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Major depressive disorder (MDD) is a leading cause of disease burden worldwide, with lifetime prevalence in the United States of 17%. Here we present the results of the first prospective, large-scale, patient- and rater-blind, randomized controlled trial evaluating the clinical importance of achieving congruence between combinatorial pharmacogenomic (PGx) testing and medication selection for MDD.
1,167 outpatients diagnosed with MDD and an inadequate response to ≥1 psychotropic medications were enrolled and randomized 1:1 to a Treatment as Usual (TAU) arm or PGx-guided care arm. Combinatorial PGx testing categorized medications in three groups based on the level of gene-drug interactions: use as directed, use with caution, or use with increased caution and more frequent monitoring. Patient assessments were performed at weeks 0 (baseline), 4, 8, 12 and 24. Patients, site raters, and central raters were blinded in both arms until after week 8. In the guided-care arm, physicians had access to the combinatorial PGx test result to guide medication selection. Primary outcomes utilized the Hamilton Depression Rating Scale (HAM-D17) and included symptom improvement (percent change in HAM-D17 from baseline), response (50% decrease in HAM-D17 from baseline), and remission (HAM-D17<7) at the fully blinded week 8 time point. The durability of patient outcomes was assessed at week 24. Medications were considered congruent with PGx test results if they were in the ‘use as directed’ or ‘use with caution’ report categories while medications in the ‘use with increased caution and more frequent monitoring’ were considered incongruent. Patients who started on incongruent medications were analyzed separately according to whether they changed to congruent medications by week8.
At week 8, symptom improvement for individuals in the guided-care arm was not significantly different than TAU (27.2% versus 24.4%, p=0.11). However, individuals in the guided-care arm were more likely than those in TAU to achieve remission (15% versus 10%; p<0.01) and response (26% versus 20%; p=0.01). Remission rates, response rates, and symptom reductions continued to improve in the guided-treatment arm until the 24week time point. Congruent prescribing increased to 91% in the guided-care arm by week 8. Among patients who were taking one or more incongruent medication at baseline, those who changed to congruent medications by week 8 demonstrated significantly greater symptom improvement (p<0.01), response (p=0.04), and remission rates (p<0.01) compared to those who persisted on incongruent medications.
Combinatorial PGx testing improves short- and long-term response and remission rates for MDD compared to standard of care. In addition, prescribing congruency with PGx-guided medication recommendations is important for achieving symptom improvement, response, and remission for MDD patients.
Funding Acknowledgements: This study was supported by Assurex Health, Inc.
Differential forms constitutes an approach to multivariable calculus that simplifies the study of integration over surfaces of any dimension in Rp. This topic introduces algebraic techniques into the study of higher dimensional geometry and allows us to recapture with rigor the results obtained in the preceding chapter.
There are many approaches to defining and exploring differential forms, all leading to the same objective. One is to just define a form as a symbol with certain properties. That was the approach taken when I first encountered the subject. Though this appeals to many and ultimately leads to the same objective, it strikes me as inconsistent with the approach we have taken. So in this chapter I have decided to follow the approach in  where a form is defined in terms that are more in line with what I think is the background of readers of this book. The reader might also want to look at , , and  where there are different approaches.
Here we will define differential forms and explore their algebraic properties and the process of differentiating them. The first definition extends that of a surface as given in the preceding chapter.
Definition. Let q ≥ 1. A q-surface domain or just a surface domain is a compact Jordan subset R of Rq such that int R is connected and R = cl (int R). A q-surface in Rp is a pair where R is a q-surface domain and is a function from R into Rp that is smooth on some neighborhood of R. The trace of is the set. If G is an open subset of Rp and, we say is a q-surface in G; let Sq(G) be the collection of all q-surfaces contained in G.
This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.
In this chapter we begin the study of p-dimensional Euclidean space, Rp, but in this beginning we will carry it a step further. We want to discuss differentiation and integration on Rp, but first we need to extend the notions of sequential convergence, the properties of sets, and the concept of continuity to the higher dimensional spaces. The effort to explore these concepts in Rp, however, is not greater than what is required to explore these notions in what are called metric spaces. In many respects the abstract spaces are easier to cope with than Rp. Moreover some of what we have already done is properly couched in metric spaces. Indeed, the material of §4.1 can be set there with little additional effort. Nevertheless during this venture into abstraction the main set of examples will be Euclidean space.
We start with the concept of distance between points. This must be general enough to encompass a variety of circumstances, but it should conform to the intuitive notion we all have of what is meant by distance. Since this is done at the start of the first section, it would be profitable before proceeding for the reader to reflect on what properties (s)he thinks should be included in an abstract concept of distance; then you can compare your thoughts with the definition that starts the following section.
The treatment of metric spaces here is based on Chapter 1 of .
Definitions and Examples
Definition. A metric space is a pair of objects, (X, d), where X is a set and d is a function d : X × X → [0,∞) called a metric, that satisfies the following for all x, y, z in X:
Condition (a) is sometimes called the symmetric property and says that the distance from x to y is the same as the distance from y to x. The second property says the obvious: the distance from a point to itself is 0 and the only point at a distance zero from x is x itself.