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Principled analysis of crossover designs: Causal effects, efficient estimation and robust inference

交叉设计的因果效应、有效估计与稳健推断

Crossover designs randomly assign each unit to receive a sequence of treatments. By comparing outcomes within the same unit, these designs can effectively eliminate between-unit variation and facilitate the identification of both instantaneous effects of current treatments and carryover effects from past treatments. They are widely used in traditional biomedical studies and are increasingly adopted in modern digital platforms. However, standard analyses of crossover designs…

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Quantifying individual risk for binary outcomes

二元结局下的个体风险量化

Abstract Understanding treatment effect heterogeneity is crucial for reliable decision-making in treatment evaluation and selection. The conditional average treatment effect (CATE) is widely used to capture treatment effect heterogeneity induced by observed covariates and to design individualized treatment policies. However, it is an average metric within subpopulations, which prevents it from revealing individual risk, potentially leading to misleading results. This article…

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Factorial Difference-in-Differences

析因双重差分

We formulate factorial difference-in-differences (FDID), a research design that extends canonical difference-in-differences (DID) to settings in which an event affects all units. In many panel data applications, researchers exploit cross-sectional variation in a baseline factor alongside temporal variation in the event, but the corresponding estimand is often implicit and the justification for applying the DID estimator remains unclear. We frame FDID as a factorial design…

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Identification and Multiply Robust Estimation of Causal Effects via Instrumental Variables from An Auxiliary Population

借助辅助总体工具变量识别与多重稳健估计因果效应

Estimating causal effects in a target population with unmeasured confounders is challenging, especially when instrumental variables (IVs) are unavailable. However, IVs from auxiliary populations with similar problems can help infer causal effects in the target population. While the homogeneous conditional average treatment effect assumption has been widely used for effect transportability, it has not been explored in IV-based data fusion. We include it as a basic approach,…

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Balancing Weights for Causal Inference in Observational Factorial Studies

观察性析因研究中用于因果推断的平衡权重

Many scientific questions in biomedical, environmental, and psychological research involve understanding the effects of multiple factors on outcomes. While factorial experiments are ideal for this purpose, randomized controlled treatment assignment is generally infeasible in many empirical studies. Therefore, investigators must rely on observational data, where drawing reliable causal inferences for multiple factors remains challenging. As the number of treatment…

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Principal stratification with continuous post-treatment variables: nonparametric identification and semiparametric estimation

连续处理后变量的主层分析:非参数识别与半参数估计

Abstract Post-treatment variables often complicate causal inference. They appear in many scientific problems, including non-compliance, truncation by death, mediation, and surrogate endpoint evaluation. Principal stratification is a strategy to address these challenges by adjusting for the potential values of the post-treatment variables, defined as the principal strata. It allows for characterizing treatment effect heterogeneity across principal strata and unveiling the…

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Berry–Esseen bounds for design-based causal inference with possibly diverging treatment levels and varying group sizes

处理水平可能增长且组规模不等时设计型因果推断的 Berry–Esseen 界

Neyman (1923/1990) introduced the randomization model, which contains the notation of potential outcomes to define causal effects and a framework for large-sample inference based on the design of the experiment. However, the existing theory for this framework is far from complete, especially when the number of treatment levels diverges and the treatment group sizes vary. We provide a unified discussion of statistical inference under the randomization model with general…

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Causal inference in network experiments: Regression-based analysis and design-based properties

网络实验中的因果推断:回归分析与基于设计的性质

Network experiments are powerful tools for studying spillover effects, which avoid endogeneity by randomly assigning treatments to units over networks. However, it is non-trivial to analyze network experiments properly without imposing strong modeling assumptions. We show that regression-based point estimators and standard errors can have strong theoretical guarantees if the regression functions and robust standard errors are carefully specified to accommodate the…

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Identifying and bounding the probability of necessity for causes of effects with ordinal outcomes

有序结果中因果必要性概率的识别与界限

Summary Although the existing causal inference literature focuses on the forward-looking perspective by estimating effects of causes, the backward-looking perspective can provide insights into causes of effects. In backward-looking causal inference, the probability of necessity measures the probability that a certain event is caused by the treatment, given the observed treatment and outcome. Most existing results focus on binary outcomes. Motivated by applications with…

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Mediation Analysis with the Mediator and Outcome Missing Not at Random

中介变量与结果非随机缺失时的中介分析

Mediation analysis is widely used for investigating direct and indirect causal pathways through which an effect arises. However, many mediation analysis studies are challenged by missingness in the mediator and outcome. In general, when the mediator and outcome are missing not at random, the direct and indirect effects are not identifiable without further assumptions. We study the identifiability of the direct and indirect effects under some interpretable mechanisms that…

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Forward selection and post-selection inference in factorial designs

析因设计中的前向选择与选择后推断

Ever since the seminal work of R. A. Fisher and F. Yates, factorial designs have been an important experimental tool to simultaneously estimate the effects of multiple treatment factors. In factorial designs, the number of treatment combinations grows exponentially with the number of treatment factors, which motivates the forward selection strategy based on the sparsity, hierarchy and heredity principles for factorial effects. Although this strategy is intuitive and has been…

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Covariate adjustment in randomized experiments with missing outcomes and covariates

结局与协变量缺失时随机实验中的协变量调整

Summary Covariate adjustment can improve precision in analysing randomized experiments. With fully observed data, regression adjustment and propensity score weighting are asymptotically equivalent in improving efficiency over unadjusted analysis. When some outcomes are missing, we consider combining these two adjustment methods with the inverse probability of observation weighting for handling missing outcomes, and show that the equivalence between the two methods breaks…

