A Theory of Medical Decision Making under Uncertainty Edi Karni December 21 2008 Johns Hopkins University Baltimore MD 21218 USA e mail address karni jhu edu I benefited from comments of Ani Guerdjikova Moshe Leshno Marzena Rostek Marie Louise Viero Kip Viscusi Peter Wakker and an anonymous referee 1 Abstract This paper presents an axiomatic model of medical decision making and discusses its potential applications The medical decision problems envisioned concern the choice of a medical treatment following a diagnosis in situations in which data allow construction of an empirical distribution over the potential outcomes associated with the alternative treatments In its descriptive interpretation the model is an hypothesis about the patient s choice behavior The theory also aims to aid physicians recommend treatments in a coherent manner Keywords Medical decision making medical treatment choice JEL classification numbers I19 D81 2 For the purpose of this paper the term medical decision making refers to the choice of a course of action action for short following a diagnosis of a patient s condition An action consists of the medical treatment itself the facility in which it is to be administered and if perceived relevant the individuals who administer it Consider for example a patient diagnosed with prostate cancer Given his specific personal characteristics medical history age physical condition and so forth the patient must choose among various treatments e g radical prostatectomy radiation therapy the medical facilities in which he is to be treated the local hospital a medical center in another city and the physician who performs the surgery or administers the therapy of choice The consequences consist of the patient s post treatment state of health including the side e ects of treatment the associated pain and inconvenience the direct monetary expenses and the potential loss of income 1 In many situations involving medical decision making the empirical probability that is the relative frequency of the di erent outcomes conditional on the treatments characteristics of the patient and choice of hospital and physician are known The question is how does or how should an informed patient choose among the possible courses of action In this paper I propose an axiomatic theory of medical decision making in which the patient s preferences are represented by an outcome dependent expected utility function More formally let a denote an action and denote by c a vector of the patient s characteristics 1 A recent study by Sommers et al 2007 underscores the importance of patients preferences for the determination of the optimal treatment defined as the expected QALY See further discussion in the concluding section 3 medical history age gender race profession family situation physical state and any other personal attributes that may bear on the outcome of the medical treatments under consideration I examine the structure of a preference relation on the set of actions that is necessary and su cient for the following representation a c 7 a X U f a c p a c v a where U is the utility function denotes the post treatment health state or outcome is the set of all outcomes associated with a given diagnosis f a c denotes the financial consequence associated with the outcome conditional on the patient s characteristics and the action p a c is the probability distribution on conditional on the action and the patient s personal characteristics and and v represent the utility cost including the pain or discomfort associated with di erent actions Note that the patient s risk attitudes captured by the utility functions of money U are outcome dependent but not action dependent 2 I assume throughout that insofar as choosing the right treatment is concerned there is no conflict of interests between physicians and the patients In other words following a diagnosis the objective of both parties is to choose the treatment that is best from the viewpoint of the patient s welfare in all its relevant aspects health financial and the nonmonetary cost 2 Outcomes represent states of health and the utility functions in this model are state dependent functions of the patient s wealth This is an important aspect of this model which is missing from that of Sommers et al 2007 Empirical evidence suggests that there are significant variations both in the level and marginal utility of wealth across states of health see Viscusi and Evans 1990 4 of the treatment The decision making problem is interactive involving the integration of the private information of the two parties The physician input includes the diagnosis the identification of the alternative treatments and the determination of the probabilities of the outcomes associated with the alternative courses of action The patient s input consists of his personal characteristics and preferences including his valuation of the health outcomes his outcome dependent risk attitudes and his valuation of the nonfinancial aspect of the cost associated with the alternative treatments The decision maker is supposed to be able to express his preferences over treatments for every conceivable probability distribution over the outcomes This richness of the framework allows the identification of the ingredients of the representation namely the utilities and the probabilities The analysis consists of two main parts The first part is an application of an extension of the von Neumann Morenstern expected utility theory developed in Karni and Safra 2000 to obtain for every given course of action an outcome dependent expected utility representation The second part which is the novel aspect of this work involves linking the representations across actions This is done by two axioms namely action independent risk attitudes and action independent preferences over lottery mixtures Action independent risk attitudes requires that the patient risk aversion is not altered by the treatment itself Action independent lottery mixtures requires that mixing lotteries belonging to the same indi erence class under di erent treatments yield lotteries that are themselves equivalent under the di erent treatments The application of this model to medical decision making requires the elicitation of the 5 utility functions U their alignment and the elicitation of the coe cients a v a for all actions a Because the model is preference based the information needed to implement it is in principle obtainable from the patient s