The Optimal Confidence Region for a Random Parameter

Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide gene-expession data for estimating individual gene- or center-specific parameters simultaneously. The new proposal is illustrated with a typical microarray data set and its performance is examined via a small simulation study.

MODELING DIFFERENTIATED TREATMENT EFFECTS FOR MULTIPLE OUTCOMES DATA

Multiple outcomes data are commonly used to characterize treatment effects in medical research, for instance, multiple symptoms to characterize potential remission of a psychiatric disorder. Often either a global, i.e. symptom-invariant, treatment effect is evaluated. Such a treatment effect may over generalize the effect across the outcomes. On the other hand individual treatment effects, varying across all outcomes, are complicated to interpret, and their estimation may lose precision relative to a global summary. An effective compromise to summarize the treatment effect may be through patterns of the treatment effects, i.e. "differentiated effects." In this paper we propose a two-category model to differentiate treatment effects into two groups. A model fitting algorithm and simulation study are presented, and several methods are developed to analyze heterogeneity presenting in the treatment effects. The method is illustrated using an analysis of schizophrenia symptom data.

A Mechanistic Latent Variable Model for Estimating Drug Concentrations in the Male Genital Tract

The purpose of this study is to develop statistical methodology to facilitate indirect estimation of the concentration of antiretroviral drugs and viral loads in the prostate gland and the seminal vesicle. The differences in antiretroviral drug concentrations in these organs may lead to suboptimal concentrations in one gland compared to the other. Suboptimal levels of the antiretroviral drugs will not be able to fully suppress the virus in that gland, lead to a source of sexually transmissible virus and increase the chance of selecting for drug resistant virus. This information may be useful selecting antiretroviral drug regimen that will achieve optimal concentrations in most of male genital tract glands. Using fractionally collected semen ejaculates, Lundquist (1949) measured levels of surrogate markers in each fraction that are uniquely produced by specific male accessory glands. To determine the original glandular concentrations of the surrogate markers, Lundquist solved a simultaneous series of linear equations. This method has several limitations. In particular, it does not yield a unique solution, it does not address measurement error, and it disregards inter-subject variability in the parameters. To cope with these limitations, we developed a mechanistic latent variable model based on the physiology of the male genital tract and surrogate markers. We employ a Bayesian approach and perform a sensitivity analysis with regard to the distributional assumptions on the random effects and priors. The model and Bayesian approach is validated on experimental data where the concentration of a drug should be (biologically) differentially distributed between the two glands. In this example, the Bayesian model-based conclusions are found to be robust to model specification and this hierarchical approach leads to more scientifically valid conclusions than the original methodology. In particular, unlike existing methods, the proposed model based approach was not affected by a common form of outliers.

Model Evaluation Based on the Distribution of Estimated Absolute Prediction Error

The construction of a reliable, practically useful prediction rule for future response is heavily dependent on the "adequacy" of the fitted regression model. In this article, we consider the absolute prediction error, the expected value of the absolute difference between the future and predicted responses, as the model evaluation criterion. This prediction error is easier to interpret than the average squared error and is equivalent to the mis-classification error for the binary outcome. We show that the distributions of the apparent error and its cross-validation counterparts are approximately normal even under a misspecified fitted model. When the prediction rule is "unsmooth", the variance of the above normal distribution can be estimated well via a perturbation-resampling method. We also show how to approximate the distribution of the difference of the estimated prediction errors from two competing models. With two real examples, we demonstrate that the resulting interval estimates for prediction errors provide much more information about model adequacy than the point estimates alone.

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.