Incidence Rate (Person-Time)

Incidence measures new cases, and the honest denominator for new cases is not people but person-time. Somebody followed for ten years had ten times the opportunity to fall ill as somebody followed for one, and counting them as one person each throws that away. Person-time adds up the time each participant was actually at risk and under observation, so 500 people followed for nine years and 200 followed for six months contribute 4,500 and 100 person-years respectively.

The unit therefore reads as cases per 1,000 person-years, or per 100,000 for a rarer outcome. The multiplier is cosmetic — chosen so the figure has digits in front of the decimal point rather than a string of zeros behind it — and comparing two published rates means checking their multipliers first. That the multiplier is arbitrary does not stop it from being the commonest source of a hundredfold error in a comparison.

What person-time buys is the ability to handle a cohort where people arrive and leave. A participant who withdraws, dies of something else, moves away or develops the outcome stops contributing at that moment, so an incomplete follow-up costs you the time you did not observe rather than invalidating the person. It is the natural denominator for open cohorts, and it is why incidence rates survive in studies that a simple proportion could not describe.

The assumption underneath is that the hazard is roughly constant over the period being summed, since 100 person-years means the same thing whether it is one person for a century or a hundred people for a year. For an outcome whose risk climbs steeply with age, or a treatment whose risk concentrates in the first weeks, that assumption is false and the pooled rate is an average across periods that behave very differently. Where the hazard varies, the rate should be stratified rather than summed — and this is the standard caution attached to person-time in every methods text that introduces it.