Cost-effectiveness analysis in R using a multi-state modelling survival analysis framework: a tutorial

This tutorial provides a step-by-step guide to performing cost-effectiveness analysis using a multi-state modelling approach. Alongside the tutorial we provide easy-to-use functions in the statistics package R. We argue this multi-state modelling approach using a package such as R has advantages over approaches where models are built in a spreadsheet package. In particular, using a syntax-based approach means there is a written record of what was done and the calculations are transparent. Reproducing the analysis is straightforward as the syntax just needs to be run again. The approach can be thought of as an alternative way to build a Markov decision analytic model, which also has the option to use a state-arrival extended approach if the Markov property does not hold. In the state-arrival extended multi-state model a covariate that represents patients’ history is included allowing the Markov property to be tested. We illustrate the building of multi-state survival models, making predictions from the models and assessing fits. We then proceed to perform a cost-effectiveness analysis including deterministic and probabilistic sensitivity analyses. Finally, we show how to create two common methods of visualising the results, namely cost-effectiveness planes and cost-effectiveness acceptability curves. The analysis is implemented entirely within R. It is based on adaptions to functions in the existing R package mstate, to accommodate parametric multi-state modelling which facilitates extrapolation of survival curves

The cost-effectiveness of nivolumab monotherapy for the treatment of advanced melanoma patients in England

Background: Nivolumab was the first programmed death receptor 1 (PD-1) immune checkpoint inhibitor to demonstrate long-term survival benefit in a clinical trial setting for advanced melanoma patients. Objective: To evaluate the cost effectiveness of nivolumab monotherapy for the treatment of advanced melanoma patients in England. Methods: A Markov state-transition model was developed to estimate the lifetime costs and benefits of nivolumab versus ipilimumab and dacarbazine for BRAF mutation-negative patients and versus ipilimumab, dabrafenib, and vemurafenib for BRAF mutation-positive patients. Covariate-adjusted parametric curves for time to progression, pre-progression survival, and post-progression survival were fitted based on patient-level data from two trials and long-term ipilimumab survival data. Indirect treatment comparisons between nivolumab, ipilimumab, and dacarbazine were informed by these covariate-adjusted parametric curves, controlling for differences in patient characteristics. Kaplan–Meier data from the literature were digitised and used to fit progression-free and overall survival curves for dabrafenib and vemurafenib. Patient utilities and resource use data were based on trial data or the literature. Patients are assumed to receive nivolumab until there is no further clinical benefit, assumed to be the first of progressive disease, unacceptable toxicity, or 2 years of treatment. Results: Nivolumab is the most cost-effective treatment option in BRAF mutation-negative and mutation-positive patients, with incremental cost-effectiveness ratios of £24,483 and £17,362 per quality-adjusted life year, respectively. The model results are most sensitive to assumptions regarding treatment duration for nivolumab and the parameters of the fitted parametric survival curves. Conclusions: Nivolumab is a cost-effective treatment for advanced melanoma patients in England

Statistical models to capture the association between progression-free and overall survival in oncology trials

In oncology trials, different clinical endpoints can be measured. For the survival analysis of patients, the most traditional primary endpoint is overall survival (OS), which is defined as the time from study entry to death from any cause. Besides, progression-free related measurements such as progression-free survival (PFS) might be also considered. For assessing the performance of therapies, OS is the most reliable endpoint. However, utilizing earlier endpoints such as information from disease progression might lead to a gain in efficiency. However, the gain in efficiency might depend on the relationship between those two endpoints. This thesis explores various statistical models for capturing the association between PFS and OS. The research is partitioned into three topics. At first, it considers methods for quantifying the association between PFS and OS in oncology trials, in terms of Kendall’s τ rank correlation rather than Pearson correlation. Copula-based, non-parametric, and illness-death model–based methods are reviewed. In addition, the approach based on an underlying illness-death model is generalized to allow general parametric models. The simulations suggest that the illness-death model–based method provides good estimates of Kendall’s τ across several scenarios. In some situations, copula-based methods Perform well but their performance is sensitive to the choice of copula. The Clayton copula is most appropriate in scenarios which might realistically reflect an oncology trial, but the use of copula models in practice is questionable. In the second and third topic, the estimation of the group difference faces the issue of non-proportionality for treatments effects. Instead of the standard hazard ratio we use the average hazard ratio for estimating the group difference as it is able to cope with non-proportional hazards well as it considers group difference depending on time. Subsequently, it compares methods for jointly modelling time-to-progression and time-to-death within a Bayesian framework. By incorporating treatment effects, we investigate an illness-death model-based approach and also copula-based approaches. According to the simulations results the Gaussian copula-based model performed the best overall, but the illness-death model-based approach showed a good performance as well. However, in contrast to the good performance of the Clayton copula-based approach in the first topic, the Clayton copula model did not perform well regarding the estimation of AHR. The third topic explores various semi-parametric multi-state model-based methods for gaining efficiency in testing for, and estimating the treatment effects in terms on, overall survival in oncology trials compared to standard methods based on directly applying Cox regression or the log-rank test. The semi-parametric multi-state model-based method fits a Cox model to (a subset of) transition intensities in an illness-death model assuming either a Markov or semi-Markov model and uses AHR to measure treatment effect. In most of the situations, the semi-parametric multi-state model-based methods perform better than the Cox-based approach. The performance of the methods in each topic is investigated by simulations and also illustrated using data from a clinical trial of treatments for advanced ovarian cancer in topic 2 and for colon cancer in topics 1 and 3

Oncology modeling for fun and profit! Key steps for busy analysts in health technology assessment

In evaluating new oncology medicines, two common modeling approaches are state transition (e.g., Markov and semi-Markov) and partitioned survival. Partitioned survival models have become more prominent in oncology health technology assessment processes in recent years. Our experience in conducting and evaluating models for economic evaluation has highlighted many important and practical pitfalls. As there is little guidance available on best practices for those who wish to conduct them, we provide guidance in the form of 'Key steps for busy analysts,' who may have very little time and require highly favorable results. Our guidance highlights the continued need for rigorous conduct and transparent reporting of economic evaluations regardless of the modeling approach taken, and the importance of modeling that better reflects reality, which includes better approaches to considering plausibility, estimating relative treatment effects, dealing with post-progression effects, and appropriate characterization of the uncertainty from modeling itself