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Incidence Density Exposure Day Factor Tool

Incidence density from explicitly supplied person-time; no assumption that events equal affected people.

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Description

Convert personYears = personDays/daysPerYear and report ratePerBaseYears = events*daysPerYear*rateBase/personDays.

An event rate needs a denominator and reporting scale. Person-time rates use accumulated time at risk, while population-scaled rates use a population count for a matching period; neither is automatically a probability.

Convert personYears = personDays/daysPerYear and report ratePerBaseYears = events*daysPerYear*rateBase/personDays.

When to use this tool

Use Incidence Density Exposure Day Factor when converting a rate's reporting base or its supplied person-time unit.

How to use the tool and how it works

  1. Enter events, personDays, daysPerYear, rateBase. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read personYears, ratePerBaseYears. Use the output convention below.

Require nonnegative whole events and positive personDays, daysPerYear and rateBase. Convert personYears = personDays/daysPerYear and report ratePerBaseYears = events*daysPerYear*rateBase/personDays. For example, rateBase = 1000 reports events per 1000 person-years under the supplied year-length convention.1

Person-time rates use accumulated time at risk, while incidence proportions use a population denominator. The conversion here changes the time and reporting scale; it does not turn a rate into an individual probability.2

Input fieldMeaning and unitsAccepted input
eventsEventsRequired. Safe integer; minimum 0.
personDaysPositive accumulated person-time measured in days.Required. Finite number; strictly above 0.
daysPerYearPositive declared number of days per modeled year.Required. Finite number; strictly above 0.
rateBasePositive reporting scale, such as 1000 for events per 1000 person-years.Required. Finite number; strictly above 0.
Output fieldInterpretationReturned shape
personYearsPerson YearsRequired. Finite number.
ratePerBaseYearsRate Per Base YearsRequired. Finite number.
json
{
  "input": {
    "events": 10,
    "personDays": 36500,
    "daysPerYear": 365,
    "rateBase": 1000
  },
  "output": {
    "personYears": 100,
    "ratePerBaseYears": 100
  }
}

Limitations and assumptions

  • No calendar follow-up, censoring or at-risk time is derived. This is a person-time event rate, not an individual's probability of disease; daysPerYear is explicitly supplied rather than inferred from dates.
  • Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
  • Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Keep event definitions and follow-up periods aligned, and use complete stratification or survival methods when the question requires adjustment or changing risk over time.

References

  1. Calculation and input contract: epidemiology/incidence-density-exposure-day-factor — tool.io

  2. Measures of risk: morbidity frequency measures — Centers for Disease Control and Prevention

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