Epidemiology Calculators

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Epidemiology is the study of the distribution and determinants of health-related events in human populations, with the goal of informing prevention and control strategies. It quantifies disease frequency (incidence, prevalence), identifies risk factors (relative risk, odds ratio, attributable risk), and uses observational and experimental study designs (cohort, case-control, randomized controlled trials) to establish causal relationships. Epidemiology is the scientific foundation of public health, clinical medicine, environmental health, and health policy.

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Disease Frequency Measures

  • Incidence rate: New cases / person-time at risk. Measures the rate of new disease occurrence.
  • Cumulative incidence: New cases / population at risk in a given period. Risk of developing disease.
  • Prevalence: Existing cases / total population at a point in time or period. Proportion currently affected. Prevalence ≈ incidence × average disease duration.

Measures of Association

  • Relative risk (RR): Incidence in exposed / incidence in unexposed. RR > 1 = increased risk; RR < 1 = protective.
  • Odds ratio (OR): Odds of exposure in cases / odds of exposure in controls. Used in case-control studies. OR approximates RR when disease is rare.
  • Attributable risk: Incidence_exposed − Incidence_unexposed. Excess risk attributable to exposure.

Study Designs

  • Cohort: Follow exposed and unexposed groups; compare incidence; gold standard for RR; efficient for common exposures; prospective or retrospective
  • Case-control: Compare exposures in cases vs. controls; efficient for rare diseases; calculates OR; susceptible to recall bias
  • Cross-sectional: Exposure and outcome at one time; prevalence study; can't establish temporality
  • RCT: Random assignment to exposure; controls confounding; highest evidence for causation

Confounding

Confounders are variables associated with both exposure and outcome (e.g., smoking as confounder in coffee-lung cancer studies). Control by: restriction; matching; stratification; multivariate regression; propensity scores.

Glossary

Incidence
New cases of disease per population at risk per time period; measures disease risk; used in cohort studies to calculate relative risk; contrasted with prevalence (existing cases).
Relative Risk (RR)
Incidence in exposed / incidence in unexposed; RR > 1 = increased risk; calculated from cohort studies; when disease is rare, OR approximates RR from case-control studies.
Confounding
A variable associated with both exposure and outcome that distorts the apparent relationship; controlled by restriction, matching, stratification, or multivariable regression.

Frequently Asked Questions

Incidence: the rate or proportion of NEW cases of a disease occurring in a defined population over a specified time period. It measures the risk of developing disease. Two types: (1) Incidence rate = new cases / person-time at risk (e.g., 50 cases/1,000 person-years); (2) Cumulative incidence (risk) = new cases / population at risk in a period. Prevalence: the proportion of a population that HAS the disease at a given point in time (or period). Prevalence ≈ incidence × average disease duration. High prevalence can result from high incidence OR long disease duration. These measure different things: incidence for acute diseases and risk factors; prevalence for chronic disease burden planning.

Relative Risk (RR): incidence in exposed / incidence in unexposed. Requires knowing disease incidence in both groups → used in cohort studies. Interpretation: RR = 2.5 means exposed individuals are 2.5× more likely to develop disease. Odds Ratio (OR): (odds of exposure in cases) / (odds of exposure in controls). Used in case-control studies (where incidence can't be calculated because cases are selected). When disease is rare (<10% incidence): OR ≈ RR. When disease is common: OR overestimates RR (OR will be further from 1 than RR). OR is still used in logistic regression for common outcomes because of mathematical convenience — just be cautious interpreting magnitude as RR when outcome is common.

Observational studies: Cohort — follows exposed/unexposed groups prospectively or retrospectively; measures incidence and calculates RR; best for common exposures and rare diseases. Case-control — selects cases (with disease) and controls (without); compares past exposure history; calculates OR; efficient for rare diseases; susceptible to recall and selection bias. Cross-sectional — measures exposure and disease simultaneously; provides prevalence; fast and cheap; cannot determine temporal sequence. Ecological — compares rates across populations; susceptible to ecological fallacy. Experimental: Randomized Controlled Trial (RCT) — randomly assigns treatment; controls confounding; highest level of evidence; not always feasible or ethical. Natural experiments: use policy changes or other non-random exposures that mimic randomization.

Confounding occurs when a third variable (confounder) is associated with both the exposure and the outcome, distorting the apparent relationship between them. Example: studies initially found coffee associated with lung cancer; smoking is the confounder — smokers drink more coffee AND get more lung cancer; controlling for smoking eliminates the coffee-cancer association. Criteria for a confounder: associated with the exposure; associated with the outcome; not on the causal pathway between them. Control methods: Restriction (study only non-smokers); Matching (match cases and controls on confounders); Stratified analysis (compare RR/OR within each stratum of the confounder); Multivariable regression (adjust for multiple confounders simultaneously); Propensity score methods.