A Case Study Examining the Usefulness of Cure Modelling for the Prediction of Survival Based on Data Maturity.

Abstract

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. 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. 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. 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. 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.