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Register a new userThe Promises of Parallel Outcomes
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Ying Zhou
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Unobserved confounding presents a major threat to the validity of causal inference from observational studies. In this paper, we introduce a novel framework that leverages the information in multiple parallel outcomes for identification and estimation of causal effects. Under a conditional independence structure among multiple parallel outcomes, we achieve nonparametric identification with at least three parallel outcomes. We further show that under a set of linear structural equation models, causal inference is possible with two parallel outcomes. We develop accompanying estimating procedures and evaluate their finite sample performance through simulation studies and a data application studying the causal effect of the tau protein level on various types of behavioral deficits.
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Multi-task learning is increasingly used to investigate the association structure between multiple responses and a single set of predictor variables in many applications. In the era of big data, the coexistence of incomplete outcomes, large number of responses, and high dimensionality in predictors poses unprecedented challenges in estimation, prediction, and computation. In this paper, we propose a scalable and computationally efficient procedure, called PEER, for large-scale multi-response regression with incomplete outcomes, where both the numbers of responses and predictors can be high-dimensional. Motivated by sparse factor regression, we convert the multi-response regression into a set of univariate-response regressions, which can be efficiently implemented in parallel. Under some mild regularity conditions, we show that PEER enjoys nice sampling properties including consistency in estimation, prediction, and variable selection. Extensive simulation studies show that our proposal compares favorably with several existing methods in estimation accuracy, variable selection, and computation efficiency.
The goal of a well-controlled study is to remove unwanted variation when estimating the causal effect of the intervention of interest. Experiments conducted in the basic sciences frequently achieve this goal using experimental controls, such as negative and positive controls, which are measurements designed to detect systematic sources of unwanted variation. Here, we introduce clear, mathematically precise definitions of experimental controls using potential outcomes. Our definitions provide a unifying statistical framework for fundamental concepts of experimental design from the biological and other basic sciences. These controls are defined in terms of whether assumptions are being made about a specific treatment level, outcome, or contrast between outcomes. We discuss experimental controls as tools for researchers to wield in designing experiments and detecting potential design flaws, including using controls to diagnose unintended factors that influence the outcome of interest, assess measurement error, and identify important subpopulations. We believe that experimental controls are powerful tools for reproducible research that are possibly underutilized by statisticians, epidemiologists, and social science researchers.
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretis
Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the unit interval, however, classical random forest approaches may severely suffer as they do not account for the heteroscedasticity in the data. A random forest approach is proposed for relating beta distributed outcomes to explanatory variables. The approach explicitly makes use of the likelihood function of the beta distribution for the selection of splits during the tree-building procedure. In each iteration of the tree-building algorithm one chooses the combination of explanatory variable and splitting rule that maximizes the log-likelihood function of the beta distribution with the parameter estimates derived from the nodes of the currently built tree. Several simulation studies demonstrate the properties of the method and compare its performance to classical random forest approaches as well as to parametric regression models.
Clinical prediction models (CPMs) are used to predict clinically relevant outcomes or events. Typically, prognostic CPMs are derived to predict the risk of a single future outcome. However, with rising emphasis on the prediction of multi-morbidity, there is growing need for CPMs to simultaneously predict risks for each of multiple future outcomes. A common approach to multi-outcome risk prediction is to derive a CPM for each outcome separately, then multiply the predicted risks. This approach is only valid if the outcomes are conditionally independent given the covariates, and it fails to exploit the potential relationships between the outcomes. This paper outlines several approaches that could be used to develop prognostic CPMs for multiple outcomes. We consider four methods, ranging in complexity and assumed conditional independence assumptions: namely, probabilistic classifier chain, multinomial logistic regression, multivariate logistic regression, and a Bayesian probit model. These are compared with methods that rely on conditional independence: separate univariate CPMs and stacked regression. Employing a simulation study and real-world example via the MIMIC-III database, we illustrate that CPMs for joint risk prediction of multiple outcomes should only be derived using methods that model the residual correlation between outcomes. In such a situation, our results suggest that probabilistic classification chains, multinomial logistic regression or the Bayesian probit model are all appropriate choices. We call into question the development of CPMs for each outcome in isolation when multiple correlated or structurally related outcomes are of interest and recommend more holistic risk prediction.
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