Optimal stopping for response-guided dosing

Jakob Kotas

doi:10.3934/nhm.2019003

Article Contents

2019, Volume 14, Issue 1: 43-52. Doi: 10.3934/nhm.2019003

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Optimal stopping for response-guided dosing

Jakob Kotas

Department of Mathematics, University of Portland, 5000 N Willamette Blvd, Portland, OR 97203, USA

Received: April 1, 2018

Published online: March 1, 2019

The first author was funded in part by the National Science Foundation through grant #CMMI 1536717 when the author was a doctoral student at the University of Washington..

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Abstract

In response-guided dosing (RGD), the goal is to make optimal dosing decisions based on the stochastic evolution of a patient's disease condition. Typically, RGD is formulated as a finite-horizon problem with decision-making occurring over a predetermined time frame. In this paper we relax the latter assumption to allow for the possibility of ending treatment early. This could occur due to remission of the disease or a finding of futility in treatment of the disease. Our framework is formulated as a stochastic dynamic program (DP) where a stop/do-not-stop decision is made in discrete sessions, and if stopping is not chosen, an optimal dose is determined for that session. Numerical simulations for rheumatoid arthritis are presented, and monotonicity of the stop/do-not-stop threshold with respect to time is proven.

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Mathematics Subject Classification: Primary: 60G40, 62L15; Secondary: 92C50.

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Figure 1. Optimal policy of tocilizumab dosing for rheumatoid arthritis. The cost functions are $ c(d) = 0.028557d + b $, with fixed cost parameter $ b $ varying among subfigures. A dose of $ -1 $ indicates a decision to stop treatment

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Figure 2. Optimal policy with the cost function $ c(d) = 0.028557d + 0.1 $. The plot is a zoomed-in version of Figure Figure 1c around the threshold area between stopping and not stopping, with refined discretization. A dose of -1 indicates a decision to stop

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