Population Risk

Aggregate supplied excess-risk estimates across nonoverlapping population strata into expected cases, not observed case counts or causal attribution.

Description

Calculate expected excess cases and population-weighted excess risk from supplied stratum risks.

An excess-risk probability describes additional risk above a defined baseline over a specified time horizon. Multiplying that probability by the number of people gives an expected excess case count. Risk estimates must be distinguished from observed case counts and from relative-risk ratios.^[1]

This tool combines nonoverlapping population strata using the risk probability supplied for each stratum. It reports expected cases for each stratum, their total, and the population-weighted excess probability.

Expected counts can be fractional: 0.5 expected cases is a statistical expectation, not half of an observed person. The population-weighted output is a fraction; multiply by 100 only if you need a percentage.

When to use Population Risk

Use it to aggregate already established excess-risk estimates across a population with different exposure or susceptibility strata, while retaining one endpoint and time horizon.

How to use Population Risk and interpret its calculation

Enter aligned, nonempty stratumPopulationSizes and excessRiskEstimates lists.
Use nonnegative safe-integer population sizes with a positive total, and risk probabilities between 0 and 1. Keep strata nonoverlapping and risk definitions consistent.
Run the calculation and read stratumExpectedExcessCases, totalExpectedExcessCases, and populationWeightedExcessRisk. Report the model, baseline, and time horizon behind the supplied risks.

expected_i = N_i × r_i; total expected = Σ expected_i; weighted excess risk = total expected / Σ N_i

N is stratum population and r is excess-risk probability, not relative risk or a hazard quotient.

The implementation preserves stratum order and does not round expected counts. Adding expectations does not require independence, but duplicate population membership would double count contributions.

json

{
  "input": {
    "stratumPopulationSizes": [
      1000,
      2000
    ],
    "excessRiskEstimates": [
      0.001,
      0.002
    ]
  },
  "output": {
    "stratumExpectedExcessCases": [
      1,
      4
    ],
    "totalExpectedExcessCases": 5,
    "populationWeightedExcessRisk": 0.0016666666666666668
  }
}

A zero-size stratum contributes no cases but its risk still must be valid. Zero risk contributes zero expected cases. A total population of zero is rejected; risk one contributes the full stratum population to the expectation.

Limitations and assumptions

No exposure-to-risk model, demographic matching, uncertainty interval, count-distribution simulation, or causal attribution is performed. The calculator cannot validate the estimated risks or identify overlap between unnamed strata.

Do not substitute relative risk, a hazard quotient, or an unconstrained model score for a probability. Risk horizons and baseline definitions must match across strata for the total to have a common interpretation.

Alternative or Complementary methods

A cancer slope-factor screen can generate a model-based excess-risk estimate when its assumptions apply, but any estimate outside 0–1 cannot be used as a probability here. Noncancer hazard quotients remain a different screening measure.

References

AirToxScreen Glossary of Terms — U.S. Environmental Protection Agency

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