Methods: Rheumatoid arthritis (RA) is a chronic condition for which a large number of disease-modifying anti-rheumatic drugs (DMARDs) are available. Typically DMARDs will be stopped after a time for reasons either of loss of efficacy or toxicity. Thus the appropriate long-term strategy for treating a patient with RA requires the use of a sequence of DMARDs. (DMARDs may also be combined in various ways.) Any possible sequence of DMARDs is in principle a candidate for cost-effectiveness analysis. With 11 commonly used DMARDs to consider, there are a total of nearly 40 million possible sequences of DMARDs, and over 100 million sequences if subsets are to be considered as well. It is clearly not possible to test all these sequences.

Sequences of DMARDs are compared using the Birmingham Rheumatoid Arthritis Model (BRAM), which was developed as part of the UK NICE technology appraisals programme. Features of the BRAM are that it allows realistic distributions to be used for the time spent on any DMARD, and that it can allow the effects of a DMARD to depend on a patient's previous history. The model is an individual sampling model, which works by generating a large number of virtual patient histories from which population mean costs and QALYs are estimated. Local search techniques from operations research are used to find the optimum sequence in a computationally feasible way. Uncertainty in data can be accounted for by deterministic or probabilistic sensitivity analysis: both approaches are discussed in this paper.

Results: Using the latest published version of the BRAM, and a threshold ICER of £30,000/QALY ($55,000/QALY), the optimal sequence in the base case analysis was found to be sulfasalazine, methotrexate, hyrdoxychloroquine, leflunomide, injectable gold, penicillamine, ciclosporin, azathioprine. Different sequences were optimal at other threshold ICERs and under other modelling assumptions.

Conclusions: This paper shows how an optimisation algorithm from operations research can be applied to a complex model for the management of a chronic condition. It also shows that deterministic sensitivity analysis can be applied, and that probabilistic sensitivity analysis can be used to estimate the expected outcome allowing for uncertainty in the model parameters.