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Article Excerpt
We analyze admission and discharge decisions when hospitals become capacity constrained on high-demand days, and develop a test for discrimination that, under certain circumstances, does not require controls for differences across patient groups. On high-demand days, patients are discharged earlier than expected compared to those discharged on low-demand days. High demand creates no statistically significant differences in hospitals' admission behavior. Thus, hospitals appear to ration capacity by hastening discharges rather than by restricting admissions. We could not reject a null hypothesis of no discrimination against Medicaid patients in discharges.
1. Introduction
* The considerable day-to-day variation in hospital utilization and its implications for capacity and costs have long been recognized. In contrast, less attention has been directed to the effects of such variation on hospital behavior regarding admissions and discharges of patients requiring different types of treatment or with different types of insurance. This article addresses these neglected issues by examining daily admission and discharge decisions when a hospital becomes capacity constrained on high-demand days.
When a hospital is capacity constrained, the constraint tan affect admission decisions, discharge decisions, or both. We use Oregon hospital data to examine how hospitals' admission and discharge behavior is affected by fluctuations in demand. We do not find statistically significant differences in hospitals' admission behavior between high- and low-demand days toward either privately insured non-HMO or Oregon Health Plan (OHP, Oregon's expanded Medicaid program) patients. However, patients discharged on days when hospitals face high demand are discharged earlier than expected when compared to those discharged on days when demand is low. Our findings thus suggest that hospitals ration capacity by hastening discharges rather than by restricting admissions.
We model a hospital that faces a continuum of patient types from two distinct patient groups in both its admission and discharge decisions. For each group, the hospital must determine the threshold that separates potential patients between those admitted and those not admitted as well as the threshold that separates current inpatients between those retained and those discharged. Our model predicts that a binding capacity constraint will cause the hospital to alter admission and/or discharge thresholds for one or both groups of patients. If patients' care-seeking behavior and health characteristics within each group are independent and identically distributed (i.i.d.) with respect to capacity constraints at hospitals, then the thresholds selected by hospitals can be observed in the cumulative distribution functions over patient types of those admitted or discharged on days with and without capacity constraints.
Because our approach identifies thresholds separately for different groups, it does not involve direct comparisons between patients belonging to different groups. A resulting test of discriminatory behavior, therefore, can eliminate a major limitation of existing research-controlling for differences across groups in underlying health conditions and care-seeking behavior (Smedley et al., 2002). Furthermore, the thresholds are observable from the distribution over patient types of those actually admitted to and discharged from hospital. Information regarding patients who are hospitalized is readily available from utilization data. The ability to detect discrimination from such widely accessible utilization data represents a significant advantage over current methods. Although our analysis of hospital discharge behavior toward privately insured non-HMO patients and patients covered by OHP is unable to reject a null hypothesis of no discrimination against OHP patients, our methodology can be adapted to detect discrimination by patient gender, race, ethnicity, or other characteristics.
The article is organized as follows. After a brief review of the literature on stochastic hospital demand in the next section, Section 3 develops a model of hospital capacity allocation when patients have different treatment requirements. Section 4 analyzes how the hospital's admission and discharge behavior is affected by fluctuations in demand that may cause it to become capacity constrained. Section 5 discusses empirical issues, including a proxy measure for the additional expected stay of current inpatients that is used in the analysis of discharge behavior. Section 5 also presents results from our analysis of Oregon data. Section 6 concludes the article and summarizes its policy implications.
2. Literature review
* The growing economic literature on fluctuations in hospital demand attests to the importance of this phenomenon and the need to better understand its many potential effects. Harris (1977) describes the decision rules--including rules of thumb, contingency plans, bargaining, and sometimes shouting and screaming--that hospitals and physicians employ to ration capacity when faced with excess demand. Joskow (1980) examines how hospitals that compete on quality make capacity decisions when facing stochastic demand. He finds that if a hospital wishes to keep the probability of turning patients away below a threshold level, then the capacity it requires will depend in part on variability in demand. Friedman and Pauly (1981, 1983) develop a model where hospital costs include a latent penalty due to deterioration in quality when demand is unexpectedly high. Gal-Or (1994) models hospital decisions to invest in capacity, and finds that uncoordinated actions by hospitals can lead to excess capacity and low occupancy rates. Gaynor and Anderson (1995) examine how uncertain demand affects cost structures and estimate the cost of empty hospital beds. Using an alternative econometric approach, Keeler and Ying (1996) estimate the impact of excess bed capacity on hospital costs. Carey (1998) develops a framework for estimating the optimal level of spare capacity when hospital demand is stochastic. More recently, Baker et al. (2004) analyze California data to estimate how variability in demand affects hospital costs, and Evans and Kim (2006) examine the effects of unanticipated spikes in admissions on patient outcomes.
