Skip to main content
main-content

Über dieses Buch

This textbook offers a comprehensive analysis of medical decision making under uncertainty by combining Test Information Theory with Expected Utility Theory. The book shows how the parameters of Bayes’ theorem can be combined with a value function of health states to arrive at informed test and treatment decisions. The authors distinguish between risk-neutral, risk-averse and prudent decision makers and demonstrate the effects of risk preferences on physicians’ decisions. They analyze individual tests, multiple tests and endogenous tests where the test outcome is chosen by the decision maker. Moreover, the topic is examined in the context of health economics by introducing a trade-off between enjoying health and consuming other goods, so that the extent of treatment and thus the potential improvement in the patient’s health becomes endogenous. Finally, non-expected utility models of choice under risk and uncertainty (i.e. ambiguity) are presented. While these models can explain observed test and treatment decisions, they are not suitable for normative analyses aimed at providing guidance on medical decision making.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
Chapter 1 introduces the topic of the book, describes its content and summarizes the main results.
Stefan Felder, Thomas Mayrhofer

Chapter 2. Basic Tools in Medical Decision Making

Abstract
We introduce the basic analytical tools used in medical decision making such as the a priori probability of illness and the sensitivity and specificity of a test. Each chapter provides illustrations, examples and exercises to sharpen the reader’s understanding of the issues discussed.
Stefan Felder, Thomas Mayrhofer

Chapter 3. Preferences, Expected Utility, Risk Aversion and Prudence

Abstract
We introduce von Neumann and Morgenstern’s expected utility theory, which is the basic normative theory for decisions under uncertainty. The concept of quality-adjusted life years (QALYs), which is an application of this theory, is increasingly used as a measure for determining the public funding of medical interventions. We present the concept of risk aversion and conclude with the notion of prudence. Both concepts are important for an understanding of physician behavior.
Stefan Felder, Thomas Mayrhofer

Chapter 4. Treatment Decisions Without Diagnostic Tests

Abstract
We consider a medical case which requires a physician’s treatment decision where no diagnostic test is available. The physician knows the particular illness and its treatment, as well as a sick person’s utility gain and a healthy person’s utility loss from treatment. But he is uncertain whether the patient is actually sick or not. To aid his decision, we derive a lower boundary for the a priori probability of the illness at which treatment is indicated. We show that a risk-averse physician should treat at a lower a priori probability than a risk-neutral physician. We also analyze the therapeutic risk, i.e., the risk that treatment fails, and derive the success probability threshold, above which the physician will undertake treatment. In contrast to the diagnostic risk, the threshold for the successful treatment probability is higher for a risk-averse decision maker than for a risk-neutral one. Finally, we consider the diagnostic risk and the therapeutic risk simultaneously and study the thresholds in this extended model.
Stefan Felder, Thomas Mayrhofer

Chapter 5. Treatment Decisions with Diagnostic Tests

Abstract
We analyze how the availability of new information from diagnostic testing affects the treatment decision. We define the value of this information as the additional expected utility resulting from the use of the test. We differentiate between a perfect and an imperfect test. A perfect test provides informational value over the whole prevalence range, while the value of information of an imperfect test is zero at the boundaries of the prevalence range. This gives rise to two prevalence thresholds, the test and the test-treatment threshold, which confine the prevalence range within which testing is indicated. The test threshold marks the minimal prevalence rate at which testing is called for, while the test-treatment threshold marks the point at which the decision maker should treat immediately without prior testing. Furthermore, we combine the diagnostic risk and the therapeutic risk and study the implication for the thresholds. Finally, we analyze the effects of potential harm and the costs of testing and treatment on the test and test-treatment thresholds.
Stefan Felder, Thomas Mayrhofer

Chapter 6. Treatment Decisions Under Comorbidity Risk

Abstract
This chapter introduces the role of uncontrollable risks such as a comorbidity for the physician’s decisions. With this type of risk underlying his test and treatment decisions, the concept of prudence becomes relevant. We demonstrate that prudent decision makers act even earlier than simply risk-averse decision makers.
Stefan Felder, Thomas Mayrhofer

Chapter 7. Optimal Strategy for Multiple Diagnostic Tests

Abstract
This chapter deals with the optimal test strategy if multiple diagnostic tests are available and can be employed simultaneously or sequentially. This complicates the task for the decision maker. He has to decide on the positivity criterion for the composite test, which can be conjunctive or disjunctive, and on the order of the tests if he uses them sequentially. If testing is potentially harmful, it is easy to understand that sequential testing always dominates parallel testing.
Stefan Felder, Thomas Mayrhofer

Chapter 8. The Optimal Cutoff Value of a Diagnostic Test

Abstract
We introduce a world where the number of available tests is infinite. This is the case if the test outcome has to be determined by the decision maker by setting a cutoff value. A good example is the prostate-specific antigen (PSA) test for the detection of prostate cancer in men. The analysis of the blood sample results in a PSA value which the physician judges to be positive or negative, depending on his chosen cutoff value. We demonstrate how the optimal cutoff value depends on the a priori probability of the illness as well as on the utility of and potential harm from testing and treatment. This chapter also introduces a novel use of the receiver operating characteristic (ROC) curve which is well known in clinical epidemiology.
Stefan Felder, Thomas Mayrhofer

Chapter 9. A Test’s Total Value of Information

Abstract
In this chapter, we depart from the optimal test and treatment strategy for individual patients and deal with aggregate choices. We present the concept of a test’s total value of information over the entire prevalence range within which it is used. To gain a dimensionless measure, we compare a given test with a perfect test. The resulting performance index lies between zero and one, where zero implies a useless test and one a perfect test.
Stefan Felder, Thomas Mayrhofer

Chapter 10. Valuing Health and Life

Abstract
This chapter establishes a bridge between medical decision making and health economics by introducing consumption and a budget constraint to the decision makers’ choice. A patient-choice trade-off then arises between enjoying health and consuming other goods, so that the extent of treatment and thus the potential improvement in the patient’s health becomes endogenous. We distinguish between health and health-survival models, where the latter captures both quality and quantity aspects of medical investments. After characterizing individual choices, we analyze the allocation chosen by a social planner who maximizes ‘the greatest good of the greatest number’. We conclude the chapter by comparing the utilitarian solution with the allocation of medical investments based on the QALY model.
Stefan Felder, Thomas Mayrhofer

Chapter 11. Imperfect Agency and Non-Expected Utility Models

Abstract
The final chapter takes a more realistic stance to medical decision making by assuming that physicians are only imperfect agents of their patients. Specifically, we assume that physicians internalize only some share of the patient’s utility and follow a profit motive in their test and treatment decisions. We then analyze the effects of imperfect agency on the thresholds and discuss the role of liability rules and medical guidelines in regulating imperfect agency. Finally, we present non-expected utility models under risk and uncertainty (i.e., ambiguity). While these models can explain observed test and treatment decisions, they are not suitable for normative analyses aimed at providing guidance on medical decision making.
Stefan Felder, Thomas Mayrhofer

Backmatter

Weitere Informationen

Premium Partner

    Bildnachweise