Differential power of placebo across major psychiatric disorders: a preliminary meta-analysis and machine learning study

The placebo effect across psychiatric disorders is still not well understood. In the present study, we conducted meta-analyses including meta-regression, and machine learning analyses to investigate whether the power of placebo effect depends on the types of psychiatric disorders. We included 108 clinical trials (32,035 participants) investigating pharmacological intervention effects on major depressive disorder (MDD), bipolar disorder (BD) and schizophrenia (SCZ). We developed measures based on clinical rating scales and Clinical Global Impression scores to compare placebo effects across these disorders. We performed meta-analysis including meta-regression using sample-size weighted bootstrapping techniques, and machine learning analysis to identify the disorder type included in a trial based on the placebo response. Consistently through multiple measures and analyses, we found differential placebo effects across the three disorders, and found lower placebo effect in SCZ compared to mood disorders. The differential placebo effects could also distinguish the condition involved in each trial between SCZ and mood disorders with machine learning. Our study indicates differential placebo effect across MDD, BD, and SCZ, which is important for future neurobiological studies of placebo effects across psychiatric disorders and may lead to potential therapeutic applications of placebo on disorders more responsive to placebo compared to other conditions

The Maximal Strichartz Family of Gaussian Distributions: Fisher Information, Index of Dispersion, and Stochastic Ordering

We define and study several properties of what we call Maximal Strichartz Family of Gaussian Distributions. This is a subfamily of the family of Gaussian Distributions that arises naturally in the context of the Linear Schrödinger Equation and Harmonic Analysis, as the set of maximizers of certain norms introduced by Strichartz. From a statistical perspective, this family carries with itself some extrastructure with respect to the general family of Gaussian Distributions. In this paper, we analyse this extrastructure in several ways. We first compute the Fisher Information Matrix of the family, then introduce some measures of statistical dispersion, and, finally, introduce a Partial Stochastic Order on the family. Moreover, we indicate how these tools can be used to distinguish between distributions which belong to the family and distributions which do not. We show also that all our results are in accordance with the dispersive PDE nature of the family

Some problems concerning a Quasilinear Schrödinger Equation

These are the slides from a talk A. Selvitella gave in the Analysis and Applied Mathematics Seminar at the University of Toronto.In this seminar we will talk about different issues concerning a Quasilinear Schrodinger Equation. In particular we will discuss a joint work with Prof. Louis Jeanjean about uniqueness and nondegeneracy of the ground state. We will also give an outline of what is known, what will be known soon (hopefully...) and what is going to be not known (for a while at least) about the Cauchy Problem for this equation

The Maximal Strichartz Family of Gaussian Distributions: Fisher Information, Index of Dispersion, and Stochastic Ordering

We define and study several properties of what we call Maximal Strichartz Family of Gaussian Distributions. This is a subfamily of the family of Gaussian Distributions that arises naturally in the context of the Linear Schrödinger Equation and Harmonic Analysis, as the set of maximizers of certain norms introduced by Strichartz. From a statistical perspective, this family carries with itself some extrastructure with respect to the general family of Gaussian Distributions. In this paper, we analyse this extrastructure in several ways. We first compute the Fisher Information Matrix of the family, then introduce some measures of statistical dispersion, and, finally, introduce a Partial Stochastic Order on the family. Moreover, we indicate how these tools can be used to distinguish between distributions which belong to the family and distributions which do not. We show also that all our results are in accordance with the dispersive PDE nature of the family

The ubiquity of the Simpson’s Paradox

Abstract The Simpson’s Paradox is the phenomenon that appears in some datasets, where subgroups with a common trend (say, all negative trend) show the reverse trend when they are aggregated (say, positive trend). Even if this issue has an elementary mathematical explanation, it has a deep statistical significance. In this paper, we discuss basic examples in arithmetic, geometry, linear algebra, statistics, game theory, gender bias in university admission and election polls, where we describe the appearance or absence of the Simpson’s Paradox. In the final part, we present our results concerning the occurrence of the Simpson’s Paradox in Quantum Mechanics with focus on the Quantum Harmonic Oscillator and the Nonlinear Schrödinger Equation. We discuss how likely it is to incur in the Simpson’s Paradox and give some concrete numerical examples. We conclude with some final comments and possible future directions

On the variability and dependence of human leg stiffness across strides during running and some consequences for the analysis of locomotion data

Typically, animal locomotion studies involve consecutive strides, which are frequently assumed to be independent with parameters that do not vary across strides. This assumption is often not tested. However, failing in particular to account for dependence across strides may cause an incorrect estimate of the uncertainty of the measurements and thereby lead to either missing (overestimating variance) or over-evaluating (underestimating variance) biological signals. In turn, this impacts replicability of the results because variability is accounted for differently across experiments. In this paper, we analyse the changes of a couple of measures of human leg stiffness across strides during running experiments, using a publicly available dataset. A major finding of this analysis is that the time series of these measurements of stiffness show autocorrelation even at large lags and so there is dependence between individual strides, even when separated by many intervening strides. Our results question the practice in biomechanics research of using each stride as an independent observation or of sub-selecting strides at small lags. Following the outcome of our analysis, we strongly recommend caution in doing so without first confirming the independence of the measurements across strides and without confirming that sub-selection does not produce spurious results