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ALND Notes Notes Anscombe Notes Allais Ellsberg Notes Notes Slides Screening Deconvolution GeNie Notes Savage Notes Notes Notes Notes Stein Blyth Back to main page |
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help. Notes are password-protected, because they are part of a book in progress. Please contact gp@jhu.edu for the password. March 27 and 29 We start by familiarizing ourselves with issues in clinical decision making by discussing in detail a case study. The topic is whether axillary lymph node dissection (ALND) is worthwhile for patients diagnosed with early breast cancer. We will encounter tools and ideas that will be studied in detail later in the course. Having seen these ideas in action from the start will help us place the foundational and methodological issues in perspective. April 3 We celebrate the birth of quantitative utility as a guide to decision making under uncertainty. We discuss Daniel Bernoulli's St. Petersburg Paradox, and present in detail von-Neumann and Morgenstern's utility theory. April 5 Where we study Anscombe and Aumann's fascinating contribution to the axiomatic justification of the use of subjective expected utility in decision making, and reveal, in a relatively simple setting, the ``secret'' assumptions of Bayesian decision theory. April 10 We start to take apart what we have built so far, by puzzling over some of the most far reaching and historically prominent criticisms of expected utility theory: Allais' and Ellsberg's. Ellsberg's is especially interesting, as it questions the Bayesian tenet that when it comes to decision making all uncertainties can be quantified by probability and averaged out. April 17 We talk about quantifying the utility of remining in a certain health state for a certain amount of time. We examine a general article and a medical article that has pioneered the utility approach in health and set the standard for many similar analyses. The article is also very good at critically assessing the implications of the many assumptions one has to make to reduce the problem to a manageable one. April 19 We discuss how decision theoretic tools can be helpful in addressing trade-offs between cheaper and less rewarding options versus more expensive but more rewarding ones. We will consider the issue from a policy standpoint, in which decision are made by an agent on behalf of a whole community. We look at the nuts and bolts of a very effective and popular approach for modeling decision making situations in medicine using simple discrete Markov Chains. April 21 The SMP (stroke policy model) is a stochastic simulation model to predict the long term outcome of patients at high risk of stroke. We will study how it works, what it took to put it together, what it can and cannot do, and how it could be improved. April 24 We conclude our survey of applications in medical decision making with a comprehensive decision model of breast cancer screening. We show how a comprehensive decision model can integrate the available knowledge about a complex health problem and help address complex choices and optimizations. April 26 GeNIe is a new development environment for building graphical decision-theoretic models. We will find out what graphical decision-theoretic models are and try out the new software, maybe. May 1 Statistical decision theory applies rational decision making to the choice of appropriate statistical strategies. We visit the birthplace of statistical decision theory, discussing the first chapter of the first book on the subject, by Wald. We also revisit some of the more traditional statistical problems, such as point estimation and testing, in the light of Wald's contribution. We study Savage's review of Wald's book. May 3 We reminded ourselves that the value of the information carried by a data set depends on what we intend to do with the data once we have collected it. We use decision trees to quantify this value. The life of a statistician is boiled down to a two-stage decision problem: what data to get, if any; and what use to make of the data in addressing the question at hand. May 8 We revisit the single most common decision statisticians make in their daily activities: how big should a data set be? We try to understand how all the machinery we have been setting in place can help us and give some examples, both static and dynamic. May 10 We study admissibility, the most basic and influential rationality requirement of classical statistical decision theory. We study connections between admissibility and sufficiency, including the Rao-Blackwell theorem. We discuss admissibility of Bayes rules and admissibility of X bar in estimating the mean of a normal. We encounter the controversy stirred by the fact that X bar is not admissible in estimating the mean of a multidimensional normal vector of observations. Stein was the first to realize this. We connect Stein's results to some of the important research direction that stemmed from his paper, including shrinkage estimation, empirical Bayes estimation, and hierarchical modeling. May 15 Student's presentations, or additional topics. May 17 Student's presentations, or additional topics. |