OBJECTIVES: Cost-effectiveness analyses often use parametric survival models fitted to clinical trial data to predict lifetime outcomes. Guidelines recommend that empirical (observed) and modelled hazard functions are presented to assess model fit and the plausibility of extrapolated hazards. The accurate estimation of the empirical hazard function is critical to making an informed choice of extrapolation. We compare different methods of estimating the empirical hazard and assess whether these methods consistently estimate the hazard function across three reported analyses of a prostate cancer study (NCT01212991).

METHODS: Pseudo-patient level data were recovered from published Kaplan-Meier plots for enzalutamide. Hazards for overall survival were estimated at data cut-offs (DCOs) with 34-, 44- and 81-months maximum follow-up. Unsmoothed hazards were estimated using the muhaz R package (pehaz function) and smoothed hazards were estimated using the muhaz and bshazard packages. The shapes of different hazard functions were compared to understand how these differed by estimation method and data availability.

RESULTS: At longest follow-up (DCO3), the empirical hazards initially increased (0-20 months), before remaining broadly constant thereafter, with muhaz and bshazard estimating similar smoothed functions. The empirical and smoothed hazards at earlier DCOs were generally consistent with DCO3 up to approximately 30 months (~4% at risk, DCO1). After month 30, muhaz estimated increasing (DCO1) and then decreasing (DCO2) hazards whilst bshazard estimated decreasing (DCO1) and constant (DCO2) hazards, respectively. In this example, bshazard provided smoother hazard functions than muhaz and was less sensitive to changes in the hazard at the tail.

CONCLUSIONS: In this study, the empirical hazard function appeared generally robust to the choice of smoothing function until numbers at risk were small. The hazard trend at the tail of the curve can differ considerably depending on function used. Where uncertain, the clinical plausibility of the empirical hazard function should also be considered when informing extrapolation.