Development of a framework for cohort simulation in cost-effectiveness analyses using a multistep ordinary differential equation solver algorithm in R

Introduction. Dynamic processes in cost-effectiveness analysis (CEA) are typically described using cohort simulations, which can be implemented as Markov models, or alternatively using systems of ordinary differential equations (ODEs). In the field of CEA, simple and potentially inaccurate single-step algorithms are commonly used for solving ODEs, which can potentially induce bias, especially if an incorrect step size is used. The aims of this project were 1) to implement and demonstrate the use of a modern and well-established hybrid linear multistep ODE solver algorithm (LSODA) in the context of CEA using the statistical scripting language R and 2) to quantify bias in outcome for a case example CEA as generated by a commonly used single-step ODE solver algorithm. Methods. A previously published CEA comparing the adjuvant breast cancer therapies anastrozole and tamoxifen was used as a case example to implement the computational framework. A commonly used single-step algorithm was compared with the proposed multistep algorithm to quantify bias in the single-step method. Results. A framework implementing the multistep ODE solver LSODA was successfully developed. When a single-step ODE solver with step size of 1 year was used, incremental life-years gained was underestimated by 0.016 years (5.6% relative error, RE) and £158 (6.8% RE) compared with the multistep method. Conclusion. The framework was found suitable for the conduct of CEAs. We demonstrated how the use of single-step algorithms with insufficiently small step sizes causes unnecessary bias in outcomes measures of CEAs. Scripting languages such as R can further improve transparency, reproducibility, and overall integrity in the field of health economics.