RE-EM Trees: A New Data Mining Approach for Longitudinal Data

Longitudinal data refer to the situation where repeated observations are available for each sampled individual. Methodologies that take this structure into account allow for systematic differences between individuals that are not related to covariates. A standard methodology in the statistics literature for this type of data is the random effects model, where these differences between individuals are represented by so-called “effects” that are estimated from the data. This paper presents a methodology that combines the flexibility of tree-based estimation methods with the structure of random effects models for longitudinal data. We apply the resulting estimation method, called the RE-EM tree, to pricing in online transactions, showing that the RE-EM tree is less sensitive to parametric assumptions and provides improved predictive power compared to linear models with random effects and regression trees without random effects. We also perform extensive simulation experiments to show that the estimator improves predictive performance relative to regression trees without random effects and is comparable or superior to using linear models with random effects in more general situations.Statistics Group, Information, Operations, and Management Science Department, Stern School of Business, New York UniversityStatistics Working Papers Serie

Efficiency and Consistency for Regularization Parameter Selection in Penalized Regression: Asymptotics and Finite-Sample Corrections

This paper studies the asymptotic and nite-sample performance of penalized regression methods when different selectors of the regularization parameter are used under the assumption that the true model is, or is not, included among the candidate model. In the latter setting, we relax assumptions in the existing theory to show that several classical information criteria are asymptotically efficient selectors of the regularization parameter. In both settings, we assess the nite-sample performance of these as well as other common selectors and demonstrate that their performance can suffer due to sensitivity to the number of variables that are included in the full model. As alternatives, we propose two corrected information criteria which are shown to outperform the existing procedures while still maintaining the desired asymptotic properties. In the non-true model world, we relax the assumption made in the literature that the true error variance is known or that a consistent estimator is available to prove that Akaike's information criterion (AIC), Cp and Generalized cross-validation (GCV) themselves are asymptotically efficient selectors of the regularization parameter and we study their performance in nite samples. In classical regression, AIC tends to select overly complex models when the dimension of the maximum candidate model is large relative to the sample size. Simulation studies suggest that AIC suffers from the same shortcomings when used in penalized regression. We therefore propose the use of the classical AICc as an alternative. In the true model world, a similar investigation into the nite sample properties of BIC reveals analogous overfitting tendencies and leads us to further propose the use of a corrected BIC (BICc). In their respective settings (whether the true model is, or is not, among the candidate models), BICc and AICc have the desired asymptotic properties and we use simulations to assess their performance, as well as that of other selectors, in nite samples for penalized regressions fit using the Smoothly clipped absolute deviation (SCAD) and Least absolute shrinkage and selection operator (Lasso) penalty functions. We nd that AICc and 10-fold cross-validation outperform the other selectors in terms of squared error loss, and BICc avoids the tendency of BIC to select overly complex models when the dimension of the maximum candidate model is large relative to the sample size.NYU Stern School of BusinessStatistics Working Papers Serie

Clinical predictors of antipsychotic use in children and adolescents with autism spectrum disorders: a historical open cohort study using electronic health records.

JOURNAL ARTICLEThe final publication is available at Springer via http://dx.doi.org/ 10.1007/s00787-015-0780-7Children with autism spectrum disorders (ASD) are more likely to receive antipsychotics than any other psychopharmacological medication, yet the psychiatric disorders and symptoms associated with treatment are unclear. We aimed to determine the predictors of antipsychotic use in children with ASD receiving psychiatric care. The sample consisted of 3482 children aged 3-17 with an ICD-10 diagnosis of ASD referred to mental health services between 2008 and 2013. Antipsychotic use outcome, comorbid diagnoses, and other clinical covariates, including challenging behaviours were extracted from anonymised patient records. Of the 3482 children (79 % male) with ASD, 348 (10 %) received antipsychotic medication. The fully adjusted model indicated that comorbid diagnoses including hyperkinetic (OR 1.44, 95 %CI 1.01-2.06), psychotic (5.71, 3.3-10.6), depressive (2.36, 1.37-4.09), obsessive-compulsive (2.31, 1.16-4.61) and tic disorders (2.76, 1.09-6.95) were associated with antipsychotic use. In addition, clinician-rated levels of aggression, self-injurious behaviours, reduced adaptive function, and overall parental concern for their child's presenting symptoms were significant risk factors for later antipsychotic use. In ASD, a number of comorbid psychiatric disorders are independent predictors for antipsychotic treatment, even after adjustment for familial, socio-demographic and individual factors. As current trial evidence excludes children with comorbidity, more pragmatic randomised controlled trials with long-term drug monitoring are needed.NIHRBiomedical Research Centre for Mental Health at South London and Maudsley NHS Foundation Trust and King’s College LondonGuy’s and St. Thomas’ CharityMaudsley CharityMR

