In 1975, S. Pauker and J. Kassirer (henceforth P. K. ) published in the New England Journal of Medicine a very influential paper where they defined the ‘treatment threshold’ in the presence of a diagnostic risk.
The basic story of the paper is a simple and pretty realistic medical problem, because there is no perfect test available. A physician and/or his patient 1 must make the (irreversible) decision to treat or not to treat while there is only suspicion that a single (well-defined) illness might be present. This risk is characterized by the a priori probability of disease (p with 0 < p < 1). Given the medical benefits and costs of the potential treatment for the patient (benefits and costs are assumed to be known with certainty), P. K. describe the critical value of p (i.e, the threshold) above which treatment becomes the best decision. Because the costs and benefits of the treatment are known with certainty while the risk relates to the true health state of the patient, we consider here - as P. K. did - a situation of ‘diagnostic risk’. 2 Of course other assumptions corresponding to other medical situations would be possible (e.g. random costs and benefits of the treatment) but they will not be considered here for the sake of brevity.
Quite clearly P. K. ’s paper is written in the spirit of the expected utility (E-U) model and it uses results known at the time. In this presentation, we discuss some extensions of P. K. ’s analysis that can be made by using new concepts developed in the framework of the E-U theory. 3 These extensions rely mostly upon the notion of prudence developed by Kimball (1990) to analyse saving decisions and extended by Eeckhoudt-Kimball (1991) to insurance problems.
The chapter is organized as follows. First we describe the main ideas and results of P. K. ’s paper for the case of a risk neutral decision maker. In the following section, we examine how risk aversion defined in a E-U framework affects the treatment threshold. Then we discuss background risks (comorbidity risks) and we show how the notion of prudence becomes important in this framework. The penultimate section extends the analysis to the case of the willingness to pay notion and we also quickly indicate how one would treat the case of therapeutic risks. Some conclusions end the chapter.