Modelling survival in hepatocellular carcinoma

Abstract

Objectives:

To identify the pattern of the risk of death over long-term in unresectable hepatocellular carcinoma by determining the appropriate distribution to extrapolate overall survival and to assess the role of the Weibull distribution as the standard survival model in oncology.

Research design and methods:

To select the appropriate distribution, three types of data sources have been analysed. Patient level data from two randomized controlled trials and published Kaplan–Meier curves from a systematic literature review provided short term follow-up data. They were supplemented with patient level data, with long-term follow-up from the Cancer Institute New South Wales, Australia. Published Kaplan–Meier curves were read in and a time-to-event dataset was created. Distributions were fitted to the data from the different sources separately. Their fit was assessed visually and compared using statistical criteria based on log-likelihood, the Akaike information criterion (AIC), and the Bayesian information criterion (BIC).

Results:

Based on both published and patient-level, and both short- and long-term follow-up data, the Weibull distribution, used very often in cost-effectiveness models in oncology, does not seem to offer a good fit in hepatocellular carcinoma among the different survival models. The best fitting distribution appears to be the lognormal, with loglogistic as the second-best fitting function. Results were consistent between the different sources of data.

Conclusions:

In unresectable hepatocellular carcinoma, the Weibull model, which is often treated at the gold standard, does not appear to be appropriate based on different sources of data (two clinical trials, a retrospective database and published Kaplan–Meier curves). Lognormal distribution seems to be the most appropriate distribution for extrapolating overall survival.

Key words::

• Decision modelling
• Decision support technique
• Hepatocellular carcinoma
• Mortality
• Survival analyses

Transparency

Declaration of funding

This study was supported by a grant from Bayer HealthCare Pharmaceuticals.

Declaration of financial/other relationships

A.V. is directly employed by Bayer Healthcare Pharmaceuticals. P.R. has received unrestricted research grants from Bayer Healthcare; however, has not received an honorarium to author this manuscript. N.M., N.K., A.B. and J.I. are employees of United BioSource Corporation. As a research organization, United BioSource conducted the analysis upon which this article is based. United BioSource Corporation has undertaken similar projects for other pharmaceutical companies. CMRO peer reviewers may have received honoraria for their review work. The peer reviewers on this manuscript have disclosed that they have no relevant financial relationships.

Acknowledgements

The authors would like to acknowledge the help of the Cancer Institute New South Wales, Australia who carried out the programming for the data from the Institute based on our statistical analysis plan. Information supplied by the Cancer Institute NSW is restricted to the analysis contained in Table 4 and Figures 3 and 4. Responsibility for the accuracy of all other information and/or views expressed in this paper is held by the authors.