Observational cohort studies are increasingly being used for comparative effectiveness research to assess the safety of therapeutics. Recently, various doubly robust methods have been proposed for average treatment effect estimation by combining the treatment model and the outcome model via different vehicles, such as matching, weighting, and regression. The key advantage of doubly robust estimators is that they require either the treatment model or the outcome model to be correctly specified to obtain a consistent estimator of average treatment effects, and therefore lead to a more accurate and often more precise inference. However, little work has been done to understand how doubly robust estimators differ due to their unique strategies of using the treatment and outcome models and how machine learning techniques can be combined to boost their performance. Here we examine multiple popular doubly robust methods and compare their performance using different treatment and outcome modeling via extensive simulations and a real-world application. We found that incorporating machine learning with doubly robust estimators such as the targeted maximum likelihood estimator gives the best overall performance. Practical guidance on how to apply doubly robust estimators is provided.
相關內容
We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to optimize than others. In this paper, we focus on models where some parameters have a linear nature, which is common in machine learning. In one routine of the proposed algorithm, the linear parameters are updated by the recursive least squares (RLS) algorithm, which is equivalent to a stochastic Newton method; then, based on the updated linear parameters, the nonlinear parameters are updated by the stochastic gradient method (SGD). The proposed algorithm can be understood as a stochastic approximation version of block coordinate gradient descent approach in which one part of the parameters is updated by a second-order SGD method while the other part is updated by a first-order SGD. Global convergence of the proposed online algorithm for non-convex cases is established in terms of the expected violation of a first-order optimality condition. Numerical experiments have shown that the proposed method accelerates convergence significantly and produces more robust training and test performance when compared to other popular learning algorithms. Moreover, our algorithm is less sensitive to the learning rate and outperforms the recently proposed slimTrain algorithm. The code has been uploaded to GitHub for validation.
Users online tend to join polarized groups of like-minded peers around shared narratives, forming echo chambers. The echo chamber effect and opinion polarization may be driven by several factors including human biases in information consumption and personalized recommendations produced by feed algorithms. Until now, studies have mainly used opinion dynamic models to explore the mechanisms behind the emergence of polarization and echo chambers. The objective was to determine the key factors contributing to these phenomena and identify their interplay. However, the validation of model predictions with empirical data still displays two main drawbacks: lack of systematicity and qualitative analysis. In our work, we bridge this gap by providing a method to numerically compare the opinion distributions obtained from simulations with those measured on social media. To validate this procedure, we develop an opinion dynamic model that takes into account the interplay between human and algorithmic factors. We subject our model to empirical testing with data from diverse social media platforms and benchmark it against two state-of-the-art models. To further enhance our understanding of social media platforms, we provide a synthetic description of their characteristics in terms of the model's parameter space. This representation has the potential to facilitate the refinement of feed algorithms, thus mitigating the detrimental effects of extreme polarization on online discourse.
Recent work has focused on the potential and pitfalls of causal identification in observational studies with multiple simultaneous treatments. Building on previous work, we show that even if the conditional distribution of unmeasured confounders given treatments were known exactly, the causal effects would not in general be identifiable, although they may be partially identified. Given these results, we propose a sensitivity analysis method for characterizing the effects of potential unmeasured confounding, tailored to the multiple treatment setting, that can be used to characterize a range of causal effects that are compatible with the observed data. Our method is based on a copula factorization of the joint distribution of outcomes, treatments, and confounders, and can be layered on top of arbitrary observed data models. We propose a practical implementation of this approach making use of the Gaussian copula, and establish conditions under which causal effects can be bounded. We also describe approaches for reasoning about effects, including calibrating sensitivity parameters, quantifying robustness of effect estimates, and selecting models that are most consistent with prior hypotheses.
We construct a reliable estimation of evolutionary parameters within the Wright-Fisher model, which describes changes in allele frequencies due to selection and genetic drift, from time-series data. Such data exists for biological populations, for example via artificial evolution experiments, and for the cultural evolution of behavior, such as linguistic corpora that document historical usage of different words with similar meanings. Our method of analysis builds on a Beta-with-Spikes approximation to the distribution of allele frequencies predicted by the Wright-Fisher model. We introduce a self-contained scheme for estimating the parameters in the approximation, and demonstrate its robustness with synthetic data, especially in the strong-selection and near-extinction regimes where previous approaches fail. We further apply to allele frequency data for baker's yeast (Saccharomyces cerevisiae), finding a significant signal of selection in cases where independent evidence supports such a conclusion. We further demonstrate the possibility of detecting time-points at which evolutionary parameters change in the context of a historical spelling reform in the Spanish language.
