Table 1

Statistical specifications and assumptions in relation to the risk interval, risk set, baseline hazard and within-person correlation in the extended Cox proportional hazards (CoxPH) models

ComponentsAndersen-Gill (A-G)FrailtyWei-Lin-Weissfeld total time (WLW-TT) marginalPrentice-Williams-Petersen gap time (PWP-GT) conditional
Risk intervalDuration since starting observationDuration since starting observationDuration since starting observationDuration since previous injury
Risk set for injury k attime tIndependent injuries (any given injury occurrence is not affected by previous injuries)A random effect (or frailty) term is used to account for the within-player correlation between injuries to enable modelling of the phenomenon by which some players are intrinsically more or less susceptible to experiencing a given injury than others areAll players who have not experienced injury k at time tAll players who have experienced injury k−1, and have not experienced injury k at time t
Baseline hazardCommon/same baseline hazard across all injuriesHeterogeneity is directly incorporated via a random effect so that the baseline hazard is allowed to vary with each injuryCommon baseline hazard for all injuries within a playerStratifies the data by injury so that the baseline hazard is allowed to vary with each injury
Within-person correlationThe within-person injuries are independentCaptures within-person correlation due to both injury dependence and heterogeneityThe within-person injuries are independentThe current injury is unaffected by earlier injuries that occurred to the player
CommentA-G model is recommended when there is no injury dependence and no covariate/injury effectsThe frailty approach accounts for heterogeneity. The random effect (the frailty) has a multiplicative effect on the baseline hazard function and the mixture of individuals with different injury risksAt any time point (matches), WLW-TT describes all players who have not yet experienced k injuries are assumed to be at risk for the kth injury which is not realistic in the sports setting injury dataPWP-GT model takes into account the ordering of events