Design and analysis for three level hierarchical structures with count response

In numerous intervention studies and education field trials, random assignment to treatment occurs in clusters rather than at the level of observation. This departure of random assignment of units may be due to logistics, political feasibility, or ecological validity. Data within the same cluster or grouping are often correlated. Application of traditional regression techniques, which assume independence between observations, to clustered data produce consistent parameter estimates. However such estimators are often inefficient as compared to methods which incorporate the clustered nature of the data into the estimation procedure (Neuhaus 1993).1 Multilevel models, also known as random effects or random components models, can be used to account for the clustering of data by estimating higher level, or group, as well as lower level, or individual variation. Designing a study, in which the unit of observation is nested within higher level groupings, requires the determination of sample sizes at each level. This study investigates the design and analysis of various sampling strategies for a 3-level repeated measures design on the parameter estimates when the outcome variable of interest follows a Poisson distribution. ^ Results study suggest that second order PQL estimation produces the least biased estimates in the 3-level multilevel Poisson model followed by first order PQL and then second and first order MQL. The MQL estimates of both fixed and random parameters are generally satisfactory when the level 2 and level 3 variation is less than 0.10. However, as the higher level error variance increases, the MQL estimates become increasingly biased. If convergence of the estimation algorithm is not obtained by PQL procedure and higher level error variance is large, the estimates may be significantly biased. In this case bias correction techniques such as bootstrapping should be considered as an alternative procedure. For larger sample sizes, those structures with 20 or more units sampled at levels with normally distributed random errors produced more stable estimates with less sampling variance than structures with an increased number of level 1 units. For small sample sizes, sampling fewer units at the level with Poisson variation produces less sampling variation, however this criterion is no longer important when sample sizes are large. ^ 1Neuhaus J (1993). “Estimation efficiency and Tests of Covariate Effects with Clustered Binary Data”. Biometrics , 49, 989–996^

THE DESIGN AND DEVELOPMENT OF A SURVEY INSTRUMENT FOR THE ASSESSMENT OF OCCUPATIONAL STRESS

Using stress and coping as a unifying theoretical concept, a series of five models was developed in order to synthesize the survey questions and to classify information. These models identified the question, listed the research study, described measurements, listed workplace data, and listed industry and national reference data.^ A set of 38 instrument questions was developed within the five coping correlate categories. In addition, a set of 22 stress symptoms was also developed. The study was conducted within two groups, police and professors, on a large university campus. The groups were selected because their occupations were diverse, but they were a part of the same macroenvironment. The premise was that police officers would be more highly stressed than professors.^ Of a total study group of 80, there were 37 respondents. The difference in the mean stress responses was observable between the two groups. Not only were the responses similar within each group, but the stress level of response was also similar within each group. While the response to the survey instrument was good, only 3 respondents answered the stress symptom survey properly. It was determined that none of the 37 respondents believed that they were ill. This perception of being well was also evidenced by the grand mean of the stress scores of 2.76 (3.0 = moderate stress). This also caused fewer independent variables to be entered in the multiple regression model.^ The survey instrument was carefully designed to be universal. Universality is the ability to transcend occupational or regional definitions as applied to stress. It is the ability to measure responses within broad categories such as physiological, emotional, behavioral, social, and cognitive functions without losing the ability to measure the detail within the individual questions, or the relationships between questions and categories.^ Replication is much easier to achieve with standardized categories, questions, and measurement procedures such as those developed for the universal survey instrument. Because the survey instrument is universal it can be used as an analytical device, an assessment device, a basic tool for planning and a follow-up instrument to measure individual response to planned reductions in occupational stress. (Abstract shortened with permission of author.) ^

Specialized managed care for children with cystic fibrosis: Resource use patterns and rate design for a high cost Medicaid population

Objective. This research study had two goals: (1) to describe resource consumption patterns for Medi-Cal children with cystic fibrosis, and (2) to explore the feasibility from a rate design perspective of developing specialized managed care plans for such a special needs population.^ Background. Children with special health care needs (CSHN) comprise about 2% of the California Medicaid pediatric population. CSHN have rare but serious health problems, such as cystic fibrosis. Medicaid programs, including Medi-Cal, are enrolling more and more beneficiaries in managed care to control costs. CSHN, however, do not fit the wellness model underlying most managed care plans. Child health advocates believe that both efficiency and quality will suffer if CSHN are removed from regionalized special care centers and scattered among general purpose plans. They believe that CSHN should be "carved out" from enrollment in general plans. One alternative is the Specialized Managed Care Plan, tailored for CSHN.^ Methods. The study population consisted of children under age 21 with CF who were eligible for Medi-Cal and California Children's Services program (CCS) during 1991. Health Care Financing Administration (HCFA) Medicaid Tape-to-Tape data were analyzed as part of a California Children's Hospital Association (CCHA) project.^ Results. Mean Medi-Cal expenditures per month enrolled were $2,302 for 457 CF children, compared to about \$1,270 for all 47,000 CCS special needs children and roughly $60 for almost 2.6 million ``regular needs'' children. For CF children, inpatient care (80\%) and outpatient drugs (9\%) were the major cost drivers, with {\it all\/} outpatient visits comprising only 2\% of expenditures. About one-third of CF children were eligible due to AFDC (Aid to Families with Dependent Children). Age group explained about 17\% of all expenditure variation. Regression analysis was used to select the best capitation rate structure (rate cells by age and eligibility group). Sensitivity analysis estimated moderate financial risk for a statewide plan (360 enrollees), but severe risk for single county implementation due to small numbers of children.^ Conclusions. Study results support the carve out of CSHN due to unique expenditure patterns. The Specialized Managed Care Plan concept appears feasible from a rate design perspective given sufficient enrollees. ^