In empirical studies with time-to-event outcomes, investigators often leverage observational data to conduct causal inference on the effect of exposure when randomized controlled trial data is unavailable. Model misspecification and lack of overlap are common issues in observational studies, and they often lead to inconsistent and inefficient estimators of the average treatment effect. Estimators targeting overlap weighted effects have been proposed to address the challenge of poor overlap, and methods enabling flexible machine learning for nuisance models address model misspecification. However, the approaches that allow machine learning for nuisance models have not been extended to the setting of weighted average treatment effects for time-to-event outcomes when there is poor overlap. In this work, we propose a class of one-step cross-fitted double/debiased machine learning estimators for the weighted cumulative causal effect as a function of restriction time. We prove that the proposed estimators are consistent, asymptotically linear, and reach semiparametric efficiency bounds under regularity conditions. Our simulations show that the proposed estimators using nonparametric machine learning nuisance models perform as well as established methods that require correctly-specified parametric nuisance models, illustrating that our estimators mitigate the need for oracle parametric nuisance models. We apply the proposed methods to real-world observational data from a UK primary care database to compare the effects of anti-diabetic drugs on cancer clinical outcomes.
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Understanding individual treatment effects in extreme regimes is important for characterizing risks associated with different interventions. This is hindered by the fact that extreme regime data may be hard to collect, as it is scarcely observed in practice. In addressing this issue, we propose a new framework for estimating the individual treatment effect in extreme regimes (ITE$_2$). Specifically, we quantify this effect by the changes in the tail decay rates of potential outcomes in the presence or absence of the treatment. Subsequently, we establish conditions under which ITE$_2$ may be calculated and develop algorithms for its computation. We demonstrate the efficacy of our proposed method on various synthetic and semi-synthetic datasets.
Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is challenging. Previous studies in the literature have tackled this challenge by employing spatial partitioning techniques to estimate the parameters that vary spatially in the covariance function. The selection of partitions is an important consideration, but it is often subjective and lacks a data-driven approach. To address this issue, in this study, we utilize the power of Convolutional Neural Networks (ConvNets) to derive subregions from the nonstationary data. We employ a selection mechanism to identify subregions that exhibit similar behavior to stationary fields. In order to distinguish between stationary and nonstationary random fields, we conducted training on ConvNet using various simulated data. These simulations are generated from Gaussian processes with Mat\'ern covariance models under a wide range of parameter settings, ensuring adequate representation of both stationary and nonstationary spatial data. We assess the performance of the proposed method with synthetic and real datasets at a large scale. The results revealed enhanced accuracy in parameter estimations when relying on ConvNet-based partition compared to traditional user-defined approaches.
Motivated by the Acute Respiratory Distress Syndrome Network (ARDSNetwork) ARDS respiratory management (ARMA) trial, we developed a flexible Bayesian machine learning approach to estimate the average causal effect and heterogeneous causal effects among the always-survivors stratum when clinical outcomes are subject to truncation. We adopted Bayesian additive regression trees (BART) to flexibly specify separate models for the potential outcomes and latent strata membership. In the analysis of the ARMA trial, we found that the low tidal volume treatment had an overall benefit for participants sustaining acute lung injuries on the outcome of time to returning home, but substantial heterogeneity in treatment effects among the always-survivors, driven most strongly by sex and the alveolar-arterial oxygen gradient at baseline (a physiologic measure of lung function and source of hypoxemia). These findings illustrate how the proposed methodology could guide the prognostic enrichment of future trials in the field. We also demonstrated through a simulation study that our proposed Bayesian machine learning approach outperforms other parametric methods in reducing the estimation bias in both the average causal effect and heterogeneous causal effects for always-survivors.
Dynamic treatment regimes (DTRs) are used in medicine to tailor sequential treatment decisions to patients by considering patient heterogeneity. Common methods for learning optimal DTRs, however, have shortcomings: they are typically based on outcome prediction and not treatment effect estimation, or they use linear models that are restrictive for patient data from modern electronic health records. To address these shortcomings, we develop two novel methods for learning optimal DTRs that effectively handle complex patient data. We call our methods DTR-CT and DTR-CF. Our methods are based on a data-driven estimation of heterogeneous treatment effects using causal tree methods, specifically causal trees and causal forests, that learn non-linear relationships, control for time-varying confounding, are doubly robust, and explainable. To the best of our knowledge, our paper is the first that adapts causal tree methods for learning optimal DTRs. We evaluate our proposed methods using synthetic data and then apply them to real-world data from intensive care units. Our methods outperform state-of-the-art baselines in terms of cumulative regret and percentage of optimal decisions by a considerable margin. Our work improves treatment recommendations from electronic health record and is thus of direct relevance for personalized medicine.
In extreme value theory and other related risk analysis fields, probability weighted moments (PWM) have been frequently used to estimate the parameters of classical extreme value distributions. This method-of-moment technique can be applied when second moments are finite, a reasonable assumption in many environmental domains like climatological and hydrological studies. Three advantages of PWM estimators can be put forward: their simple interpretations, their rapid numerical implementation and their close connection to the well-studied class of U-statistics. Concerning the later, this connection leads to precise asymptotic properties, but non asymptotic bounds have been lacking when off-the-shelf techniques (Chernoff method) cannot be applied, as exponential moment assumptions become unrealistic in many extreme value settings. In addition, large values analysis is not immune to the undesirable effect of outliers, for example, defective readings in satellite measurements or possible anomalies in climate model runs. Recently, the treatment of outliers has sparked some interest in extreme value theory, but results about finite sample bounds in a robust extreme value theory context are yet to be found, in particular for PWMs or tail index estimators. In this work, we propose a new class of robust PWM estimators, inspired by the median-of-means framework of Devroye et al. (2016). This class of robust estimators is shown to satisfy a sub-Gaussian inequality when the assumption of finite second moments holds. Such non asymptotic bounds are also derived under the general contamination model. Our main proposition confirms theoretically a trade-off between efficiency and robustness. Our simulation study indicates that, while classical estimators of PWMs can be highly sensitive to outliers.