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No star is good news: A unified look at rerandomization based on p -values from covariate balance tests

没有显著性星号是好消息:基于协变量平衡检验 p 值的再随机化

Randomized experiments balance all covariates on average and are considered the gold standard for estimating treatment effects. Chance imbalances are nonetheless common in realized treatment allocations. To inform readers of the comparability of treatment groups at baseline, contemporary scientific publications often report covariate balance tables with not only covariate means by treatment group but also the associated p-values from significance tests of their differences.…

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Power and sample size calculations for rerandomization

再随机化设计的检验功效与样本量计算

Summary Power analyses are an important aspect of experimental design, because they help determine how experiments are implemented in practice. It is common to specify a desired level of power and compute the sample size necessary to obtain that power. Such calculations are well known for completely randomized experiments, but there can be many benefits to using other experimental designs. For example, it has recently been established that rerandomization, where subjects are…

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To Adjust or not to Adjust? Estimating the Average Treatment Effect in Randomized Experiments with Missing Covariates

调整还是不调整?协变量缺失时随机实验平均处理效应的估计

Complete randomization allows for consistent estimation of the average treatment effect based on the difference in means of the outcomes without strong modeling assumptions on the outcome-generating process. Appropriate use of the pretreatment covariates can further improve the estimation efficiency. However, missingness in covariates is common in experiments and raises an important question: should we adjust for covariates subject to missingness, and if so, how? The…

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Randomization Tests for Peer Effects in Group Formation Experiments

群组形成实验中同伴效应的随机化检验

Measuring the effect of peers on individuals' outcomes is a challenging problem, in part because individuals often select peers who are similar in both observable and unobservable ways. Group formation experiments avoid this problem by randomly assigning individuals to groups and observing their responses; for example, do first‐year students have better grades when they are randomly assigned roommates who have stronger academic backgrounds? In this paper, we propose…

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An instrumental variable method for point processes: generalized Wald estimation based on deconvolution

点过程的工具变量方法:基于反卷积的广义 Wald 估计

Summary Point processes are probabilistic tools for modelling event data. While there exists a fast-growing literature on the relationships between point processes, how such relationships connect to causal effects remains unexplored. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define…

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Design-based theory for cluster rerandomization

整群再随机化的设计型理论

Summary Complete randomization balances covariates on average, but covariate imbalance often exists in finite samples. Rerandomization can ensure covariate balance in the realized experiment by discarding the undesired treatment assignments. Many field experiments in public health and social sciences assign the treatment at the cluster level due to logistical constraints or policy considerations. Moreover, they are frequently combined with re-randomization in the design…

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Covariate adjustment in multiarmed, possibly factorial experiments

多处理臂及可能包含析因结构的实验中的协变量调整

Abstract Randomized experiments are the gold standard for causal inference and enable unbiased estimation of treatment effects. Regression adjustment provides a convenient way to incorporate covariate information for additional efficiency. This article provides a unified account of its utility for improving estimation efficiency in multiarmed experiments. We start with the commonly used additive and fully interacted models for regression adjustment in estimating average…

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Same Root Different Leaves: Time Series and Cross‐Sectional Methods in Panel Data

同根异叶:面板数据中的时间序列与横截面方法

One dominant approach to evaluate the causal effect of a treatment is through panel data analysis, whereby the behaviors of multiple units are observed over time. The information across time and units motivates two general approaches: (i) horizontal regression (i.e., unconfoundedness), which exploits time series patterns, and (ii) vertical regression (e.g., synthetic controls), which exploits cross‐sectional patterns. Conventional wisdom often considers the two approaches to…

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Estimation Based on Nearest Neighbor Matching: From Density Ratio to Average Treatment Effect

基于最近邻匹配的估计:从密度比到平均处理效应

Nearest neighbor (NN) matching is widely used in observational studies for causal effects. Abadie and Imbens (2006) provided the first large‐sample analysis of NN matching. Their theory focuses on the case with the number of NNs, M fixed. We reveal something new out of their study and show that once allowing M to diverge with the sample size an intrinsic statistic in their analysis constitutes a consistent estimator of the density ratio with regard to covariates across the…

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Multiply Robust Estimation of Causal Effects under Principal Ignorability

主分层可忽略性下因果效应的多重稳健估计

Abstract Causal inference concerns not only the average effect of the treatment on the outcome but also the underlying mechanism through an intermediate variable of interest. Principal stratification characterizes such a mechanism by targeting subgroup causal effects within principal strata, which are defined by the joint potential values of an intermediate variable. Due to the fundamental problem of causal inference, principal strata are inherently latent, rendering it…

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Regression-based causal inference with factorial experiments: estimands, model specifications and design-based properties

析因实验中的回归因果推断:目标量、模型设定与基于设计的性质

Summary Factorial designs are widely used because of their ability to accommodate multiple factors simultaneously. Factor-based regression with main effects and some interactions is the dominant strategy for downstream analysis, delivering point estimators and standard errors simultaneously via one least-squares fit. Justification of these convenient estimators from the design-based perspective requires quantifying their sampling properties under the assignment mechanism…

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Peng Ding’s Contribution to the Discussion of ‘Assumption-Lean Inference for Generalised Linear Model Parameters’ by Vansteelandt and Dukes

彭鼎对《广义线性模型参数的弱假设推断》的讨论

I want to congratulate the authors on a thought-provoking paper on statistical inference with misspecified models. It deepens our understanding of the role of models in causal inference. I offer two comments. Comparison of the conditional and marginal estimands based on 105 Monte Carlo samples. The parameters of the distributions of L and Y are all drawn independently from Uniform(0, 1) The authors provide inspiring derivations of the novel average effect and interaction…

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