds that an exposed group develops a disease at more than twice the rate of an unexposed group (relative risk > 2.0), some courts reason that any single exposed individual who gets the disease was more likely than not (probability > 50%) caused by the exposure — because more than half of the excess cases in the exposed group are attributable to the agent. This is mathematically equivalent to saying the attributable fraction exceeds 50% once relative risk exceeds 2.0, and courts have used it as a bridge from group-level epidemiology to the individual "preponderance of the evidence" standard required to win a toxic-tort case.

In the Book

The Epidemiology reference guide lays out the reasoning and then spends several pages on its caveats: the underlying study must be valid (free of bias or confounding that could inflate an apparent relative risk near 2.0); the study subjects must resemble the plaintiff in dose, duration, and competing risk factors, or extrapolation requires "strong (and questionable) assumptions"; and there is real scholarly disagreement about whether 2.0 should be a hard requirement or just a "taking-off point." The manual cites the Restatement (Third) of Torts cataloguing courts on both sides of that split, and notes commentators who argue that relative risks under 2.0 (or even under 3.0) may reflect "unperceived bias or confounding" rather than a true causal effect. It also flags the doctrine's harsh edge cases: a defendant whose agent produces a relative risk just above 2.0 can be held liable for the entire disease, not just the excess portion actually attributable to it, while a defendant whose agent falls just below 2.0 may owe nothing — an all-or-nothing cliff that some judges (Judge Posner among them) have argued should be replaced with proportional, probability-weighted damages.

Why It Matters

This is a case study in what happens when a continuous, uncertain quantity (a risk ratio with a confidence interval) has to be converted into a binary legal decision (liable / not liable) at a threshold chosen for administrative convenience rather than derived from first principles. The same move — picking a round number on a continuous scale and treating crossing it as qualitatively different from not crossing it — recurs anywhere a probability estimate must produce a yes/no decision: credit scoring cutoffs, clinical diagnostic thresholds, statistical significance itself. Recognizing the threshold as a policy choice, not a natural boundary, is what lets you ask whether it's calibrated to the actual cost of false positives versus false negatives on either side of it.