Studying Effects of Primary Care Physicians and Patients on the Trade-Off Between Charges for Primary Care and Specialty Care Using a Hierarchical Multivariate Two-Part Model

Objective. To examine effects of primary care physicians (PCPs) and patients on the association between charges for primary care and specialty care in a point-of-service (POS) health plan. Data Source. Claims from 1996 for 3,308 adult male POS plan members, each of whom was assigned to one of the 50 family practitioner-PCPs with the largest POS plan member-loads. Study Design. A hierarchical multivariate two-part model was fitted using a Gibbs sampler to estimate PCPs' effects on patients' annual charges for two types of services, primary care and specialty care, the associations among PCPs' effects, and within-patient associations between charges for the two services. Adjusted Clinical Groups (ACGs) were used to adjust for case-mix. Principal Findings. PCPs with higher case-mix adjusted rates of specialist use were less likely to see their patients at least once during the year (estimated correlation: –.40; 95% CI: –.71, –.008) and provided fewer services to patients that they saw (estimated correlation: –.53; 95% CI: –.77, –.21). Ten of 11 PCPs whose case-mix adjusted effects on primary care charges were significantly less than or greater than zero (p < .05) had estimated, case-mix adjusted effects on specialty care charges that were of opposite sign (but not significantly different than zero). After adjustment for ACG and PCP effects, the within-patient, estimated odds ratio for any use of primary care given any use of specialty care was .57 (95% CI: .45, .73). Conclusions. PCPs and patients contributed independently to a trade-off between utilization of primary care and specialty care. The trade-off appeared to partially offset significant differences in the amount of care provided by PCPs. These findings were possible because we employed a hierarchical multivariate model rather than separate univariate models.

FAST ADAPTIVE PENALIZED SPLINES

This paper proposes a numerically simple routine for locally adaptive smoothing. The locally heterogeneous regression function is modelled as a penalized spline with a smoothly varying smoothing parameter modelled as another penalized spline. This is being formulated as hierarchical mixed model, with spline coe±cients following a normal distribution, which by itself has a smooth structure over the variances. The modelling exercise is in line with Baladandayuthapani, Mallick & Carroll (2005) or Crainiceanu, Ruppert & Carroll (2006). But in contrast to these papers Laplace's method is used for estimation based on the marginal likelihood. This is numerically simple and fast and provides satisfactory results quickly. We also extend the idea to spatial smoothing and smoothing in the presence of non normal response.

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.