Abstract
Introduction
Mixture modelling is increasingly being considered where a potential cure leads to a long life. Traditional methods use relative survival models for frail populations or cure models that have improper survival functions with theoretical infinite lifespans. Additionally, much of the work uses population data with long follow-up or theoretical data for method development.
Objective
This case study uses life table data to create a proper survival function in a real-world clinical trial context. In particular, we discuss the impact of the length of trial follow-up on the accuracy of model estimation and the impact of extrapolation to capture long-term survival.
Methods
A review of recent National Institute for Health and Clinical Excellence (NICE) immuno-oncological and chimeric antigen receptor (CAR) T-cell therapy submissions was performed to assess industry uptake and NICE acceptance of survival analysis methods incorporating the potential for long-term survivorship. The case study analysed a simulated trial-based dataset investigating a curative treatment with long-term mortality based on population life tables. The analysis examined three timepoints corresponding to early trial, end-of-trial follow-up and complete follow-up. Mixture modelling approaches were considered, including both cure modelling and relative survival approaches. The curves were evaluated based on the ability to estimate cure fractions and mean life in years within the time span the models are based on and when extrapolating to capture long-term behaviour. The survival curves were fitted with Weibull distributions using non-mixture and mixture cure models.
Results
The performance of the cure modelling methods depended on the relative maturity of the data, indicating that care is needed when deciding when the methods should be applied. For progression-free survival, the cure fraction simulated was 15%. The cure fractions estimated using the traditional mixture cure model were 43% (95% confidence interval [CI] 30–57) at the first analysis time point (40 months), 15% (95% CI 12–20) at the end-of-study follow-up (153 months) and 0% (95% CI 0–100) at the end of follow-up. Other standard cure modelling methods produced similar results. For overall survival, we observed a similar pattern of goodness of fit, with a good fit for the end-of-study follow-up and poor fit for the other two data cuts. However, in this case, the estimate of the cure fraction was below the true value in the first analysis data.
Conclusions
This case study suggests cure modelling works well with data in which the disease-specific events have had time to occur. Care is needed when extrapolating from immature data, and further information should support the estimation rather than relying on statistical estimates based on the trial alone.
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Data Availability
The simulated data generated for this study is included in the supplementary information supplied with this article.
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Acknowledgements
Tim Grant performed analyses and wrote sections of the article. Darren Burns conducted the literature review and wrote sections of the article. Dawn Lee validated the analyses and wrote sections of the article. Christopher Kiff provided the data for the analyses and contributed to the writing and editing of the article. Tim Grant will act as the overall guarantor.
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Financial support for this study was provided by a contract with Bristol-Myers Squibb Pharmaceuticals Ltd. The funding agreement ensured the authors’ independence in designing the study, interpreting the data and writing and publishing the report.
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TG, DB and DL are employees of BresMed Health Solutions Ltd. CK is an employee and stockholder of Bristol-Myers Squibb Pharmaceuticals Ltd, which provided funding for this work. BresMed has received consulting fees from Bristol-Myers Squibb Pharmaceuticals Ltd for producing this manuscript.
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Grant, T.S., Burns, D., Kiff, C. et al. A Case Study Examining the Usefulness of Cure Modelling for the Prediction of Survival Based on Data Maturity. PharmacoEconomics 38, 385–395 (2020). https://doi.org/10.1007/s40273-019-00867-5
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DOI: https://doi.org/10.1007/s40273-019-00867-5