The Optimal Time to Initiate HIV Therapy Under Ordered Health States

Shechter, Steven M.; Bailey, Matthew D.; Schaefer, Andrew J.; Roberts, Mark S.

doi:10.1287/opre.1070.0480

Cited by 132 publications

(81 citation statements)

References 81 publications

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“…In particular, the TPMs are constructed to have the decreasing failure rate property, meaning that patients in better health states have a lower probability of moving to any particular health state or worse (including death). This property has been observed, for example, in Markov models of HIV progression [4,5] and is formalized later. In addition, we assume that the most likely event is that the patient's next health state will be identical to his current health state, that is,…”

Section: Constructing the Experimental Transition Probability Matricesmentioning

confidence: 88%

State‐space size considerations for disease‐progression models

Regnier

Shechter

2013

Statistics in Medicine

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Markov models of disease progression are widely used to model transitions in patients' health state over time. Usually, patients' health status may be classified according to a set of ordered health states. Modelers lump together similar health states into a finite and usually small, number of health states that form the basis of a Markov chain disease-progression model. This increases the number of observations used to estimate each parameter in the transition probability matrix. However, lumping together observably distinct health states also obscures distinctions among them and may reduce the predictive power of the model. Moreover, as we demonstrate, precision in estimating the model parameters does not necessarily improve as the number of states in the model declines. This paper explores the tradeoff between lumping error introduced by grouping distinct health states and sampling error that arises when there are insufficient patient data to precisely estimate the transition probability matrix.

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Section: Constructing the Experimental Transition Probability Matricesmentioning

confidence: 88%

State‐space size considerations for disease‐progression models

Regnier

Shechter

2013

Statistics in Medicine

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“…In the medical literature, Markov models have explored very diverse problems such as timing of liver transplant [8], HIV therapy [9], breast cancer [10], Hepatitis C [11], statin therapy [12] or hospital discharge management [5,13]. Markov models can be used to describe various health states in a population of interest, and to detect the effects of various policies or therapeutic choices.…”

Section: Medical Applications Of Markov Modelsmentioning

confidence: 99%

Markov Models and Cost Effectiveness Analysis: Applications in Medical Research

Komorowski

Raffa

2016

Secondary Analysis of Electronic Health Records

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Learning ObjectivesUnderstand how Markov models can be used to analyze medical decisions and perform cost-effectiveness analysis.This case study introduces concepts that should improve understanding of the following:1. Markov models and their use in medical research. 2. Basics of health economics. 3. Replicating the results of a large prospective randomized controlled trial using a Markov Chain and Monte Carlo simulations, and 4. Relating quality-adjusted life years (QALYs) and cost of interventions to each state of a Markov Chain, in order to conduct a simple cost-effectiveness analysis. IntroductionMarkov models were initially theroreticized at the beginning of the 20th century by Russian mathematician Andrey Markov [1]. They are stochastic processes that undergo transitions from one state to another. Over the years, they have found countless applications, especially for modeling processes and informing decision making, in the fields of physics, queuing theory, finance, social sciences, statistics and of course medicine. Markov models are useful to model environments and problems involving sequential, stochastic decisions over time. Representing such environments with decision trees would be confusing or intractable, if at all possible, and would require major simplifying assumptions [2]. Markov models can be examined by an array of tools including linear algebra (brute force), cohort simulations, Monte Carlo simulations and, for Markov Decision Processes, dynamic programming and reinforcement learning [3,4].

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“…In the context of medical procedure planning, MDP's have been developed to assist in decisions such as timing for liver transplants (Alagoz et al, 2005), discharge times for severe sepsis cases (Kreke et al, 2005), and start dates for HIV drug cocktail treatment (Shechter et al, 2005). MDP's and dynamic programming have also been used in a variety of robotics applications, including planning paths for mobile robots (Dean et al, 1995;LaValle and Hutchinson, 1998;Ferguson and Stentz, 2004;LaValle, 2006).…”

Section: Related Workmentioning

confidence: 99%

Motion Planning Under Uncertainty for Image-guided Medical Needle Steering

Alterovitz

Branicky

Goldberg

2008

The International Journal of Robotics Research

162

117

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We develop a new motion planning algorithm for a variant of a Dubins car with binary left/right steering and apply it to steerable needles, a new class of flexible bevel-tip medical needles that physicians can steer through soft tissue to reach clinical targets inaccessible to traditional stiff needles. Our method explicitly considers uncertainty in needle motion due to patient differences and the difficulty in predicting needle/tissue interaction. The planner computes optimal steering actions to maximize the probability that the needle will reach the desired target. Given a medical image with segmented obstacles and target, our method formulates the planning problem as a Markov Decision Process based on an efficient discretization of the state space, models motion uncertainty using probability distributions, and computes optimal steering actions using Dynamic Programming. This approach only requires parameters that can be directly extracted from images, allows fast computation of the optimal needle entry point, and enables intra-operative optimal steering of the needle using the pre-computed dynamic programming look-up table. We apply the method to generate motion plans for steerable needles to reach targets inaccessible to stiff needles, and we illustrate the importance of considering uncertainty during motion plan optimization.

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The Optimal Time to Initiate HIV Therapy Under Ordered Health States

Cited by 132 publications

References 81 publications

State‐space size considerations for disease‐progression models

State‐space size considerations for disease‐progression models

Markov Models and Cost Effectiveness Analysis: Applications in Medical Research

Motion Planning Under Uncertainty for Image-guided Medical Needle Steering

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