General description of frequently used time-to-event statistical analyses
| Description of analysis | Quantity estimated | Competing risks |
| The naïve cumulative incidence function estimated by the complement of the Kaplan-Meier estimate (1- KM) is used to estimate the probability that the event of interest will occur in the absence of competing events | Net risk | Not of interest, ignored |
| The cause-specific cumulative incidence function is used to estimate the probability that the event of interest will occur in people at risk (often Fine-Gray, but also possible from cause-specific hazard models)* | Risk | Of interest and included |
| The proportional cause-specific Cox hazard ratio is used to estimate the relatively higher or lower rate of the event of interest, with estimation of hazards not affected by censoring due to competing event | Rate | Not of interest, censored |
| The proportional subdistribution hazard ratio (Fine-Gray) is used to estimate the relatively higher or lower probability of the event of interest | Risk | Of interest and included |
Table created by the authors.
*Note that a cause-specific cumulative incidence can also be obtained from cause-specific Cox hazard models if these are fitted for both the event of interest and the competing risk, and not assuming independence. Then competing risks are included and a different quantity estimated.