Factorial designs are widely used due to their ability to accommodate multiple factors simultaneously. The factor-based regression with main effects and some interactions is the dominant strategy for downstream data analysis, delivering point estimators and standard errors via one single regression. Justification of these convenient estimators from the design-based perspective requires quantifying their sampling properties under the assignment mechanism conditioning on the potential outcomes. To this end, we derive the sampling properties of the factor-based regression estimators from both saturated and unsaturated models, and demonstrate the appropriateness of the robust standard errors for the Wald-type inference. We then quantify the bias-variance trade-off between the saturated and unsaturated models from the design-based perspective, and establish a novel design-based Gauss--Markov theorem that ensures the latter's gain in efficiency when the nuisance effects omitted indeed do not exist. As a byproduct of the process, we unify the definitions of factorial effects in various literatures and propose a location-shift strategy for their direct estimation from factor-based regressions. Our theory and simulation suggest using factor-based inference for general factorial effects, preferably with parsimonious specifications in accordance with the prior knowledge of zero nuisance effects.
A framework for causal inference from two-level factorial designs is proposed. The framework utilizes the concept of potential outcomes that lies at the center stage of causal inference and extends Neyman's repeated sampling approach for estimation of causal effects and randomization tests based on Fisher's sharp null hypothesis to the case of 2-level factorial experiments. The framework allows for statistical inference from a finite population, permits definition and estimation of estimands other than "average factorial effects" and leads to more flexible inference procedures than those based…
We systematically investigate issues due to mis-specification that arise in estimating causal effects when (treatment) interference is informed by a network available pre-intervention, i.e., in situations where the outcome of a unit may depend on the treatment assigned to other units. We develop theory for several forms of interference through the concept of exposure neighborhood, and develop the corresponding semi-parametric representation for potential outcomes as a function of the exposure neighborhood. Using this representation, we extend the definition of two popular classes of causal est…
Intensity-based multistate models provide a useful framework for characterizing disease processes, the introduction of interventions, loss to follow-up, and other complications arising in the conduct of randomized trials studying complex life history processes. Within this framework we discuss the issues involved in the specification of estimands and show the limiting values of common estimators of marginal process features based on cumulative incidence function regression models. When intercurrent events arise we stress the need to carefully define the target estimand and the importance of av…
From Estimands to Robust Inference of Treatment Effects in Master Protocol Trials
University of Washington（华盛顿大学）；The University of Texas MD Anderson Cancer Center（德克萨斯大学安德森癌症中心）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Eli Lilly and Company（礼来公司）；Food and Drug Administration（食品药品监督管理局）；Seattle Children’s Research Institute（西雅图儿童研究所）
Most causal inference studies rely on the assumption of overlap to estimate population or sample average causal effects. When data exhibit non-overlap, estimation of these estimands requires reliance on model specifications, due to poor data support. All existing methods to address non-overlap, such as trimming or down-weighting data in regions of poor support, change the estimand. In environmental health research, where study results are often intended to influence policy, changes in the estimand can diminish the study's impact, because estimates may not be representative of effects in the po…
Randomized experiments are the gold standard for causal inference, and justify simple comparisons across treatment groups. 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 multi-armed experiments. We start with the commonly used additive and fully interacted models for regression adjustment, and clarify the trade-offs between the resulting ordinary least-squares (OLS) estimators for estimating average treatment effects in terms of finite-s…
Population means and standard deviations are the most common estimands to quantify effects in factorial layouts. In fact, most statistical procedures in such designs are built towards inferring means or contrasts thereof. For more robust analyses, we consider the population median, the interquartile range (IQR) and more general quantile combinations as estimands in which we formulate null hypotheses and calculate compatible confidence regions. Based upon simultaneous multivariate central limit theorems and corresponding resampling results, we derive asymptotically correct procedures in general…
In semicompeting risks problems, nonterminal time-to-event outcomes such as time to hospital readmission are subject to truncation by death. These settings are often modeled with illness-death models for the hazards of the terminal and nonterminal events, but evaluating causal treatment effects with hazard models is problematic due to conditioning on survival (a post-treatment outcome) that is embedded in the definition of a hazard. Extending an existing survivor average causal effect (SACE) estimand, we frame the evaluation of treatment effects in the context of semicompeting risks with princ…
Factorial clinical trials in the presence and absence of plausible statistical interactions between treatment factors. A historical review of the methodological literature
University of Leeds（利兹大学）；HITAP（卫生技术评估研究所）；University of Nottingham（诺丁汉大学）；King’s College London（伦敦国王学院）
No man is an island, as individuals interact and influence one another daily in our society. When social influence takes place in experiments on a population of interconnected individuals, the treatment on a unit may affect the outcomes of other units, a phenomenon known as interference. This thesis develops a causal framework and inference methodology for experiments where interference takes place on a network of influence (i.e. network interference). In this framework, the network potential outcomes serve as the key quantity and flexible building blocks for causal estimands that represent a …
Semiparametric Double Reinforcement Learning with Applications to Long-Term Causal Inference
Department of Statistics, University of Washington, USA（华盛顿大学统计系）；Netflix Research, USA（Netflix研究）；Cornell Tech, Cornell University, USA（康奈尔科技学院、康奈尔大学）
Gilead Sciences, Inc.（吉利德科学公司）；Fred Hutchinson Cancer Center（弗雷德·哈钦森癌症中心）；University of Washington（华盛顿大学）
Heterogeneous treatment effects (HTE) based on patients' genetic or clinical factors are of significant interest to precision medicine. Simultaneously modeling HTE and corresponding main effects for randomized clinical trials with high-dimensional predictive markers is challenging. Motivated by the modified covariates approach, we propose a two-stage statistical learning procedure for estimating HTE with optimal efficiency augmentation, generalizing to arbitrary interaction model and exploiting powerful extreme gradient boosting trees (XGBoost). Target estimands for HTE are defined in the scal…
Motivated by recent findings in the field of consumer science, this paper evaluates the causal effect of debit cards on household consumption using population-based data from the Italy Survey on Household Income and Wealth (SHIW). Within the Rubin Causal Model, we focus on the estimand of population average treatment effect for the treated (PATT). We consider three existing estimators, based on regression, mixed matching and regression, propensity score weighting, and propose a new doubly-robust estimator. Semiparametric specification based on power series for the potential outcomes and the pr…
Mediation analysis is critical to understanding the mechanisms underlying exposure-outcome relationships. In this paper, we identify the instrumental variable (IV)-direct effect of the exposure on the outcome not through the mediator, using randomization of the instrument. To our knowledge, such an estimand has not previously been considered or estimated. We propose and evaluate several estimators for this estimand: a ratio of inverse-probability of treatment-weighted estimators (IPTW), a ratio of estimating equation estimators (EE), a ratio of targeted minimum loss-based estimators (TMLE), an…
