Cumulative Incidence and Incidence Rate Calculation

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Epidemiology Calculator: Risk & Rate

The number of individuals who developed the disease/outcome during the specified period.
Used to calculate Cumulative Incidence (Risk). Must be larger than new cases.
Sum of time each person was at risk (e.g., Person-Years). Used for Incidence Rate.
None (Proportion) Per 100 (%) Per 1,000 Per 10,000 Per 100,000
Standard unit for reporting the result (e.g., cases per 100,000).
Cumulative Incidence (Risk)
Incidence Rate (Incidence Density)
function calculateIncidence() { var newCasesInput = document.getElementById('newCases'); var initialPopInput = document.getElementById('initialPop'); var personTimeInput = document.getElementById('personTime'); var multiplierInput = document.getElementById('multiplier'); var errorDisplay = document.getElementById('errorDisplay'); var resultsDiv = document.getElementById('results'); // Reset display errorDisplay.style.display = 'none'; resultsDiv.style.display = 'none'; // Parse values var cases = parseFloat(newCasesInput.value); var pop = parseFloat(initialPopInput.value); var pTime = parseFloat(personTimeInput.value); var mult = parseInt(multiplierInput.value); // Validation if (isNaN(cases) || cases 0) { if (cases > pop) { errorDisplay.innerText = "Error: Number of cases cannot exceed the initial population at risk."; errorDisplay.style.display = 'block'; return; } ciVal = (cases / pop) * mult; showCI = true; } // Incidence Rate Logic if (!isNaN(pTime) && pTime > 0) { irVal = (cases / pTime) * mult; showIR = true; } if (!showCI && !showIR) { errorDisplay.innerText = "Please enter Population size (for Risk) or Person-Time (for Rate) to calculate."; errorDisplay.style.display = 'block'; return; } // Display Logic resultsDiv.style.display = 'block'; var unitLabel = ""; if (mult === 100) unitLabel = "%"; else if (mult === 1) unitLabel = ""; else unitLabel = " per " + mult.toLocaleString(); // Update CI UI var ciResultDiv = document.getElementById('ciResult'); var ciTextDiv = document.getElementById('ciText'); if (showCI) { var ciDisplay = mult === 100 ? ciVal.toFixed(2) + "%" : ciVal.toFixed(2) + unitLabel; ciResultDiv.innerText = ciDisplay; ciTextDiv.innerHTML = "Probability of developing the outcome over the specified period."; } else { ciResultDiv.innerText = "N/A"; ciTextDiv.innerText = "Enter Initial Population to calculate."; } // Update IR UI var irResultDiv = document.getElementById('irResult'); var irTextDiv = document.getElementById('irText'); if (showIR) { irResultDiv.innerText = irVal.toFixed(4) + unitLabel + " person-time units"; irTextDiv.innerHTML = "Speed at which new cases are occurring relative to total exposure time."; } else { irResultDiv.innerText = "N/A"; irTextDiv.innerText = "Enter Person-Time to calculate."; } }

Understanding Disease Frequency: Cumulative Incidence vs. Incidence Rate

In epidemiology, accurately measuring how often a disease or health outcome occurs is fundamental to public health surveillance, risk assessment, and clinical research. While both measures describe the frequency of new cases, they answer slightly different questions and are used in different contexts.

1. Cumulative Incidence (Risk)

Cumulative Incidence, often referred to simply as "Risk," measures the proportion of people who develop the outcome during a specific time period. It answers the question: "What is the probability that an individual at risk will develop the disease over this time frame?"

The formula is:

Cumulative Incidence = (Number of New Cases) / (Total Population at Risk at Start)

Key Characteristics:

  • It is a proportion (range 0 to 1).
  • It requires a closed population (no new members adding in) or clear follow-up for the duration.
  • Time must be specified (e.g., "5-year risk").

2. Incidence Rate (Incidence Density)

Incidence Rate incorporates time directly into the denominator. Instead of just counting people, it sums up the total time that each person in the study population was at risk (Person-Time). It answers the question: "How fast is the disease occurring in the population?"

The formula is:

Incidence Rate = (Number of New Cases) / (Total Person-Time at Risk)

Key Characteristics:

  • The denominator is measured in units like person-years, person-months, or person-days.
  • It can handle dynamic populations (people entering and leaving the study).
  • It is a true rate (range 0 to infinity).

Calculation Example

Imagine a study following 1,000 people for 1 year. During this year, 10 people develop the disease.

Cumulative Incidence Calculation:

The risk is simply 10 divided by 1,000.

  • CI = 10 / 1000 = 0.01
  • Expressed as a percentage: 1%

Incidence Rate Calculation:

To calculate the rate, we need Person-Time. If we assume the 10 people developed the disease exactly halfway through the year, they contributed 0.5 years each. The 990 healthy people contributed 1.0 year each.

  • Person-Time (Cases) = 10 * 0.5 = 5 years
  • Person-Time (Healthy) = 990 * 1 = 990 years
  • Total Person-Time = 995 person-years
  • IR = 10 / 995 = 0.01005 cases per person-year
  • Standardized: 10.05 cases per 1,000 person-years

When to Use Which?

  • Use Cumulative Incidence when you want to communicate personal risk to patients or the public (e.g., "You have a 5% risk of flu this season").
  • Use Incidence Rate in research studies with variable follow-up times or dynamic populations, where you want to measure the force of morbidity.

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