Weak convergence of probability measures on product spaces with applications to sums of random vectors

Weak convergence of probability measures on product spaces with applications to sums of random vector

Diffusion approximations in collective risk theory

Collective risk theory concerned with random fluctuations of total assets of insurance compan

Should a Sentinel Node Biopsy Be Performed in Patients with High-Risk Breast Cancer?

A negative sentinel lymph node (SLN) biopsy spares many breast cancer patients the complications associated with lymph node irradiation or additional surgery. However, patients at high risk for nodal involvement based on clinical characteristics may remain at unacceptably high risk of axillary disease even after a negative SLN biopsy result. A Bayesian nomogram was designed to combine the probability of axillary disease prior to nodal biopsy with customized test characteristics for an SLN biopsy and provides the probability of axillary disease despite a negative SLN biopsy. Users may individualize the sensitivity of an SLN biopsy based on factors known to modify the sensitivity of the procedure. This tool may be useful in identifying patients who should have expanded upfront exploration of the axilla or comprehensive axillary irradiation

Functional central limit theorems for vicious walkers

We consider the diffusion scaling limit of the vicious walker model that is a system of nonintersecting random walks. We prove a functional central limit theorem for the model and derive two types of nonintersecting Brownian motions, in which the nonintersecting condition is imposed in a finite time interval $(0,T]$ for the first type and in an infinite time interval $(0,\infty)$ for the second type, respectively. The limit process of the first type is a temporally inhomogeneous diffusion, and that of the second type is a temporally homogeneous diffusion that is identified with a Dyson's model of Brownian motions studied in the random matrix theory. We show that these two types of processes are related to each other by a multi-dimensional generalization of Imhof's relation, whose original form relates the Brownian meander and the three-dimensional Bessel process. We also study the vicious walkers with wall restriction and prove a functional central limit theorem in the diffusion scaling limit.Comment: AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for publicatio

A primary care, multi-disciplinary disease management program for opioid-treated patients with chronic non-cancer pain and a high burden of psychiatric comorbidity

BACKGROUND: Chronic non-cancer pain is a common problem that is often accompanied by psychiatric comorbidity and disability. The effectiveness of a multi-disciplinary pain management program was tested in a 3 month before and after trial. METHODS: Providers in an academic general medicine clinic referred patients with chronic non-cancer pain for participation in a program that combined the skills of internists, clinical pharmacists, and a psychiatrist. Patients were either receiving opioids or being considered for opioid therapy. The intervention consisted of structured clinical assessments, monthly follow-up, pain contracts, medication titration, and psychiatric consultation. Pain, mood, and function were assessed at baseline and 3 months using the Brief Pain Inventory (BPI), the Center for Epidemiological Studies-Depression Scale scale (CESD) and the Pain Disability Index (PDI). Patients were monitored for substance misuse. RESULTS: Eighty-five patients were enrolled. Mean age was 51 years, 60% were male, 78% were Caucasian, and 93% were receiving opioids. Baseline average pain was 6.5 on an 11 point scale. The average CESD score was 24.0, and the mean PDI score was 47.0. Sixty-three patients (73%) completed 3 month follow-up. Fifteen withdrew from the program after identification of substance misuse. Among those completing 3 month follow-up, the average pain score improved to 5.5 (p = 0.003). The mean PDI score improved to 39.3 (p < 0.001). Mean CESD score was reduced to 18.0 (p < 0.001), and the proportion of depressed patients fell from 79% to 54% (p = 0.003). Substance misuse was identified in 27 patients (32%). CONCLUSIONS: A primary care disease management program improved pain, depression, and disability scores over three months in a cohort of opioid-treated patients with chronic non-cancer pain. Substance misuse and depression were common, and many patients who had substance misuse identified left the program when they were no longer prescribed opioids. Effective care of patients with chronic pain should include rigorous assessment and treatment of these comorbid disorders and intensive efforts to insure follow up