Estimating population size when duplicates are present.

Each of K mental health programmes reports the number of patients served in a year. The sum of these numbers, y, is an overcount because some patients are seen in more than one programme. Health care planners need to know the unduplicated number served by the mental health system. Thus, there is an unknown number, M, of distinct individuals who appear on one or more of K lists; some appear on multiple lists and the duplicates are not readily identifiable. Let X be the number of lists on which a randomly selected individual appears. When E(X) is known, y/E(X) is the natural estimator of M. We assume that we know the number of programmes, Xi, used by the ith individual in a random sample of recipients of service. Here, the intuitive estimator, Y/X has desirable statistical properties. We give confidence interval estimators for M. We apply the method to estimate the number of individuals served in 1991 by the mental health programmes in New York State.

Ethnic differences in seclusion and restraint.

Data on seclusions or restraints were analyzed by ethnic group for 587 patients in 19 New York State psychiatric hospitals for a 4-week period. No differences among White, Black, or Hispanic patients were found for sex; type of ward where episode occurred; frequency of, length of, or reason for confinement; or the administration of medication as needed. The groups did differ in age, diagnosis, and target of their assaults. When analyzed by age groups, minority patients were not overrepresented in the secluded/restrained sample. Age was the most important variable to account for ethnic differences in confinement.

Variations in seclusion and restraint practices by hospital location.

Data from a survey of seclusion and restraint practices in New York state hospitals were analyzed to determine if they differed by hospital location. The study included 19 hospitals--five in New York City, four in New York City suburbs, three in large towns, and seven in small towns. Overall, New York City and large-town hospitals had the highest rates of seclusion and restraint, but analysis by age group showed that New York City had the lowest rate for patients under age 35, who constituted the majority of patients who were secluded or restrained, and large towns had the highest rate. Compared with suburban and small-town hospitals, city and large-town hospitals used seclusion more often than restraint and had a higher ward census and a lower-staff patient ratio. In all groups males and blacks were overrepresented compared with the hospital population. The authors believe clarification of regional variations in assaultive behavior is important for treatment and system planning.

An analytic approach to quantifying pain scores.

Statistical problems in clinical trials frequently involve fitting regression lines when the underlying data are categorical or ordinal response variables. Usually an ad hoc a priori quantification is used to assign values to these ordinal responses. For pain intensity data collected in analgesic trials, the usual approach is to set none equal to 0, mild equal to 1, moderate equal to 2, and severe equal to 3. While this scheme has been generally accepted, on the basis that for similar clinical trials reasonably similar results are obtained by different investigators, concern exists that the distances between pain scores are probably not equal. A method is presented for quantifying categorical responses so that the resulting scores maximize the simultaneous fit of the dose-response regression lines. The optimal scores derived by this technique may then be used in a bioassay analysis to estimate the relative potency of 2 compounds. As illustrative examples, this method was applied to data from 2 clinical trials and the results were compared to the usual method.

Quantitative differences in aspirin analgesia in three models of clinical pain.

An analysis was made of data from over 4000 postepisiotomy, uterine cramping, and postsurgical patients complaining of moderate or severe pain. They had received 325, 650, or 1300 mg aspirin or placebo while they were subjects in 10 analgesic clinical trials. On the average, for the same verbally expressed pain intensity level and the same treatment, more relief was obtained by a patient with uterine cramping than one with episiotomy pain, who in turn obtained more relief than a patient with surgical pain. A new mathematical model which characterizes the probability that an analgesic provides complete relief as a function of dose, severity of pain intensity, and pain etiology is developed. The model utilizes the data itself to estimate the numerical score corresponding to verbal pain intensities. The results indicate that the numerical score quantifying severe surgical pain is 1.4 times greater than the score for severe episiotomy pain, which in turn is 3.2 times greater than the score for severe uterine cramping. Clinical trials must be designed to take these differences into account. Also, clinicians must be cognizant of such differences when choosing among drugs and dosages for patients with different pain intensity and etiology.