OBJECTIVES: Cox proportional hazard ratios (HRs) reported in trials for survival outcomes are often used to indirectly compare treatments (ITC) for health economic modelling purposes. In these economic models, the HRs from the ITC are combined with the parametric fit of the control arm of the pivotal trial to estimate the mean survival outcomes of different therapies. There are various methods to obtain proportional HRs, including the semi-parametric Cox regression, and parametric methods which assume proportional hazards using the Weibull, Gompertz or exponential distribution. The National Institute for Health and Care Excellence suggests that it is theoretically incorrect to apply a HR derived from a different parametric model, or one from a Cox proportional hazard model to a parametric curve. The aim of this study was to investigate the impact of using different methods for estimating HRs on its point estimate and corresponding confidence interval.

METHODS: Patient-level data of twenty oncology trials were reconstructed using the Guyot algorithm. For each trial, HRs were derived using Cox regression, and the Weibull, Gompertz and exponential parametric distribution. The Schoenfeld test was applied to assess the proportional HR assumption of each dataset. The HRs were compared on point estimate and corresponding uncertainty.

RESULTS: Compared to the Cox HR, the Weibull parametric HR showed relative HR of on average 1.02 [min: 0.89, max: 1.07]. Compared to the Cox, the Gompertz and exponential parametric HRs showed a relative HR of 1.00 [min: 0.95. max: 1.05] and 0.99 [min: 0.89, max: 1.08], respectively. The uncertainty around the Cox, Weibull, Gompertz and exponential HR was comparable.

CONCLUSIONS: This study showed that applying HRs either derived from a semi-parametric Cox or from a parametric model are similar.