In addition to economic analyses, a distinct operations research literature has focused on the factors underlying variability in demand for inpatient treatment (e.g., Bagust et al., 1999); models of hospital occupancy (e.g., Millard et al., 2001); and methods for forecasting hospital demand (e.g., Sterk and Shryock, 1987; Jones et al., 2002). Discharge decisions under congestion are also prominent in that literature (e.g., Berk and Moinzadeh, 1998).
Despite the growing scholarly attention, many of the potential consequences of fluctuations in short-term hospital demand have yet to be determined. Our model produces testable predictions that are unique to the literature regarding the effects of rationing on admission and discharge patterns when hospitals are capacity constrained.
3. Capacity allocation model
* Consider daily admission and discharge decisions at a hospital that serves patients belonging to insurance plans x and y when the (stochastic) number and type of patients that it treats are elements in the hospital's objective function. On each day, the hospital must select those that it will admit from among potential inpatients, and it must select those who will be discharged from among current inpatients. Patients presenting for potential admission differ in the resources their treatment requires in terms of the intensity and length of hospital care. Current inpatients comprise the pool of potential discharges and differ in the benefit they derive from continued hospitalization. At the beginning of each day, the hospital learns the number and type of its current inpatients as well as the number and type of potential new patients for that day from both insurance plans. The hospital then simultaneously determines which current inpatients will be discharged and which potential patients will be admitted subject to the condition that the total number of patients in the hospital cannot exceed available capacity. The hospital selects patients for admission and discharge with a view to maximizing the cumulative net benefit it derives from treating all newly admitted and retained patients. We assume that hospital capacity, the number and type of potential new patients, as well as the number and types of current inpatients on each day are predetermined variables when the hospital makes admission and discharge decisions for the day. The hospital becomes capacity constrained when the numbers and types of current and potential patients are such that the hospital must deny admission to patients that it would admit or discharge patients it would retain if additional capacity were available.
Following Medicare's practice of assigning diagnosis-related group (DRG) relative weights that reflect intensity of resource use, let t > denote the expected hospital resources used in the treatment of the condition for which a specific patient is admitted. We assume without loss of generality that the hospital restricts admissions to patient types within its service range T [equivalent to] {t | t [member of] [[t.sub.min], [t.sub.max]]}. Let [f.sub.ij](t) > for all t [member of] T denote the probability density function, and let [s.sub.ij] > denote the number of patients--both scheduled and unscheduled--belonging to plan j [member of] {x, y} who present themselves for possible admission on day i. [F.sub.ij](t) is the cumulative distribution function (CDF) corresponding to [f.sub.ij](t).
Let v denote the marginal patient benefit when one current inpatient of type v remains hospitalized for an extra day. V [equivalent to] {v|v [member of] [[v.sub.min], [v.sub.max]]} is the set of all possible types of current inpatients. Let [h.sub.ij](v) > for all v [member of] V denote the probability density function, and let [n.sub.ij] > denote the number of inpatients belonging to plan j who are in the hospital at the beginning of day i. [H.sub.ij](v) is the CDF corresponding to [h.sub.ij](v).
The hospital derives benefit [[beta].sub.j]B(t) when it admits one plan j patient with resource requirement t, where [[beta].sub.x] [greater than or equal to] [[beta].sub.y] > 0, and B(t) > for all t [member of] T; it also incurs marginal cost ct > due to the admission. We assume that [[beta].sub.y]B([t.sub.max]) - [[beta].sub.x] > B([t.sub.min]) - c[t.sub.min] > 0, that B(t) is a continuous, twice differentiable function, and that B'(t) > O, [[beta].sub.j]B'(t) - c > for all t [member of] T and j [member of] {x, y}. [[beta].sub.y]B([t.sub.max]) - c[t.sub.max] > [[beta].sub.x]B([t.sub.min) - c[t.sub.min] > ensures that patient types that yield a net benefit from admission exist in the entire service range, and that the hospital never excludes all plan y patients in favor of those...
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