Causal inference for extreme events has many potential applications in fields such as medicine, climate science and finance. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximations and uses a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators even in the setting of extremal quantiles, and we propose a consistent variance estimator to achieve valid statistical inference. In simulation studies we illustrate the advantages of our methodology over competitors, and we apply it to a real data set.
相關內容
Despite the recent progress in the field of causal inference, to date there is no agreed upon methodology to glean treatment effect estimation from observational data. The consequence on clinical practice is that, when lacking results from a randomized trial, medical personnel is left without guidance on what seems to be effective in a real-world scenario. This article proposes a pragmatic methodology to obtain preliminary but robust estimation of treatment effect from observational studies, to provide front-line clinicians with a degree of confidence in their treatment strategy. Our study design is applied to an open problem, the estimation of treatment effect of the proning maneuver on COVID-19 Intensive Care patients.
We propose a theoretical study of two realistic estimators of conditional distribution functions and conditional quantiles using random forests. The estimation process uses the bootstrap samples generated from the original dataset when constructing the forest. Bootstrap samples are reused to define the first estimator, while the second requires only the original sample, once the forest has been built. We prove that both proposed estimators of the conditional distribution functions are consistent uniformly a.s. To the best of our knowledge, it is the first proof of consistency including the bootstrap part. We also illustrate the estimation procedures on a numerical example.
We provide a comprehensive theory of conducting in-sample statistical inference about receiver operating characteristic (ROC) curves that are based on predicted values from a first stage model with estimated parameters (such as a logit regression). The term "in-sample" refers to the practice of using the same data for model estimation (training) and subsequent evaluation, i.e., the construction of the ROC curve. We show that in this case the first stage estimation error has a generally non-negligible impact on the asymptotic distribution of the ROC curve and develop the appropriate pointwise and functional limit theory. We propose methods for simulating the distribution of the limit process and show how to use the results in practice in comparing ROC curves.
We consider a randomized controlled trial between two groups. The objective is to identify a population with characteristics such that the test therapy is more effective than the control therapy. Such a population is called a subgroup. This identification can be made by estimating the treatment effect and identifying interactions between treatments and covariates. To date, many methods have been proposed to identify subgroups for a single outcome. There are also multiple outcomes, but they are difficult to interpret and cannot be applied to outcomes other than continuous values. In this paper, we propose a multivariate regression method that introduces latent variables to estimate the treatment effect on multiple outcomes simultaneously. The proposed method introduces latent variables and adds Lasso sparsity constraints to the estimated loadings to facilitate the interpretation of the relationship between outcomes and covariates. The framework of the generalized linear model makes it applicable to various types of outcomes. Interpretation of subgroups is made by visualizing treatment effects and latent variables. This allows us to identify subgroups with characteristics that make the test therapy more effective for multiple outcomes. Simulation and real data examples demonstrate the effectiveness of the proposed method.
Unbiased and consistent variance estimators generally do not exist for design-based treatment effect estimators because experimenters never observe more than one potential outcome for any unit. The problem is exacerbated by interference and complex experimental designs. In this paper, we consider variance estimation for linear treatment effect estimators under interference and arbitrary experimental designs. Experimenters must accept conservative estimators in this setting, but they can strive to minimize the conservativeness. We show that this task can be interpreted as an optimization problem in which one aims to find the lowest estimable upper bound of the true variance given one's risk preference and knowledge of the potential outcomes. We characterize the set of admissible bounds in the class of quadratic forms, and we demonstrate that the optimization problem is a convex program for many natural objectives. This allows experimenters to construct less conservative variance estimators, making inferences about treatment effects more informative. The resulting estimators are guaranteed to be conservative regardless of whether the background knowledge used to construct the bound is correct, but the estimators are less conservative if the knowledge is reasonably accurate.
The Ethereum ecosystem is maintained by a distributed global network of computers that currently require massive amounts of computational power. Previous work on estimating the energy use and emissions of the Ethereum network has relied on top-down economic analysis and rough estimates of hardware efficiency and emissions factors. In this work we provide a bottom-up analysis that works from hashrate to an energy usage estimate, and from mining locations to an emissions factor estimate, and combines these for an overall emissions estimate.
Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored at all the nodes of the network using only near-neighbor communications. In real-world scenarios, these communications must undergo quantization, which introduces distortion to the internode messages. In this thesis, a model for the evolution of the network state statistics at each iteration is developed under the assumptions of Gaussian data and additive quantization error. It is shown that minimization of the communication load in terms of aggregate source coding rate can be posed as a generalized geometric program, for which an equivalent convex optimization can efficiently solve for the global minimum. Optimization procedures are developed for rate-distortion-optimal vector quantization, uniform entropy-coded scalar quantization, and fixed-rate uniform quantization. Numerical results demonstrate the performance of these approaches. For small numbers of iterations, the fixed-rate optimizations are verified using exhaustive search. Comparison to the prior art suggests competitive performance under certain circumstances but strongly motivates the incorporation of more sophisticated coding strategies, such as differential, predictive, or Wyner-Ziv coding.
Increasing the efficiency of randomized trial estimates via linear adjustment for a prognostic score
Estimating causal effects from randomized experiments is central to clinical research. Reducing the statistical uncertainty in these analyses is an important objective for statisticians. Registries, prior trials, and health records constitute a growing compendium of historical data on patients under standard-of-care that may be exploitable to this end. However, most methods for historical borrowing achieve reductions in variance by sacrificing strict type-I error rate control. Here, we propose a use of historical data that exploits linear covariate adjustment to improve the efficiency of trial analyses without incurring bias. Specifically, we train a prognostic model on the historical data, then estimate the treatment effect using a linear regression while adjusting for the trial subjects' predicted outcomes (their prognostic scores). We prove that, under certain conditions, this prognostic covariate adjustment procedure attains the minimum variance possible among a large class of estimators. When those conditions are not met, prognostic covariate adjustment is still more efficient than raw covariate adjustment and the gain in efficiency is proportional to a measure of the predictive accuracy of the prognostic model above and beyond the linear relationship with the raw covariates. We demonstrate the approach using simulations and a reanalysis of an Alzheimer's Disease clinical trial and observe meaningful reductions in mean-squared error and the estimated variance. Lastly, we provide a simplified formula for asymptotic variance that enables power calculations that account for these gains. Sample size reductions between 10% and 30% are attainable when using prognostic models that explain a clinically realistic percentage of the outcome variance.
This paper investigates the estimation and inference of the average treatment effect (ATE) using deep neural networks (DNNs) in the potential outcomes framework. Under some regularity conditions, the observed response can be formulated as the response of a mean regression problem with both the confounding variables and the treatment indicator as the independent variables. Using such formulation, we investigate two methods for ATE estimation and inference based on the estimated mean regression function via DNN regression using a specific network architecture. We show that both DNN estimates of ATE are consistent with dimension-free consistency rates under some assumptions on the underlying true mean regression model. Our model assumptions accommodate the potentially complicated dependence structure of the observed response on the covariates, including latent factors and nonlinear interactions between the treatment indicator and confounding variables. We also establish the asymptotic normality of our estimators based on the idea of sample splitting, ensuring precise inference and uncertainty quantification. Simulation studies and real data application justify our theoretical findings and support our DNN estimation and inference methods.
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models that does not require knowledge of the form of the likelihood function or any derived quantities, but can be shown to be equivalent to maximizing likelihood under some conditions. Our result holds in the non-asymptotic parametric setting, where both the capacity of the model and the number of data examples are finite. We also demonstrate encouraging experimental results.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191