Benefit efficient statistical distributions on patient lists

Abstract

ABSTRACT. In this paper we consider statistical distributions of different types of patients on the patient lists of doctors. In our framework different types of patients have different preferences regarding their preferred choice of doctor. Assuming that the system is benefit efficient in the sense that distributions with larger total utility have higher probability, we can construct unique probability measures describing the statistical distribution of the different types of patients.

Uncovering preferences from patient list data using benefit efficient models

“…The model in [1] can be described briefly as follows: Assume that there are S groups of patients, T types of doctors, and let P ts denote the number of patients in group s that has a doctor of type t, s = 1, 2, ... , S, t = 1, 2, … , T.  Patients: We assume that there is a total of E s patients belonging to group s, s = 1, 2, ..., S. A patient belonging to group s is assumed to have a utility U ts of having a doctor of type t, t = 1, 2, …, T. It may sometimes happen that a patient prefer to wait for a vacancy of a suitable doctor rather than being assigned to a doctor of a type that the patient dislikes. We let P t(s+S) denote the number of patients of type s waiting for a doctor of type t (not being assigned to any doctor), and let U t(s+S) denote the utility of these patients.…”

“…The basic hypothesis in [1], however, is to assume that the system is benefit efficient in the sense that states with large aggregate utility (sum of the utility of all patients and doctors) are more probable than states with smaller total utility. If the system is benefit efficient with a large number of patients in every group, it is possible to prove, see [1], that the allocation will settle at a statistical equilibrium given by the following explicit formula: …”

“…In [1] Ubøe and Lillestøl suggested a new statistical framework for this context, enable to answer questions of this kind, based on the concept of benefit efficiency. The next research challenge was then to see if the model allowed inferences, i.e., to say something about the preference structure based on an observed allocation.…”

“…In the inverse problem we consider in this paper, the parameter can be set to 1 without loss of generality. Then the resulting allocation will be as given by Formula (1) in the theory section below, where we briefly recall the model construction in [1], and then show how we can obtain unique representations of preferences. To enhance readability, proofs and technical arguments are given in appendices.…”

“…JBiSE is described in some detail in [1], and we refer to this paper for a review of the system. Note that our modeling framework extends beyond the Norwegian patient list system and it can be understood without any particular knowledge of that system.…”