Broadening the candidate set of parametric models when extrapolating survival: the case for models with U-shaped hazards.

In health technology assessment (HTA), extrapolation of time-to-event data is common to estimate the benefit of a new health technology beyond the observed period of data. The regular set of parametric models commonly used for extrapolation does not include models which assume a U-shaped hazard rate, that is initially decreasing and then increasing hazard rate. We compared the visual and statistical fit and prediction of models which assume a U-shaped hazard rate (Chen, bathtub and Rayleigh) to the regular set of parametric models (exponential, log-normal, log-logistic, Weibull, generalised gamma, Gompertz) across a range of settings and data types, including hip arthroplasty, functional tricuspid regurgitation and knee osteoarthritis. U-shaped hazard models outperformed or matched standard parametric models in visual fit, goodness of fit statistics and long-term predictions when compared to extended follow-up. Bathtub models should feature routinely in HTA submissions involving extrapolation of survival data, allowing for exploration of a wider range of scenarios and potentially more accurate predictions, resulting in better informed valuation and decision making for emerging health technologies.