If $X,Y,Z$ denote sets of random variables, two different data sources may contain samples from $P_{X,Y}$ and $P_{Y,Z}$, respectively. We argue that causal discovery can help inferring properties of the `unobserved joint distributions' $P_{X,Y,Z}$ or $P_{X,Z}$. The properties may be conditional independences (as in `integrative causal inference') or also quantitative statements about dependences. More generally, we define a learning scenario where the input is a subset of variables and the label is some statistical property of that subset. Sets of jointly observed variables define the training points, while unobserved sets are possible test points. To solve this learning task, we infer, as an intermediate step, a causal model from the observations that then entails properties of unobserved sets. Accordingly, we can define the VC dimension of a class of causal models and derive generalization bounds for the predictions. Here, causal discovery becomes more modest and better accessible to empirical tests than usual: rather than trying to find a causal hypothesis that is `true' a causal hypothesis is {\it useful} whenever it correctly predicts statistical properties of unobserved joint distributions. This way, a sparse causal graph that omits weak influences may be more useful than a dense one (despite being less accurate) because it is able to reconstruct the full joint distribution from marginal distributions of smaller subsets. Within such a `pragmatic' application of causal discovery, some popular heuristic approaches become justified in retrospect. It is, for instance, allowed to infer DAGs from partial correlations instead of conditional independences if the DAGs are only used to predict partial correlations.
In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a Bayesian approach, which is nonparametric for the outcome distribution and can be combined with an informative prior on the sensitivity parameter. We give insight in the posterior and provide theoretical guarantees in the form of Bernstein-von Mises theorems for estimating the mean outcome. We study different parametrisations of the model involving Dirichlet process priors on the distribution of the outcome and on the distribution of the outcome conditional on the subject being treated. We show that these parametrisations incorporate a prior on the sensitivity parameter in different ways and discuss the relative merits. We also present a simulation study, showing the performance of the methods in finite sample scenarios.
In many fields of biomedical sciences, it is common that random variables are measured repeatedly across different subjects. In such a repeated measurement setting, dependence structures among random variables that are between subjects and within a subject may differ and should be estimated differently. Ignoring this fact may lead to questionable or even erroneous scientific conclusions. In this paper, we study the problem of sparse and positive-definite estimation of between-subject and within-subject covariance matrices for high-dimensional repeated measurements. Our estimators are defined as solutions to convex optimization problems that can be solved efficiently. We establish estimation error rates for our proposed estimators of the two target matrices, and demonstrate their favorable performance through theoretical analysis and comprehensive simulation studies. We further apply our methods to recover two covariance graphs of clinical variables from hemodialysis patients.
1. Citizen and community-science (CS) datasets have great potential for estimating interannual patterns of population change given the large volumes of data collected globally every year. Yet, the flexible protocols that enable many CS projects to collect large volumes of data typically lack the structure necessary to keep consistent sampling across years. This leads to interannual confounding, as changes to the observation process over time are confounded with changes in species population sizes. 2. Here we describe a novel modeling approach designed to estimate species population trends while controlling for the interannual confounding common in citizen science data. The approach is based on Double Machine Learning, a statistical framework that uses machine learning methods to estimate population change and the propensity scores used to adjust for confounding discovered in the data. Additionally, we develop a simulation method to identify and adjust for residual confounding missed by the propensity scores. Using this new method, we can produce spatially detailed trend estimates from citizen science data. 3. To illustrate the approach, we estimated species trends using data from the CS project eBird. We used a simulation study to assess the ability of the method to estimate spatially varying trends in the face of real-world confounding. Results showed that the trend estimates distinguished between spatially constant and spatially varying trends at a 27km resolution. There were low error rates on the estimated direction of population change (increasing/decreasing) and high correlations on the estimated magnitude. 4. The ability to estimate spatially explicit trends while accounting for confounding in citizen science data has the potential to fill important information gaps, helping to estimate population trends for species, regions, or seasons without rigorous monitoring data.
We study a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. Our robust Bayesian approach involves two adjustment steps: first, we make a correction for prior distributions of the conditional mean function; second, we introduce a recentering term on the posterior distribution of the resulting ATE. We prove asymptotic equivalence of our Bayesian estimator and double robust frequentist estimators by establishing a new semiparametric Bernstein-von Mises theorem under double robustness; i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian point estimator internalizes the bias correction as the frequentist-type doubly robust estimator, and the Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, we find that this robust Bayesian procedure leads to significant bias reduction of point estimation and accurate coverage of confidence intervals, especially when the dimensionality of covariates is large relative to the sample size and the underlying functions become complex. We illustrate our method in an application to the National Supported Work Demonstration.
Deep neural networks (DNNs) have become a proven and indispensable machine learning tool. As a black-box model, it remains difficult to diagnose what aspects of the model's input drive the decisions of a DNN. In countless real-world domains, from legislation and law enforcement to healthcare, such diagnosis is essential to ensure that DNN decisions are driven by aspects appropriate in the context of its use. The development of methods and studies enabling the explanation of a DNN's decisions has thus blossomed into an active, broad area of research. A practitioner wanting to study explainable deep learning may be intimidated by the plethora of orthogonal directions the field has taken. This complexity is further exacerbated by competing definitions of what it means ``to explain'' the actions of a DNN and to evaluate an approach's ``ability to explain''. This article offers a field guide to explore the space of explainable deep learning aimed at those uninitiated in the field. The field guide: i) Introduces three simple dimensions defining the space of foundational methods that contribute to explainable deep learning, ii) discusses the evaluations for model explanations, iii) places explainability in the context of other related deep learning research areas, and iv) finally elaborates on user-oriented explanation designing and potential future directions on explainable deep learning. We hope the guide is used as an easy-to-digest starting point for those just embarking on research in this field.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191