chapter  10
Analysis of Time to Event Data
Pages 18

The odds ratio and relative risk, which were introduced earlier, give us good measures for risk assuming that the follow-up times averaged over individuals within two or more cohorts are equal. In reality, some individuals are followed for shorter periods of time due to the death of some subjects, withdrawals from the study, and general loss of follow-up of some individuals. The crudest measure that can give us information about risk while adjusting for follow-up is known as incidence density. The statistic associated with this measure is simply defined as the number of events in a cohort divided by the total person-time in that cohort. The total person-time in a given group is calculated by summing over all persons’ follow-up (or exposure) times. If Xj is a random variable with a value of 0 if individual j is event-free and 1 if individual j has had an event, and Tj is the follow-up time for that individual then ID is formally defined as

ID ≡ ∑n

, (10.1)

where n is the number of individuals. To calculate this quantity we need only the number of events of interest and the total person-time for the n individuals.