Differences between two time-to-event approaches, the Cox proportional hazards regression model and the generalised linear model (pseudo-observation method)
| Method | Description |
| Cox regression | |
| Measure of association | Hazard rate ratio. An injury rate (hazard rate) in each exposure group is estimated and the rates are compared on a relative scale (ratio). |
| Graphical presentation | Individual or average survival curves. |
| Main assumptions | Hazard rate ratio has to be constant (proportional hazard rates). The assumptions behind the Cox model can be validated using a log-minus-log plot. Do not condition on the future. |
| Time-varying exposure | Inclusion of one or more time-varying exposures is possible. |
| Time-varying outcome | Inclusion of a time-varying outcome is possible. |
| Advantage | The difference between groups is calculated across all points of the time scale—hence, only one estimate needs to be presented. |
| Events per variable | 10 |
| Shortcomings | It is not plausible to interpret a hazard rate ratio as a risk if the injury incidence mostly exceeds 10% in sports injury studies. A hazard rate ratio becomes meaningless if the assumption of proportionality is violated. |
| Pseudo-observation method | |
| Measures of association | An injury proportion (cumulative risk) in each exposure group is estimated and the proportions are compared on an additive scale (cumulative risk difference) or on a relative scale (cumulative relative risk). Alternatively, the area under the Kaplan-Meier curve (restricted mean) or under the Aalen-Johansen curve (number of years/session/time-spent sport lost) can be estimated and the difference can be compared across exposure groups. |
| Graphical presentation | Kaplan-Meier graph (single event) or Aalen-Johansen graph (competing risk). |
| Main assumptions | Right censored observations, you do not condition on the future. |
| Time-varying exposure | Inclusion of one or more time-varying exposures is possible. |
| Time-varying outcome | Inclusion of a time-varying outcome is possible. |
| Advantages | Cumulative risk difference and cumulative relative risk is easier to interpret than a hazard rate ratio because the difference between groups is calculated at a single point on the time scale. |
| Events per variable | 10 (risk difference) or 15 (relative risk). |
| Shortcomings | Requires a priori selection (and justification) of one or more time points at which comparisons are made. |
Adapted with permission from Nielsen et al.3