We investigate computational and mechanism design aspects of scarce resource allocation, where the primary rationing mechanism is through waiting times. Specifically we consider allocating medical treatments to a population of patients. Each patient needs exactly one treatment, and can choose from @math hospitals. Hospitals have different costs, which are fully paid by a third party ---the "payer". The payer has a fixed budget @math , and each hospital will have its own waiting time. At equilibrium, each patient will choose his most preferred hospital given his intrinsic preferences and the waiting times. The payer thus computes the waiting times so that at equilibrium the budget constraint is satisfied and the social welfare is maximized. We first show that the optimization problem is NP-hard, yet if the budget can be relaxed to @math for an arbitrarily small @math , then the optimum under budget @math can be approximated efficiently. Next, we study the endogenous emergence of waiting time from the dynamics between hospitals and patients, and show that there is no need for the payer to explicitly enforce the optimal waiting times. Under certain conditions, all he need is to enforce the amount of money he wants to pay to each hospital. The dynamics will always converge to the desired waiting times in finite time. We then go beyond equilibrium solutions and investigate the optimization problem over a much larger class of mechanisms containing the equilibrium ones as special cases. With two hospitals, we show that under a natural assumption on the patients' preference profiles, optimal welfare is in fact attained by the randomized assignment mechanism, which allocates patients to hospitals at random subject to the budget constraint, but avoids waiting times. Finally, we discuss potential policy implications of our results, as well as follow-up directions and open problems.
The authors of @cite_14 study quality and waiting times with the existence of ex post moral hazard. They assume that the patients are ex ante identical, and that the treatment has objective quality levels with which both the valuations and the costs are monotonically increasing. But notice that if the patients are identical, rationing by waiting times is bounded to burn a lot of social welfare since at equilibrium every patient has to be treated in the same way ---as elaborated in our results. In our model the patients' valuations can be arbitrarily associated with different hospitals, reflecting subjective views they may have, and the hospitals' costs can also be arbitrary and do not necessarily reflect their real quality.
@cite_14
2058115997 1592804782 2101134120 1968161699
We examine the role of quality and waiting time in health insurance when there is ex post moral hazard. Quality and waiting time provide additional instruments to control demand and potentially can improve the trade-off between optimal risk bearing and optimal consumption of health care. We show that optimal quality is lower than it would be in the absence of ex post moral hazard. But it is never optimal to have a positive waiting time if the marginal cost of waiting is higher for patients with greater benefits from health care. We deal with a cost-allocation problem arising from sharing a medical service in the presence of queues. We use a standard queuing theory model in a context of several medical procedures, a certain demand for treatment and a maximum average waiting-time guaranteed by the government. We show that the sharing of an operating-theatre to treat patients of different medical disciplines leads to a cost reduction. We then compute an optimal fee per procedure for the use of the operating theatre, based on the Shapley value. Afterwards, considering the recovery time, we characterize the conditions under which the co-operation among treatments has a positive impact on the post-operative costs. Finally, a numerical example, constructed on the basis of real data, is provided to highlight the main features of our model. Graphical abstractDisplay Omitted New method to estimate patient condition during a hospital visit.Patient condition is computed by summing risks measured in each of 26 variables.Leverages data already in the EMR: vital signs, lab results, nursing assessments.Rothman Index, a measure of patient condition, is independent of diagnosis and spans all acuity levels.May help clinicians to improve continuity of care and to detect trends. Patient condition is a key element in communication between clinicians. However, there is no generally accepted definition of patient condition that is independent of diagnosis and that spans acuity levels. We report the development and validation of a continuous measure of general patient condition that is independent of diagnosis, and that can be used for medical-surgical as well as critical care patients.A survey of Electronic Medical Record data identified common, frequently collected non-static candidate variables as the basis for a general, continuously updated patient condition score. We used a new methodology to estimate in-hospital risk associated with each of these variables. A risk function for each candidate input was computed by comparing the final pre-discharge measurements with 1-year post-discharge mortality. Step-wise logistic regression of the variables against 1-year mortality was used to determine the importance of each variable. The final set of selected variables consisted of 26 clinical measurements from four categories: nursing assessments, vital signs, laboratory results and cardiac rhythms. We then constructed a heuristic model quantifying patient condition (overall risk) by summing the single-variable risks. The model's validity was assessed against outcomes from 170,000 medical-surgical and critical care patients, using data from three US hospitals.Outcome validation across hospitals yields an area under the receiver operating characteristic curve(AUC) of Â?0.92when separating hospice deceased from all other discharge categories, an AUC of Â?0.93 when predicting 24-h mortalityand an AUC of 0.62 when predicting 30-day readmissions. Correspondence with outcomesreflective of patient condition across the acuity spectrum indicates utility in both medical-surgical unitsand critical care units. The model output, which we call the Rothman Index, may provide clinicians witha longitudinal view of patient condition to help address known challenges in caregiver communication,continuity of care, and earlier detection of acuity trends. Rationale: Impulsivity is implicated in drug dependence. Recent studies show problems with alcohol and opioid dependence are associated with rapid discounting of the value of delayed outcomes. Furthermore, discounting may be particularly steep for the drug of dependence. Objectives: We determined if these findings could be extended to the behavior of cigarette smokers. In particular, we compared the discounting of hypothetical monetary outcomes by current, never, and ex-smokers of cigarettes. We also examined discounting of delayed hypothetical cigarettes by current smokers. Methods: Current cigarette smokers (n=23), never-smokers (n=22) and ex-smokers (n=21) indicated preference for immediate versus delayed money in a titration procedure that determined indifference points at various delays. The titration procedure was repeated with cigarettes for smokers. The degree to which the delayed outcomes were discounted was estimated with two non-linear decay models: an exponential model and a hyperbolic model. Results: Current smokers discounted the value of delayed money more than did the comparison groups. Never- and ex-smokers did not differ in their discounting of money. For current smokers, delayed cigarettes lost subjective value more rapidly than delayed money. The hyperbolic equation provided better fits to the data than did the exponential equation for 74 out of 89 comparisons. Conclusions: Cigarette smoking, like other forms of drug dependence, is characterized by rapid loss of subjective value for delayed outcomes, particularly for the drug of dependence. Never- and ex-smokers could discount similarly because cigarette smoking is associated with a reversible increase in discounting or due to selection bias.