The Analysis of Variance.

We demonstrate the effectiveness of using machine learning for model-free prediction of spatiotemporally chaotic systems of arbitrarily large spatial extent and attractor dimension purely from observations of the system's past evolution. We present a parallel scheme with an example implementation based on the reservoir computing paradigm and demonstrate the scalability of our scheme using the Kuramoto-Sivashinsky equation as an example of a spatiotemporally chaotic system.

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Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach

We consider the problem of identifying a subgroup of patients who may have an enhanced treatment effect in a randomized clinical trial, and it is desirable that the subgroup be defined by a limited number of covariates. For this problem, the development of a standard, pre-determined strategy may help to avoid the well-known dangers of subgroup analysis. We present a method developed to find subgroups of enhanced treatment effect. This method, referred to as 'Virtual Twins', involves predicting response probabilities for treatment and control 'twins' for each subject. The difference in these probabilities is then used as the outcome in a classification or regression tree, which can potentially include any set of the covariates. We define a measure Q(Â) to be the difference between the treatment effect in estimated subgroup Â and the marginal treatment effect. We present several methods developed to obtain an estimate of Q(Â), including estimation of Q(Â) using estimated probabilities in the original data, using estimated probabilities in newly simulated data, two cross-validation-based approaches, and a bootstrap-based bias-corrected approach. Results of a simulation study indicate that the Virtual Twins method noticeably outperforms logistic regression with forward selection when a true subgroup of enhanced treatment effect exists. Generally, large sample sizes or strong enhanced treatment effects are needed for subgroup estimation. As an illustration, we apply the proposed methods to data from a randomized clinical trial.

Subgroup identification from randomized clinical trial data

Complicated intra-abdominal infections (cIAIs) are tissue-invasive infections leading to abscess formation or generalized peritonitis. The management of cIAIs involves operative or percutaneous intervention to obtain surgical control of the source. Nonetheless, patients with cIAIs are at risk of sepsis and mortality [1–4].

Empiric antimicrobial therapy with appropriate agents is an important component of treatment [5, 6]. Initial empiric therapy that is not effective against infecting pathogens increases costs, treatment failure, and death [7–10]. Because of this, cIAIs are an important infection category for evaluation of the efficacy of investigational agents.

The well-recognized appearance of antimicrobial resistance among gram-negative bacteria has stimulated the development of novel agents [11], particularly those targeting Enterobacteriaceae that produce extended-spectrum β-lactamases (ESBLs) [12], which confer resistance to most β-lactam antimicrobial agents [1].

Ceftolozane/tazobactam consists of a novel cephalosporin and an established β-lactamase inhibitor that is being developed to address antimicrobial resistance in serious infections caused by gram-negative pathogens, including cIAI, complicated urinary tract infection/pyelonephritis (cUTI), and ventilated nosocomial pneumonia. In vitro activity of ceftolozane/tazobactam has been confirmed against ESBL-producing Enterobacteriaceae, drug-resistant Pseudomonas aeruginosa [13–16], and some Streptococcus species [17]. The results from a phase 2 study with ceftolozane/tazobactam in combination with metronidazole in cIAI supported further development for this indication [18].

We now report the results from ASPECT-cIAI (Assessment of the Safety Profile and Efficacy of Ceftolozane/Tazobactam in Complicated Intra-abdominal Infections), a large global phase 3 clinical program that evaluated intravenous ceftolozane/tazobactam plus metronidazole vs meropenem for the treatment of hospitalized adult patients with cIAI.

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Ceftolozane/Tazobactam Plus Metronidazole for Complicated Intra-abdominal Infections in an Era of Multidrug Resistance: Results From a Randomized, Double-Blind, Phase 3 Trial (ASPECT-cIAI)

We consider a setting in which we have a treatment and a potentially large number of covariates for a set of observations, and wish to model their relationship with an outcome of interest. We propose a simple method for modeling interactions between the treatment and covariates. The idea is to modify the covariate in a simple way, and then fit a standard model using the modified covariates and no main effects. We show that coupled with an efficiency augmentation procedure, this method produces clinically meaningful estimators in a variety of settings. It can be useful for practicing personalized medicine: determining from a large set of biomarkers, the subset of patients that can potentially benefit from a treatment. We apply the method to both simulated datasets and real trial data. The modified covariates idea can be used for other purposes, for example, large scale hypothesis testing for determining which of a set of covariates interact with a treatment variable. Supplementary materials for this articl...