We present new results on average causal effects in settings with unmeasured exposure-outcome confounding. Our results are motivated by a class of estimands, e.g., frequently of interest in medicine and public health, that are currently not targeted by standard approaches for average causal effects. We recognize these estimands as queries about the average causal effect of an intervening variable. We anchor our introduction of these estimands in an investigation of the role of chronic pain and opioid prescription patterns in the opioid epidemic, and illustrate how conventional approaches will lead unreplicable estimates with ambiguous policy implications. We argue that our altenative effects are replicable and have clear policy implications, and furthermore are non-parametrically identified by the classical frontdoor formula. As an independent contribution, we derive a new semiparametric efficient estimator of the frontdoor formula with a uniform sample boundedness guarantee. This property is unique among previously-described estimators in its class, and we demonstrate superior performance in finite-sample settings. Theoretical results are applied with data from the National Health and Nutrition Examination Survey.
Estimating heterogeneous treatment effects is crucial for informing personalized treatment strategies and policies. While multiple studies can improve the accuracy and generalizability of results, leveraging them for estimation is statistically challenging. Existing approaches often assume identical heterogeneous treatment effects across studies, but this may be violated due to various sources of between-study heterogeneity, including differences in study design, confounders, and sample characteristics. To this end, we propose a unifying framework for multi-study heterogeneous treatment effect estimation that is robust to between-study heterogeneity in the nuisance functions and treatment effects. Our approach, the multi-study R-learner, extends the R-learner to obtain principled statistical estimation with modern machine learning (ML) in the multi-study setting. The multi-study R-learner is easy to implement and flexible in its ability to incorporate ML for estimating heterogeneous treatment effects, nuisance functions, and membership probabilities, which borrow strength across heterogeneous studies. It achieves robustness in confounding adjustment through its loss function and can leverage both randomized controlled trials and observational studies. We provide asymptotic guarantees for the proposed method in the case of series estimation and illustrate using real cancer data that it has the lowest estimation error compared to existing approaches in the presence of between-study heterogeneity.
A very classical problem in statistics is to test the stochastic superiority of one distribution to another. However, many existing approaches are developed for independent samples and, moreover, do not take censored data into account. We develop a new estimand-driven method to compare the effectiveness of two treatments in the context of right-censored survival data with matched pairs. With the help of competing risks techniques, the so-called relative treatment effect is estimated. It quantifies the probability that the individual undergoing the first treatment survives the matched individual undergoing the second treatment. Hypothesis tests and confidence intervals are based on a studentized version of the estimator, where resampling-based inference is established by means of a randomization method. In a simulation study, we found that the developed test exhibits good power, when compared to competitors which are actually testing the simpler null hypothesis of the equality of both marginal survival functions. Finally, we apply the methodology to a well-known benchmark data set from a trial with patients suffering from with diabetic retinopathy.
The problem of generalization and transportation of treatment effect estimates from a study sample to a target population is central to empirical research and statistical methodology. In both randomized experiments and observational studies, weighting methods are often used with this objective. Traditional methods construct the weights by separately modeling the treatment assignment and study selection probabilities and then multiplying functions (e.g., inverses) of their estimates. In this work, we provide a justification and an implementation for weighting in a single step. We show a formal connection between this one-step method and inverse probability and inverse odds weighting. We demonstrate that the resulting estimator for the target average treatment effect is consistent, asymptotically Normal, multiply robust, and semiparametrically efficient. We evaluate the performance of the one-step estimator in a simulation study. We illustrate its use in a case study on the effects of physician racial diversity on preventive healthcare utilization among Black men in California. We provide R code implementing the methodology.
Pre-trained deep neural network language models such as ELMo, GPT, BERT and XLNet have recently achieved state-of-the-art performance on a variety of language understanding tasks. However, their size makes them impractical for a number of scenarios, especially on mobile and edge devices. In particular, the input word embedding matrix accounts for a significant proportion of the model's memory footprint, due to the large input vocabulary and embedding dimensions. Knowledge distillation techniques have had success at compressing large neural network models, but they are ineffective at yielding student models with vocabularies different from the original teacher models. We introduce a novel knowledge distillation technique for training a student model with a significantly smaller vocabulary as well as lower embedding and hidden state dimensions. Specifically, we employ a dual-training mechanism that trains the teacher and student models simultaneously to obtain optimal word embeddings for the student vocabulary. We combine this approach with learning shared projection matrices that transfer layer-wise knowledge from the teacher model to the student model. Our method is able to compress the BERT_BASE model by more than 60x, with only a minor drop in downstream task metrics, resulting in a language model with a footprint of under 7MB. Experimental results also demonstrate higher compression efficiency and accuracy when compared with other state-of-the-art compression techniques.
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