BAYESIAN APPROACH TO MODELING THE RESPONSE OF A PATIENT TO DRUG TREATMENT
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Date
2022-12-13
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Johns Hopkins University
Abstract
Drug viability is an important driver in determining the success of treatment. Developing customized treatment means developing a model for the patient. In this work, we use Hill's Equation to model a drug’s viability as function of dosage and time. The model parameters in Hill’s equation can be determined from measurement of viability. The goals of this work is to do parameter estimation on three decisive parameters of the model. We devise two methods for determining the model parameters. The first method is based on Maximum Likelihood Estimation where we formulate a least-squares fit between the measured data and the model prediction. Bayesian Optimization deployed to perform the estimation. The second is a Bayesian approach where we sample from the posterior distribution to obtain confidence bounds on the parameters from the measurements. Then we do comparison and draw to the conclusion of Bayesian Approaches in the model.
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Keywords
Hill's Equation, Bayesian Optimization, Maximum Likelihood Estimation, Metropolis-Hastings Algorithm