John E. Rolph

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.

Empirical Bayes Methods Applied to Estimating Fire Alarm Probabilities

Abstract An empirical Bayes approach is used to derive a Stein-type estimator of a multivariate normal mean when the components have unequal variances. This estimator is applied to estimating the probability that a fire alarm reported from a particular street box signals a structural fire rather than a false alarm or other emergency. The approach is to group alarm boxes into relatively homogeneous neighborhoods and to make empirical Bayes estimates of the “probability structural” for each box in the neighborhood from yearly (1967–1969) Bronx data. A dispatching rule based on the estimates is evaluated on 1970 data.

Omission-Related Malpractice Claims and the Limits of Defensive Medicine

To describe the malpractice environment as it relates to defensive medicine, the authors studied omission-related claims from a large physician-owned malpractice insurer covering 70 percent of physicians in a northeastern state. During a 12-year period (1977-1989), claims resulting from alleged diagnostic omissions were considered important in less than 9 percent of claims and of central importance in 4 percent. Compared with other claim types, omission-related claims were more likely to be paid, had a higher median payment, and were more often associated with significant patient injury or death; the association with more frequent payments remained after controlling for physician specialty, geographic region, and degree of patient injury. Malpractice claims alleging diagnostic and monitoring omissions are relatively uncommon but appear difficult to defend relative to other claim types. Taken in light of the changing health care environment, these results highlight the limits of defensive medicine and support an expanded focus for medical liability reform.

Choosing shrinkage estimators for regression problems

A Bayesian formulation of the canonical form of the standard regression model is used to compare various Stein-type estimators and the ridge estimator of regression coefficients, A particular (“constant prior”) Stein-type estimator having the same pattern of shrinkage as the ridge estimator is recommended for use.

Attrition in the RAND Health Insurance Experiment: A Response to Nyman

In a prior article in this journal, John Nyman argues that the effect on health care use and spending found in the RAND Health Insurance Experiment is an artifact of greater voluntary attrition in the cost-sharing plans relative to the free care plan. Specifically, he speculates that those in the cost-sharing plans, when faced with a hospitalization, withdrew. His argument is implausible because (1) families facing a hospitalization would be worse off financially by withdrawing; (2) a large number of observational studies find a similar effect of cost sharing on use; (3) those who left did not differ in their utilization prior to leaving; (4) if there had been no attrition and cost sharing did not reduce hospitalization rates, each adult in each family that withdrew would have had to have been hospitalized once each year for the duration of time they would otherwise have been in the experiment, an implausibly high rate; (5) there are benign explanations for the higher attrition in the cost-sharing plans. Finally, we obtained follow-up health-status data on the great majority of those who left prematurely. We found the health-status findings were insensitive to the inclusion of the attrition cases.

Selective Incapacitation Strategies Based on Estimated Crime Rates

Methods for estimating the crime commission rates of criminal offenders are discussed in the context of a potential selective incapacitation strategy that would assign different sentence lengths according to whether the estimated crime rate is above or below a specified threshold. Any such strategy is subject to error because the true crime rate of an offender may differ from his estimated crime rate. For two strategies having the same cost, one of them is favored over the other if it has a higher expected number of crimes averted or if it has a lower probability of assigning long sentences to offenders with low crime rates. Both of these criteria are met by using a Bayes estimate of the crime rate rather than a maximum likelihood estimate. This is demonstrated by calculating the distribution of true crime rates for offenders whose estimates are above a threshold.

The Effect of Deductibles on the Demand for Medical Care Services

Abstract Using data on insurance premiums for policies with varying deductibles, together with a distribution of medical expense at a fixed (

Use, costs, and quality of medical services: impact of the New Mexico peer review system. A 1971-1975 study.

50) deductible, we estimate the relationship between deductibles and the demand for medical care. We assume that as the deductible changes, the distribution shrinks toward zero in a multiplicative fashion. The results indicate that demand is quite sensitive to variation in a deductible in the region of

Automobile Accident Compensation: Who Pays How Much How Soon?

50 and becomes steadily less sensitive as the deductible rises above

Medical School Admission and Residence of Applicants: Empirical Bayes Estimates of Logit Coffficients:

75, which is consistent with a theoretical model of demand for medical care. The size of the deductible will importantly affect the costs of a national health insurance program.