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Full-Text Articles in Applied Mathematics
Decision-Analytic Models Using Reinforcement Learning To Inform Dynamic Sequential Decisions In Public Policy, Seyedeh Nazanin Khatami
Decision-Analytic Models Using Reinforcement Learning To Inform Dynamic Sequential Decisions In Public Policy, Seyedeh Nazanin Khatami
Doctoral Dissertations
We developed decision-analytic models specifically suited for long-term sequential decision-making in the context of large-scale dynamic stochastic systems, focusing on public policy investment decisions. We found that while machine learning and artificial intelligence algorithms provide the most suitable frameworks for such analyses, multiple challenges arise in its successful adaptation. We address three specific challenges in two public sectors, public health and climate policy, through the following three essays. In Essay I, we developed a reinforcement learning (RL) model to identify optimal sequence of testing and retention-in-care interventions to inform the national strategic plan “Ending the HIV Epidemic in the US”. …
Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore
Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore
All HMC Faculty Publications and Research
In this paper, we use control theory to determine optimal treatment regimens for HIV patients, taking into account treatment-resistant mutations of the virus. We perform optimal control analysis on a model developed previously for the dynamics of HIV with strains of various resistance to treatment (Moore and Gu, 2005). This model incorporates three types of resistance to treatments: strains that are not responsive to protease inhibitors, strains not responsive to reverse transcriptase inhibitors, and strains not responsive to either of these treatments. We solve for the optimal treatment regimens analytically and numerically. We find parameter regimes for which optimal dosing …
A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu
A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu
All HMC Faculty Publications and Research
In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …
History-Adjusted Marginal Structural Models And Statically-Optimal Dynamic Treatment Regimes, Mark J. Van Der Laan, Maya L. Petersen
History-Adjusted Marginal Structural Models And Statically-Optimal Dynamic Treatment Regimes, Mark J. Van Der Laan, Maya L. Petersen
U.C. Berkeley Division of Biostatistics Working Paper Series
Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a treatment. These models, introduced by Robins, model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates. Marginal structural models are particularly useful in the context of longitudinal data structures, in which each subject's treatment and covariate history are measured over time, and an outcome is recorded at a final time point. However, the utility of these models for some applications has been limited by their inability to incorporate modification of the causal effect of treatment by time-varying covariates. …