Per 1 person-time unit
Per 100 person-time units
Per 1,000 person-time units
Per 10,000 person-time units
Per 100,000 person-time units
function calculatePersonTimeRate() {
var events = parseFloat(document.getElementById('ptr_events').value);
var persons = parseFloat(document.getElementById('ptr_persons').value);
var duration = parseFloat(document.getElementById('ptr_duration').value);
var multiplier = parseFloat(document.getElementById('ptr_multiplier').value);
var unit = document.getElementById('ptr_unit').value;
var resultDiv = document.getElementById('ptr_result');
// Validation
if (isNaN(events) || isNaN(persons) || isNaN(duration)) {
resultDiv.style.display = 'block';
resultDiv.innerHTML = 'Please enter valid numbers for all fields.';
return;
}
if (persons <= 0 || duration <= 0) {
resultDiv.style.display = 'block';
resultDiv.innerHTML = 'Persons and Duration must be greater than zero.';
return;
}
// Calculation Logic
// 1. Calculate Total Person-Time (Denominator)
var totalPersonTime = persons * duration;
// 2. Calculate Raw Rate (Events / Person-Time)
var rawRate = events / totalPersonTime;
// 3. Apply Multiplier
var adjustedRate = rawRate * multiplier;
// Formatting Output
var unitLabel = "Person-" + unit; // e.g. Person-Years
var html = '
Calculating the person-time rate, often referred to in epidemiology as the incidence density rate, is a critical method for measuring the frequency at which new events occur within a population over a specific period. Unlike simple percentages, person-time accounts for the fact that not all individuals are observed for the same duration.
What is Person-Time?
Person-time is a measurement that combines the number of people in a study with the amount of time each person spends in the study. It represents the total time-at-risk for the entire group. Common units include person-years, person-months, or person-days.
For example, if one person is observed for 10 years, they contribute 10 person-years. If 10 people are observed for 1 year each, they also contribute a total of 10 person-years (10 people × 1 year).
The Formula
The formula for calculating the person-time incidence rate is:
Rate = (Number of New Events) / (Total Person-Time at Risk)
To make the result easier to interpret, the rate is often multiplied by a standard factor (k), such as 1,000 or 100,000.
Rate = (Events / Person-Time) × k
Step-by-Step Calculation Example
Imagine you are conducting a study on workplace injuries in a factory over the course of 5 years.
Step 1: Determine the Number of Persons. Let's say you are tracking 500 employees.
Step 2: Determine Average Duration. On average, each employee was tracked for 4 years.
Step 3: Calculate Total Person-Time. 500 employees × 4 years = 2,000 person-years.
Step 4: Count the Events. During this time, 10 injuries occurred.
Step 5: Apply the Formula. Rate = 10 / 2,000 = 0.005 injuries per person-year.
To report this more clearly, you might multiply by 1,000:
0.005 × 1,000 = 5 injuries per 1,000 person-years.
Why Use Person-Time Rate?
This metric is superior to cumulative incidence (simple risk) when:
Participants join or leave the study at different times (dynamic populations).
Participants are lost to follow-up before the study ends.
The risk of the event varies over time.
By using the calculator above, you can accurately determine the incidence density for research, public health monitoring, or reliability engineering projects.