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A Simple Method for Estimating Interactions Between a Treatment and a Large Number of Covariates

This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the methods and techniques described in the book. It covers the fundamental theories in linear regression analysis and is extremely useful for future research in this area. The examples of regression analysis using the Statistical Application System (SAS) are also included. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject fields. Introduction Simple Linear Regression Multiple Linear Regression Detection of Outliers and Influential Observations in Multiple Linear Regression Model Selection Model Diagnostics Extensions of Least Squares Generalized Linear Models Bayesian Linear Regression

Linear Regression Analysis: Theory and Computing

We propose an interaction tree (IT) procedure to optimize the subgroup analysis in comparative studies that involve censored survival times. The proposed method recursively partitions the data into two subsets that show the greatest interaction with the treatment, which results in a number of objectively defined subgroups: in some of them the treatment effect is prominent while in others the treatment may have a negligible or even negative effect. The resultant tree structure can be used to explore the overall interaction between treatment and other covariates and help identify and describe possible target populations on which an experimental treatment demonstrates desired efficacy. We follow the standard CART (Breiman, et al., 1984) methodology to develop the interaction tree structure. Variable importance information is extracted via random forests of interaction trees. Both simulated experiments and an analysis of the primary billiary cirrhosis (PBC) data are provided for evaluation and illustration of the proposed procedure.

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Interaction trees with censored survival data.

Assessing treatment effects in observational studies is a multifaceted problem that not only involves heterogeneous mechanisms of how the treatment or cause is exposed to subjects, known as propensity, but also differential causal effects across sub-populations. We introduce a concept termed the facilitating score to account for both the confounding and interacting impacts of covariates on the treatment effect. Several approaches for estimating the facilitating score are discussed. In particular, we put forward a machine learning method, called causal inference tree (CIT), to provide a piecewise constant approximation of the facilitating score. With interpretable rules, CIT splits data in such a way that both the propensity and the treatment effect become more homogeneous within each resultant partition. Causal inference at different levels can be made on the basis of CIT. Together with an aggregated grouping procedure, CIT stratifies data into strata where causal effects can be conveniently assessed within each. Besides, a feasible way of predicting individual causal effects (ICE) is made available by aggregating ensemble CIT models. Both the stratified results and the estimated ICE provide an assessment of heterogeneity of causal effects and can be integrated for estimating the average causal effect (ACE). Mean square consistency of CIT is also established. We evaluate the performance of proposed methods with simulations and illustrate their use with the NSW data in Dehejia and Wahba (1999) where the objective is to assess the impact of a labor training program, the National SupportedWork (NSW) demonstration, on post-intervention earnings.

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Facilitating score and causal inference trees for large observational studies

This article proposes the stratified Wilson confidence interval for multiple binomial proportions and the stratified Newcombe confidence intervals for multiple binomial proportion differences. Both confidence intervals are presented in closed forms to facilitate easy calculations. The confidence levels of the proposed intervals are theoretically justified and demonstrated through extensive simulations. The coverage rates are found to be rather satisfactory. When the Wilson and Newcombe methods are used in unstratified analysis, the proposed methods may serve as the counterparts for stratified analysis. The proposed methods are applied to a vaccine trial to compute the stratified sero-conversion rate and rate difference over multiple clinical centers.

Xin Yan

Papers

Linear Regression Analysis: Theory and Computing

Interaction trees with censored survival data.

Facilitating score and causal inference trees for large observational studies

Stratified Wilson and Newcombe Confidence Intervals for Multiple Binomial Proportions

On Local Moments