Emmett B. Keeler

A theorem on contraction mappings

Abstract : In this note (X, rho) will be a complete metric space and f a mapping of X into itself. A well-known theorem of Banach states: If there exists an alpha < 1 such that for all x, y epsilon X rho(f(x), f(y)) = or < alpha . rho (x,y), alpha < 1 then f has a unique fixpoint (i.e., point xi such that f (xi) = xi). It is shown that the conclusion of Banachs Theorem holds more generally from a condition of weakly uniformly strict contraction. (Author)

The optimal control of pollution

Pollution we define to be any stock or flow of physical substances which impairs man’s capacity to enjoy life. So defined, pollution is a pervasive phenomenon. Physical garbage, air and water pollution, soil exhaustion via excessive use, D.D.T., radiation, and the running down of any natural resource faster than it can rejuvenate itself (if it can rejuvenate itself), are all problems of pollution in this extended sense. By operating at such an all-inclusive level we may miss some of the interesting aspects of particular pollutants. We hope to gain in return by illuminating the conceptual similarities among apparently diverse problems. From the time of Professor Pigou, economists have regarded pollution as a problem of externalities. It is not our purpose to suggest that his view of the problem is in error. On the other hand, it is increasingly evident that the traditional remedies proposed for simple cases of market failure may be inadequate to achieve desirable outcomes where matters of pollution are involved. Efforts to deal with these complex and intractable matters may require some form of centralized coordination and control. An approach beyond the usual externalities analysis seems called for. The framework of control theory provides us with insights on the use of mechanisms to direct patterns of consumption and production. The optimal control of pollution may require curtailing certain types of consumption, limiting the use of some productive processes and perhaps even restricting the growth of population. There are strong intertemporal aspects of the pollution problem. They reinforce the relevance of the dynamic approach of control theory. Before proceeding to a formal model, we shall mention three important distinctions that relate to the economic effects of pollutants. The first is whether the pollutant has its major impact on consumption, on production,

The changing effects of competition on non-profit and for-profit hospital pricing behavior

Has the nature of hospital competition changed from a medical arms race in which hospitals compete for patients by offering their doctors high quality services to a price war for the patients of payors? This paper uses time-series cross-sectional methods on California hospital discharge data from 1986-1994 to show the association of hospital prices with measures of market concentration changed steadily over this period, with prices now higher in less competitive areas, even for non-profit hospitals. Regression results are used to simulate the price impact of hypothetical hospital mergers.

Reducing the Global Burden of Tuberculosis: The Contribution of Improved Diagnostics

We estimated the impact of hypothetical new diagnostic tests for tuberculosis (TB) in patients with persistent cough in developing countries. We found that a variety of new tests could help better identify TB cases and target treatment, thereby reducing the burden of disease.

An Evaluation of Collaborative Interventions to Improve Chronic Illness Care Framework and Study Design

The authors’dual-purpose evaluation assesses the effectiveness of formal collaboratives in stimulating organizational changes to improve chronic illness care (the chronic care model or CCM). Intervention and comparison sites are compared before and after introduction of the CCM. Multiple data sources are used to measure the degree of implementation, patient-level processes and outcomes, and organizational and team factors associated with success. Despite challenges in timely recruitment of sites and patients, data collection on 37 participating organizations, 22 control sites, and more than 4,000 patients with diabetes, congestive heart failure, asthma, or depression is nearing completion. When analyzed, these data will shed new light on the effectiveness of collaborative improvement methods and the CCM.

The demand for episodes of treatment in the Health Insurance Experiment.

This paper analyzes claims data from the RAND Insurance Experiment, which were grouped into episodes of treatment. The insurance plans in the experiment have coinsurance and a cap on out-of-pocket spending. Using new statistical techniques to adjust for the increased sickliness of those who exceed the cap, the effects of coinsurance on cost per episode and number of episodes are estimated. Cost sharing reduced the number of episodes but had little effect on cost per episode. People in the experiment responded myopically as their current insurance status changed through the year. The price elasticity of spending was about -0.2 throughout the range of coinsurance studied. When data permit it, the study of episodes complements analyses of annual medical spending by revealing more about how decisions to spend are made within the year.