Efficiency and Consistency for Regularization Parameter Selection in Penalized Regression: Asymptotics and Finite-Sample Corrections

This paper studies the asymptotic and nite-sample performance of penalized regression methods when different selectors of the regularization parameter are used under the assumption that the true model is, or is not, included among the candidate model. In the latter setting, we relax assumptions in the existing theory to show that several classical information criteria are asymptotically efficient selectors of the regularization parameter. In both settings, we assess the nite-sample performance of these as well as other common selectors and demonstrate that their performance can suffer due to sensitivity to the number of variables that are included in the full model. As alternatives, we propose two corrected information criteria which are shown to outperform the existing procedures while still maintaining the desired asymptotic properties. In the non-true model world, we relax the assumption made in the literature that the true error variance is known or that a consistent estimator is available to prove that Akaike's information criterion (AIC), Cp and Generalized cross-validation (GCV) themselves are asymptotically efficient selectors of the regularization parameter and we study their performance in nite samples. In classical regression, AIC tends to select overly complex models when the dimension of the maximum candidate model is large relative to the sample size. Simulation studies suggest that AIC suffers from the same shortcomings when used in penalized regression. We therefore propose the use of the classical AICc as an alternative. In the true model world, a similar investigation into the nite sample properties of BIC reveals analogous overfitting tendencies and leads us to further propose the use of a corrected BIC (BICc). In their respective settings (whether the true model is, or is not, among the candidate models), BICc and AICc have the desired asymptotic properties and we use simulations to assess their performance, as well as that of other selectors, in nite samples for penalized regressions fit using the Smoothly clipped absolute deviation (SCAD) and Least absolute shrinkage and selection operator (Lasso) penalty functions. We nd that AICc and 10-fold cross-validation outperform the other selectors in terms of squared error loss, and BICc avoids the tendency of BIC to select overly complex models when the dimension of the maximum candidate model is large relative to the sample size.NYU Stern School of BusinessStatistics Working Papers Serie

Bounds on Integrals of the Wigner Function

The integral of the Wigner function over a subregion of the phase-space of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over all possible states, reduces to the problem of finding the greatest and least eigenvalues of an hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.Comment: 10 pages, 1 PostScript figure, Latex file; revised following referees' comments; to appear in Physical Review Letter

Moving from development to implementation of digital innovations within the NHS: myHealthE, a remote monitoring system for tracking patient outcomes in child and adolescent mental health services

OBJECTIVE: This paper aims to report our experience of developing, implementing, and evaluating myHealthE (MHE), a digital innovation for Child and Adolescents Mental Health Services (CAMHS), which automates the remote collection and reporting of Patient-Reported Outcome Measures (PROMs) into National Health Services (NHS) electronic healthcare records. METHODS: We describe the logistical and governance issues encountered in developing the MHE interface with patient-identifiable information, and the steps taken to overcome these development barriers. We describe the application's architecture and hosting environment to enable its operability within the NHS, as well as the capabilities needed within the technical team to bridge the gap between academic development and NHS operational teams. RESULTS: We present evidence on the feasibility and acceptability of this system within clinical services and the process of iterative development, highlighting additional functions that were incorporated to increase system utility. CONCLUSION: This article provides a framework with which to plan, develop, and implement automated PROM collection from remote devices back to NHS infrastructure. The challenges and solutions described in this paper will be pertinent to other digital health innovation researchers aspiring to deploy interoperable systems within NHS clinical systems

