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A Novel Causal Mediation Analysis Approach for Zero-Inflated Mediators

针对零膨胀中介变量的新型因果中介分析方法

Mediation analyses play important roles in making causal inference in biomedical research to examine causal pathways that may be mediated by one or more intermediate variables (i.e., mediators). Although mediation frameworks have been well established such as counterfactual-outcomes (i.e., potential-outcomes) models and traditional linear mediation models, little effort has been devoted to dealing with mediators with zero-inflated structures due to challenges associated with…

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Estimating individual treatment effects under unobserved confounding using binary instruments

利用二元工具变量在未观测混杂下估计个体处理效应

Estimating conditional average treatment effects (CATEs) from observational data is relevant in many fields such as personalized medicine. However, in practice, the treatment assignment is usually confounded by unobserved variables and thus introduces bias. A remedy to remove the bias is the use of instrumental variables (IVs). Such settings are widespread in medicine (e.g., trials where the treatment assignment is used as binary IV). In this paper, we propose a novel,…

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Kernel regression analysis of tie-breaker designs

混合随机化与断点设计的核回归分析

Tie-breaker experimental designs are hybrids of Randomized Controlled Trials (RCTs) and Regression Discontinuity Designs (RDDs) in which subjects with moderate scores are placed in an RCT while subjects with extreme scores are deterministically assigned to the treatment or control group. In settings where it is unfair or uneconomical to deny the treatment to the more deserving recipients, the tie-breaker design (TBD) trades off the practical advantages of the RDD with the…

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On the relation between extremal dependence and concomitants

极端依赖与伴随次序统计量的关系

The study of concomitants has recently met a renewed interest due to its applications in selection procedures. For instance, concomitants are used in ranked-set sampling, to achieve efficiency and reduce cost when compared to the simple random sampling. In parallel, the search for new methods to provide a rich description of extremal dependence among multiple time series has rapidly grown, due also to its numerous practical implications and the lack of suitable models to…

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Causal Inference under Data Restrictions

数据受限条件下的因果推断

This dissertation focuses on modern causal inference under uncertainty and data restrictions, with applications to neoadjuvant clinical trials, distributed data networks, and robust individualized decision making. In the first project, we propose a method under the principal stratification framework to identify and estimate the average treatment effects on a binary outcome, conditional on the counterfactual status of a post-treatment intermediate response. Under mild…

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Covariate-Adjusted Log-Rank Test: Guaranteed Efficiency Gain and Universal Applicability

协变量调整的对数秩检验:效率增益与广泛适用性

Nonparametric covariate adjustment is considered for log-rank type tests of treatment effect with right-censored time-to-event data from clinical trials applying covariate-adaptive randomization. Our proposed covariate-adjusted log-rank test has a simple explicit formula and a guaranteed efficiency gain over the unadjusted test. We also show that our proposed test achieves universal applicability in the sense that the same formula of test can be universally applied to simple…

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On regression-adjusted imputation estimators of the average treatment effect

平均处理效应的回归调整插补估计量

Imputing missing potential outcomes using an estimated regression function is a natural idea for estimating causal effects. In the literature, estimators that combine imputation and regression adjustments are believed to be comparable to augmented inverse probability weighting. Accordingly, people for a long time conjectured that such estimators, while avoiding directly constructing the weights, are also doubly robust (Imbens, 2004; Stuart, 2010). Generalizing an earlier…

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Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap

稳定概率加权:有限重叠下多值处理异质性因果效应的估计与推断

In this paper, I try to tame "Basu's elephants" (data with extreme selection on observables). I propose new practical large-sample and finite-sample methods for estimating and inferring heterogeneous causal effects (under unconfoundedness) in the empirically relevant context of limited overlap. I develop a general principle called "Stable Probability Weighting" (SPW) that can be used as an alternative to the widely used Inverse Probability Weighting (IPW) technique, which…

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Optimal Transport for Counterfactual Estimation: A Method for Causal Inference

用于反事实估计的最优传输方法

Many problems ask a question that can be formulated as a causal question: "what would have happened if...?" For example, "would the person have had surgery if he or she had been Black?" To address this kind of questions, calculating an average treatment effect (ATE) is often uninformative, because one would like to know how much impact a variable (such as skin color) has on a specific individual, characterized by certain covariates. Trying to calculate a conditional ATE…

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Principal Stratification with Time-to-Event Outcomes

事件时间结局的主分层分析

Post-randomization events, also known as intercurrent events, such as treatment noncompliance and censoring due to a terminal event, are common in clinical trials. Principal stratification is a framework for causal inference in the presence of intercurrent events. Despite the extensive existing literature, there lacks generally applicable and accessible methods for principal stratification analysis with time-to-event outcomes. In this paper, we specify two causal estimands…

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Non-parametric identifiability and sensitivity analysis of synthetic control models

合成控制模型的非参数可识别性与敏感性分析

Quantifying cause and effect relationships is an important problem in many domains. The gold standard solution is to conduct a randomised controlled trial. However, in many situations such trials cannot be performed. In the absence of such trials, many methods have been devised to quantify the causal impact of an intervention from observational data given certain assumptions. One widely used method are synthetic control models. While identifiability of the causal estimand in…

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Robust Estimating Method for Propensity Score Models and its Application to Some Causal Estimands: A review and proposal

倾向得分模型的稳健估计及因果目标量应用:综述与新方案

In observational study, the propensity score has the central role to estimate causal effects. Since the propensity score is usually unknown, estimating by appropriate procedures is an indispensable step. A point to note that a causal effect estimator might have some bias if a propensity score model was misspecified; valid model construction is important. To overcome the problem, a variety of interesting methods has been proposed. In this paper, we review four methods: using…

