Predicting Difference in Mean Survival Time from Reported Hazard Ratios for Cancer Patients

Gain in mean survival time from new cancer treatments is a core component of cost-effectiveness analyses frequently used by payers for reimbursement decisions. Due to limited follow-up time, clinical trials rarely report this measure, whereas they often report hazard ratios comparing treatment groups.

We aimed to explore the empirical relationship between gain in mean survival time and the hazard ratio for cancer patients.

We included all patients in Norway diagnosed from 1965 through 2004 with late-stage cancer at the point of diagnosis and with one of the following cancers: stomach, colon, rectal, pancreas, lung and trachea, kidney excluding renal pelvis, and metastasized breast and prostate. Patients were followed until emigration, death, or June 30, 2016, whichever came first. Observed mean survival times and hazard ratios were obtained in subcohorts defined by patients' sex, age, cancer type, and time period of diagnosis, which had nearly complete follow-up. Based on theoretical considerations, we fitted a linear relationship between observed differences in mean survival and logarithmic hazard ratios. For validation, we estimated differences in mean survival from hazard ratios of bootstrap samples with artificially induced censoring and compared with fitting a Weibull distribution.

The relationship between differences in mean survival time and corresponding logarithmic hazard ratios was linear for each of the included cancers. The predicted differences in mean survival of the empirical approach generally had smaller bias than the Weibull approach.

For cancer diagnoses with poor prognosis, differences in mean survival times could be predicted from corresponding hazard ratios. This hazard ratio-based approach outperforms or is similar to fitting Weibull models to data with incomplete follow-up, while making fewer assumptions.