'Everyday memory' impairments in autism spectrum disorders

‘Everyday memory’ is conceptualised as memory within the context of day-to-day life and, despite its functional relevance, has been little studied in individuals with autism spectrum disorders (ASDs). In the first study of its kind, 94 adolescents with an ASD and 55 without an ASD completed measures of everyday memory from the Rivermead Behavioural Memory Test (RBMT) and a standard word recall task (Children’s Auditory Verbal Learning Test-2: CAVLT-2). The ASD group showed significant impairments on the RBMT, including in prospective memory, alongside impaired performance on the CAVLT-2. Social and communication ability was significantly associated with prospective remembering in an everyday memory context but not with the CAVLT-2. The complex nature of everyday memory and its relevance to ASD is discussed

Prenatal antidepressant use and risk of attention-deficit/hyperactivity disorder in offspring:population based cohort study

textabstractObjective To assess the potential association between prenatal use of antidepressants and the risk of attention-deficit/hyperactivity disorder (ADHD) in offspring. Design Population based cohort study. Setting Data from the Hong Kong population based electronic medical records on the Clinical Data Analysis and Reporting System. Participants 190 618 children born in Hong Kong public hospitals between January 2001 and December 2009 and followed-up to December 2015. Main outcome measure Hazard ratio of maternal antidepressant use during pregnancy and ADHD in children aged 6 to 14 years, with an average follow-up time of 9.3 years (range 7.4-11.0 years). Results Among 190 618 children, 1252 had a mother who used prenatal antidepressants. 5659 children (3.0%) were given a diagnosis of ADHD or received treatment for ADHD. The crude hazard ratio of maternal antidepressant use during pregnancy was 2.26 (P<0.01) compared with non-use. After adjustment for potential confounding factors, including maternal psychiatric disorders and use of other psychiatric drugs, the adjusted hazard ratio was reduced to 1.39 (95% confidence interval 1.07 to 1.82, P=0.01). Likewise, similar results were observed when comparing children of mothers who had used antidepressants before pregnancy with those who were never users (1.76, 1.36 to 2.30, P<0.01). The risk of ADHD in the children of mothers with psychiatric disorders was higher compared with the children of mothers without psychiatric disorders even if the mothers had never used antidepressants (1.84, 1.54 to 2.18, P<0.01). All sensitivity analyses yielded similar results. Sibling matched analysis identified no significant difference in risk of ADHD in siblings exposed to antidepressants during gestation and those not exposed during gestation (0.54, 0.17 to 1.74, P=0.30). Conclusions The findings suggest that the association between prenatal use of antidepressants and risk of ADHD in offspring can be partially explained by confounding by indication of antidepressants. If there is a causal association, the size of the effect is probably smaller than that reported previously

Local linear density estimation for filtered survival data, with bias correction

A class of local linear kernel density estimators based on weighted least-squares kernel estimation is considered within the framework of Aalen's multiplicative intensity model. This model includes the filtered data model that, in turn, allows for truncation and/or censoring in addition to accommodating unusual patterns of exposure as well as occurrence. It is shown that the local linear estimators corresponding to all different weightings have the same pointwise asymptotic properties. However, the weighting previously used in the literature in the i.i.d. case is seen to be far from optimal when it comes to exposure robustness, and a simple alternative weighting is to be preferred. Indeed, this weighting has, effectively, to be well chosen in a 'pilot' estimator of the survival function as well as in the main estimator itself. We also investigate multiplicative and additive bias-correction methods within our framework. The multiplicative bias-correction method proves to be the best in a simulation study comparing the performance of the considered estimators. An example concerning old-age mortality demonstrates the importance of the improvements provided

Regression, developmental trajectory and associated problems in disorders in the autism spectrum: the SNAP study

We report rates of regression and associated findings in a population derived group of 255 children aged 9-14 years, participating in a prevalence study of autism spectrum disorders (ASD); 53 with narrowly defined autism, 105 with broader ASD and 97 with non-ASD neurodevelopmental problems, drawn from those with special educational needs within a population of 56,946 children. Language regression was reported in 30% with narrowly defined autism, 8% with broader ASD and less than 3% with developmental problems without ASD. A smaller group of children were identified who underwent a less clear setback. Regression was associated with higher rates of autistic symptoms and a deviation in developmental trajectory. Regression was not associated with epilepsy or gastrointestinal problems