Response-Guided Dosing for Rheumatoid Arthritis

Abstract

Rheumatoid arthritis (RA) is an auto-immune disease with an unknown cause. Many patients receiving traditional methotrexate treatment continue to exhibit progressive joint damage and are then often treated with biologics. Biologic treatment is difficult owing to the uncertainty in dose-response, high cost, side effects, and intravenous administration. Recent clinical trials have therefore attempted response-guided dosing (RGD), where the hope is to adapt biologic doses over the treatment course based on each individual patient's observed evolution of the 28-joint disease activity score (DAS28). We provide a rigorous, stochastic dynamic programming (DP) framework to facilitate RGD. We first present a concrete formulation where the DAS28 response is modeled using a stochastic Michaelis-Menten formula. The goal is to balance the DAS28 attained at the end of the course with the weighted total dose administered. We perform numerical experiments using data from the OPTION trial and observe that the optimal dosing policy has a monotone structure -- it gives higher doses in worse DAS28 scores. Our sensitivity analyses bring forth the intuitive trend that optimal doses decrease with increasing biologic efficacy and with increasing aversion to dose. We also provide a so-called efficient frontier that is obtained by varying dose weights; this makes explicit the trade-off between DAS28 scores and total doses administered, and it could be used as a decision-making tool in practice. The sensitivity analyses also reveal that a more aggressive treatment strategy, that administers a larger incremental dose over two given states, is optimal when there is more uncertainty in dose-response. Our basic formulation is then extended to a general stochastic DP for RGD. This is applicable mot only to RA, but also to other diseases such as hepatitis C, cholesterol, hypertension, and AIDS, where the measured disease condition could correspond to viral loads, LDL cholesterol levels, blood pressure, or CD4 counts. The DP allows for an arbitrary dose-response function, and balances the disutility of doses with the disutility of the disease condition reached. We prove that, when the decision-maker is risk-averse and the dose-response is supermodular and convex, there exists an optimal policy that gives higher doses in worse disease conditions. We provide several examples where these conditions are met, and also show by counterexamples that such a monotone policy may not be optimal when convexity is violated.