Table 1.

Worked example of the derivation of the combined hazard of death at example time-points for an individual who sustained a hip fracture and first tested positive for COVID-19 155 days after fracture

Time points are chosen to highlight the changes in COVID-19 time-dependent risk which occur after testing positive for COVID-19, according to binary step functions defined by a Cox proportional hazards model. The table illustrates how, at each time point after hip fracture, the combined hazard is calculated by multiplying the baseline hazard by the relative risk for time-fixed covariates (chosen in this example to include a range of co-morbidities conferring a relative risk of 7.1) and multiplying again by the relative risk for the time-varying exposure of testing positive for COVID-19

RR Relative risk

^a The relative risk for testing + ve for COVID-19 is described by four binary step functions which ‘turn on’ as the individual enters four pre-defined time-windows of varying COVID-19 risk – namely from 0 to 2 weeks (C_0-2w, RR = 12.1), 2 to 4 weeks (C_-2-4w, RR = 7), 4 to 6 weeks (C_4-6w, RR = 2.6), and 6 to 12 weeks (C_6-12w, RR = 1.6) following testing + ve for COVID-19 and return to a relative risk of 1 once the individual moves outside the time window defined by the step function