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Robust and efficient Breusch-Pagan test-statistic: an application of the beta-score Lagrange multipliers test for non-identically distributed individuals

稳健且兼顾效率的 Breusch–Pagan 检验:β 得分 LM 方法

In Econometrics, the Breusch-Pagan test-statistic has become an iconic application of the Lagrange multipliers (LM) test. We shall introduce beta-score LM tests for heteroscedasticity in linear regression models, which trades-off the degree of robustness and efficiency is through a tuning parameter beta>=0, being beta =0 the classical Breusch-Pagan test-statistic, the most efficient one under absence of outliers. A very elegant expression is obtained, with an appealing least…

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Score Equivalence for Staged Trees

阶段树模型的评分等价性

Staged trees are a recently-developed, powerful family of probabilistic graphical models. An equivalence class of staged trees has now been characterised, and two fundamental statistical operators have been defined to traverse the equivalence class of a given staged tree. Here, two staged trees are said to be statistically equivalent when they represent the same set of distributions. Probabilistic graphical models such as staged trees are increasingly being used for causal…

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A resampling approach for causal inference on novel two-point time-series with application to identify risk factors for type-2 diabetes and cardiovascular disease

无对照组两时点数据的重抽样因果推断及健康风险应用

Two-point time-series data, characterized by baseline and follow-up observations, are frequently encountered in health research. We study a novel two-point time series structure without a control group, which is driven by an observational routine clinical dataset collected to monitor key risk markers of type-$2$ diabetes (T2D) and cardiovascular disease (CVD). We propose a resampling approach called 'I-Rand' for independently sampling one of the two time points for each…

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Universal Prediction Band via Semi-Definite Programming

利用半正定规划构造通用预测带

We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the now-standard conformal prediction for uncertainty quantification, with novel theoretical insights and computational advantages. The data-adaptive prediction band is universally applicable with minimal distributional assumptions, has strong…

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Statistical inference for the logarithmic spatial heteroskedasticity model with exogenous variables

含外生变量的对数空间异方差模型及统计推断

The spatial dependence in mean has been well studied by plenty of models in a large strand of literature, however, the investigation of spatial dependence in variance is lagging significantly behind. The existing models for the spatial dependence in variance are scarce, with neither probabilistic structure nor statistical inference procedure being explored. To circumvent this deficiency, this paper proposes a new generalized logarithmic spatial heteroscedasticity model with…

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Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models

加性单指标协整时间序列模型的稳健 M 估计

Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing the resultant estimators rests on the nonsmoothness of these losses. Generalized functions have advantages over ordinary functions in several aspects, especially generalized functions possess derivatives of any order. Generalized…

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Testing for Coefficient Randomness in Local-to-Unity Autoregressions

局部单位根自回归中的系数随机性检验

In this study, we propose a test for the coefficient randomness in autoregressive models where the autoregressive coefficient is local to unity, which is empirically relevant given the results of earlier studies. Under this specification, we theoretically analyze the effect of the correlation between the random coefficient and disturbance on tests' properties, which remains largely unexplored in the literature. Our analysis reveals that the correlation crucially affects the…

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Deep Counterfactual Estimation with Categorical Background Variables

类别型背景变量下的深度反事实估计

Referred to as the third rung of the causal inference ladder, counterfactual queries typically ask the "What if ?" question retrospectively. The standard approach to estimate counterfactuals resides in using a structural equation model that accurately reflects the underlying data generating process. However, such models are seldom available in practice and one usually wishes to infer them from observational data alone. Unfortunately, the correct structural equation model is…

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Doubly-Robust Inference for Conditional Average Treatment Effects with High-Dimensional Controls

高维控制变量下条件平均处理效应的双重稳健推断

Plausible identification of conditional average treatment effects (CATEs) may rely on controlling for a large number of variables to account for confounding factors. In these high-dimensional settings, estimation of the CATE requires estimating first-stage models whose consistency relies on correctly specifying their parametric forms. While doubly-robust estimators of the CATE exist, inference procedures based on the second stage CATE estimator are not doubly-robust. Using…

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Causal mediation analysis: From simple to more robust strategies for estimation of marginal natural (in)direct effects

因果中介分析:边际自然直接与间接效应的稳健估计策略

This paper aims to provide practitioners of causal mediation analysis with a better understanding of estimation options. We take as inputs two familiar strategies (weighting and model-based prediction) and a simple way of combining them (weighted models), and show how a range of estimators can be generated, with different modeling requirements and robustness properties. The primary goal is to help build intuitive appreciation for robust estimation that is conducive to sound…

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Resampling techniques for a class of smooth, possibly data-adaptive empirical copulas

平滑且可数据自适应的经验 Copula 重抽样方法

We investigate the validity of two resampling techniques when carrying out inference on the underlying unknown copula using a recently proposed class of smooth, possibly data-adaptive nonparametric estimators that contains empirical Bernstein copulas (and thus the empirical beta copula). Following \cite{KirSegTsu21}, the first resampling technique is based on drawing samples from the smooth estimator and can only can be used in the case of independent observations. The…

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A Framework for Generalization and Transportation of Causal Estimates Under Covariate Shift

协变量偏移下因果效应推广与迁移的分析框架

Randomized experiments are an excellent tool for estimating internally valid causal effects with the sample at hand, but their external validity is frequently debated. While classical results on the estimation of Population Average Treatment Effects (PATE) implicitly assume random selection into experiments, this is typically far from true in many medical, social-scientific, and industry experiments. When the experimental sample is different from the target sample along…

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