The demand for episodes of mental health services

Observational studies of demand for mental health services showed much greater use by those with more generous insurance, but this difference may have been due to adverse selection, rather than in response to price. This paper avoids the adverse selection problem by using data from a randomized trial, the RAND Health Insurance Experiment (HIE). Participating families were randomly assigned to insurance plans that either provided free care or were a mixture of first dollar coinsurance and free care after a cap on out-of-pocket spending was reached. We estimate that separate effects of coinsurance and the cap on the demand for episodes of outpatient mental health services. We find that outpatient mental health use is more responsive to price than is outpatient medical use, but not as responsive as most observational studies have indicated. Those with no insurance coverage would spend about one-quarter as much on mental health care as they would with free care. Coinsurance reduces the number of episodes of treatment, but has only a small effect on the duration and intensity of use within episodes. Users appear to anticipate exceeding the cap, and spend at more than the free rate after they do so.

The Impact of Functional Status on Life Expectancy in Older Persons

BACKGROUNDnAlthough life tables provide a basis for estimating remaining life by age, gender, and race, these tables do not consider clinical characteristics or functional status, which can lead to wide variations in remaining years. Inclusion of functional status may permit more precise prognostic estimates of life expectancy and proportion of time in various functional states.nnnMETHODSnWe used longitudinal data from the Established Populations for Epidemiologic Studies of the Elderly to determine transition probabilities between three functional states (independent in activities of daily living [ADL] and mobility, dependent in mobility but independent in ADL, and dependent in ADL) and death. These were used to estimate total life expectancy and life expectancy in each functional state.nnnRESULTSnIn general, the largest proportion of remaining life expectancy was spent in the persons baseline functional status category. Persons younger than 80 years with dependencies, however, spend substantial proportions of their remaining years in a better functional status category, and mobility-disabled 70-year-old persons spend the greatest part of their life expectancy in the independent functional state. Functional status has a dramatic impact on life expectancy. For example, 75-year-old men and women without limitations have life expectancies 5 years longer than those with ADL limitation and more than 1 year longer than those limited in mobility. The life expectancy of an ADL-disabled 75-year-old is similar to that of an 85-year-old independent person; thus, the impact of the disability approximates being 10 years older with much more of the remaining life spent disabled.nnnCONCLUSIONSnBoth ADL and mobility disability result in diminished survival and more of that survival period spent in disabled states.

Lack of Progress in Labor as a Reason for Cesarean

Objective To estimate the prevalence of lack of progress in labor as a reason for cesarean delivery and to compare published diagnostic criteria with the labor characteristics of women with this diagnosis. Methods We reviewed medical records and did a postpartum telephone survey to collect data from 733 women who delivered full-term, nonbreech infants by unplanned cesarean between March 1993 and February 1994. These were a subset of 2447 births sampled at delivery from 30 hospitals in Los Angeles County and Iowa. We measured the proportion of unplanned cesareans done for lack of progress in labor, the cervical dilatation at the time of cesarean, length of the second stage, and slope of the active phase among the women. We estimated the proportion of these cesareans that conformed to the ACOG criteria for the diagnosis of lack of progress. Results Lack of progress was a reason for 68% of unplanned, vertex cesareans. At least 16% of the subjects who had cesareans for lack of progress were in the latent phase of labor according to ACOG criteria. The second stage was not prolonged in 36% of the women who delivered at 10 cm. Conclusion Lack of progress in labor is a dominant reason for cesarean delivery. Many cesareans are done during the latent phase of labor, and in the second stage of labor when it is not prolonged. These practices do not conform to published diagnostic criteria for lack of progress.

Costing medical care: Using medicare administrative data

This paper describes how the PORTS are using data from the Medicare administrative records systems to study the medical care costs of specific conditions. The general strengths and weaknesses of the Medicare databases for studying cost related issues are discussed, and the relevant data elements are examined in detail. Changes in the nature of the data collected over time are noted. Information is provided on how the PORTS are using these data to estimate the cost to Medicare of treating Medicare beneficiaries with specific conditions and the social (opportunity) cost of treating these patients. Furthermore, information is provided on how data from the Medicare administrative records system can be used to determine the cost of services for patients who have been identified through other large databases (i.e., state hospital discharge tapes) or who have been enrolled in prospective cohort studies.