Predicting Mean Survival Time from Reported Median Survival Time for Cancer Patients

Background: Mean duration of survival following treatment is a prerequisite for cost-effectiveness analyses used for assessing new and costly life-extending therapies for cancer patients. Mean survival time is rarely reported due to censoring imposed by limited follow-up time, whereas the median survival time often is. The empirical relationship between mean and median survival time for cancer patients is not known. Aim: To derive the empirical associations between mean and median survival time across cancer types and to validate this empirical prediction approach and compare it with the standard approach of fitting a Weibull distribution. Methods: We included all patients in Norway diagnosed from 1960 to 1999 with one of the 13 most common solid tumor cancers until emigration, death, or 31 December 2011, whichever came first. Observed median, restricted mean, and mean survival times 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 means and medians on the log scale. For validation, we estimated mean survival from medians of bootstrap samples with artificially induced censoring and compared with fitting a Weibull distribution. Results: A linear relationship between log-mean survival time and log-median survival time was identified for the 6 cancers with shortest survival plus metastasized breast and prostate cancers. The predicted means of the empirical approach had smaller bias than the standard Weibull approach. Conclusion: For cancer diagnoses with poor prognosis, mean survival times could be predicted from corresponding medians. This empirical prediction approach is useful for validation of estimates of mean survival time and sensitivity analyses in settings with aggregated data only.