Visual Comparison of Datasets Using Mixture Decompositions

This article describes how a mixture of two densities, f0 and f1, may be decomposed into a different mixture consisting of three densities. These new densities, f+, f−, and f=, summarize differences between f0 and f1: f+ is high in areas of excess of f1 compared to f0; f− represents deficiency of f1 compared to f0 in the same way; f= represents commonality between f1 and f0. The supports of f+ and f− are disjoint. This decomposition of the mixture of f0 and f1 is similar to the set-theoretic decomposition of the union of two sets A and B into the disjoint sets A\B, B\A, and A ∩ B. Sample points from f0 and f1 can be assigned to one of these three densities, allowing the differences between f0 and f1 to be visualized in a single plot, a visual hypothesis test of whether f0 is equal to f1. We describe two similar such decompositions and contrast their behavior under the null hypothesis f0 = f1, giving some insight into how such plots may be interpreted. We present two examples of uses of these methods: visualization of departures from independence, and of a two-class classification problem. Other potential applications are discussed

Visual Comparison of Datasets using Mixture Decompositions

We describe how a mixture of two densities f 0 and f 1 may be decomposed into a different mixture consisting of three densities. These new densities, f+ , f \Gamma , and f= , summarize differences between f 0 and f 1 : f+ is high in areas of excess of f 1 compared to f 0 ; f \Gamma represents deficiency of f 1 compared to f 0 in the same way; f= represents commonality between f 1 and f 0 . The supports of f+ and f \Gamma are disjoint. This decomposition of the mixture of f 0 and f 1 is similar to the set-theoretic decomposition of the union of two sets A and B into the disjoint sets AnB, BnA, and A " B. Sample points from f 0 and f 1 can be assigned to one of these three densities, allowing the differences between f 0 and f 1 to be visualized in a single plot, a visual hypothesis test of whether f 0 is equal to f 1 . We describe two similar such decompositions and contrast their behavior under the null hypothesis f 0 = f 1 , giving some insight into how such plots may be interpreted. ..

Pharmacokinetic and Pharmacodynamic Principles of Anti-infective Dosing

PURPOSE: An understanding of the pharmacokinetic (PK) and pharmacodynamic (PD) principles that determine response to antimicrobial therapy can provide the clinician with better-informed dosing regimens. Factors influential on antibiotic disposition and clinical outcome are presented, with a focus on the primary site of infection. Techniques to better understand antibiotic PK and optimize PD are acknowledged. METHODS: PubMed (inception – April 2016) was reviewed for relevant publications assessing antimicrobial exposures within different anatomical locations and clinical outcomes for various infection sites. FINDINGS: A limited literature base indicates variable penetration of antibiotics to different target sites of infection, with drug solubility and extent of protein binding providing significant PK influences in addition to the major clearing pathway of the agent. PD indices derived from in vitro and animal models determine the optimal magnitude and frequency of dosing regimens for patients. PK/PD modeling and simulation has been shown an efficient means of assessing these PD endpoints against a variety of PK determinants, clarifying the unique effects of infection site and patient characteristics to inform the adequacy of a given antibiotic regimen. IMPLICATIONS: Appreciation of the PK properties of an antibiotic and its PD measure of efficacy can maximize the utility of these life-saving drugs. Unfortunately, clinical data remains limited for a number of infection site-antibiotic exposure relationships. Modeling and simulation can bridge preclinical and patient data for the prescription of optimal antibiotic dosing regimens, consistent with the tenets of personalized medicine