General versus specific causation
Toxic-tort causation is usually decomposed into two distinct questions. General causation asks whether an exposure is capable of causing a given type of harm in a population at all — for example, whether a chemical can cause a particular cancer. Specific causation asks the narrower question of whether the exposure actually caused this plaintiff's harm.
Epidemiology is well suited to the first question. It studies groups, not individuals, and is designed to detect and quantify associations between exposures and outcomes across populations. The second question is harder, because population-level data do not directly tell us what happened inside one person's body. The "doubling of the risk" argument is one widely discussed attempt to use population epidemiology to reason about an individual — and understanding both its logic and its limits is essential when the parties' experts disagree.
What relative risk actually measures
Relative risk (RR) is a ratio. It compares the risk of an outcome in an exposed group to the risk of that same outcome in an unexposed group:
RR = (risk in the exposed group) ÷ (risk in the unexposed group).
Suppose that, over a defined period, 6 of every 1,000 unexposed people develop a condition, while 12 of every 1,000 exposed people develop it. The risk in the exposed group is 12/1,000 and in the unexposed group is 6/1,000, so the relative risk is 2.0. Exposed people, as a group, experienced twice the rate of the condition.
A relative risk of 1.0 means the two groups had the same risk — no association. A relative risk above 1.0 indicates a higher rate in the exposed group; below 1.0 indicates a lower rate. Importantly, relative risk describes the average experience of the groups studied. It is a property of populations, not a statement about any single person.
The "doubling of the risk" argument
The bridge from group risk to individual causation runs through a quantity called the attributable fraction (sometimes the attributable proportion among the exposed). Among exposed people who developed the outcome, it estimates the share of cases that would not have occurred absent the exposure:
Attributable fraction = (RR − 1) ÷ RR.
When RR = 2.0, the attributable fraction is (2 − 1) / 2 = 0.50, or 50%. The intuition behind the argument is that if more than half of the cases in the exposed group are attributable to the exposure, then for a randomly chosen exposed case the exposure is "more likely than not" the cause — which maps onto the preponderance-of-the-evidence standard. By this reasoning, a relative risk above 2 corresponds to an attributable fraction above 50%.
| Relative risk (RR) | Attributable fraction |
|---|---|
| 1.5 | ~33% |
| 2.0 | 50% |
| 3.0 | ~67% |
| 4.0 | 75% |
Courts have not treated this logic uniformly. Some have found a relative risk above 2 to be relevant to, or supportive of, specific causation, viewing the "more likely than not" framing as a natural fit for the civil burden of proof. Others have declined to adopt any bright-line rule, holding that a relative risk above 2 is neither necessary nor sufficient and that specific causation must be assessed on the full record. The statistical caution below explains why a rigid threshold is difficult to defend.
Where the inference breaks down
The "doubling" argument rests on several assumptions that frequently do not hold. A relative-risk point estimate above 2 does not, by itself, establish specific causation.
Uncertainty: confidence intervals and significance
A relative risk is an estimate from sampled data, and it carries uncertainty. A point estimate of 2.5 with a 95% confidence interval running from, say, 0.9 to 6.0 is statistically consistent with no effect at all. A point estimate above 2 whose confidence interval crosses 2 — or crosses 1 — does not reliably show that the true relative risk exceeds 2. Reading only the central estimate while ignoring the interval is one of the most common errors in this area.
Confounding and bias
An observed association may be inflated (or masked) by confounding factors that differ between the exposed and unexposed groups, by selection effects, or by measurement and recall bias. A relative risk of 2.2 that shrinks toward 1 after adjusting for smoking, age, or co-exposures may not reflect a true doubling. The quality of the adjustment, not just the headline number, drives the inference.
Heterogeneity across people and doses
A single population-average relative risk can conceal wide variation. Risk may be far higher at heavy exposure and negligible at low exposure; it may differ by genotype, sex, age, or the presence of other conditions. A plaintiff with low exposure or short latency may not resemble the high-exposure subgroup that drives an average above 2.
Individual susceptibility and competing causes
The attributable-fraction argument treats an exposed case as if drawn at random from the studied population. Real plaintiffs are not random draws. Competing causes, individual susceptibility, biomarkers, and the specific clinical picture can all push an individual assessment away from the population average in either direction.
One study versus the body of evidence
Resting a causation opinion on a single study with a relative risk above 2 is fragile. Sound analysis weighs the entire body of evidence — multiple studies, designs, and populations — and asks whether the finding is consistent and replicated, not whether one favorable estimate cleared a numeric bar.
RR, odds ratio, and hazard ratio are not interchangeable
Many studies report an odds ratio (common in case-control designs) or a hazard ratio (common in time-to-event analyses) rather than a relative risk. For rare outcomes the odds ratio approximates the relative risk, but for common outcomes it can substantially overstate it. A hazard ratio describes an instantaneous rate over follow-up, not a cumulative risk ratio. Plugging an odds ratio or hazard ratio into the attributable-fraction formula as though it were a relative risk can distort the result.
How statisticians evaluate these arguments
A rigorous review does not stop at the relative-risk value. It examines study design and quality; the width and bounds of the confidence interval; how thoroughly confounding was adjusted for; whether a dose-response relationship is present; and whether findings are consistent across independent studies. These are the kinds of considerations associated with the Bradford Hill viewpoints — strength, consistency, dose-response, biological plausibility, and the like — used to weigh whether an association reflects causation.
The central diagnostic question is how the relative risk is being used. Treated as one piece of evidence within a careful, transparent analysis, a relative risk above 2 can be informative. Treated as a mechanical rule — "above 2 proves it, below 2 disproves it" — it overstates what the statistic can deliver, in either direction.
A balanced note
The doubling-of-the-risk argument is invoked by plaintiff and defense experts alike, and it is frequently misused on both sides. A plaintiff's expert may lean on a single point estimate above 2 while ignoring a confidence interval that crosses 1. A defense expert may dismiss a well-supported causal inference solely because a relative risk fell below 2, treating the threshold as a bright-line bar the law does not require. The value of independent statistical review is in separating what the data actually support from what the threshold is being asked to carry.
This article explains general statistical and epidemiological principles for educational purposes only. It is not legal, statistical, medical, or regulatory advice for any specific matter, and it does not reflect the views of the U.S. Food and Drug Administration, any former employer, or any client. Reading it does not create an attorney-client, consulting, or expert-witness relationship. Any engagement begins only upon a signed written agreement and clearance of a conflicts-of-interest check.
Lei Li, Ph.D., is a biostatistician and former FDA/CDRH statistical reviewer. Learn more about Dr. Li.