In this article, we study the hypothesis testing of the blip / net effects of treatments in a treatment sequence. We illustrate that the likelihood ratio test and the score test may suffer from the curse of dimensionality, the null paradox and the high-dimensional constraint on standard parameters under the null hypothesis. On the other hand, we construct the Wald test via a small number of point effects of treatments in single-point causal inference. We show that the Wald test can avoid these problems under the same assumptions as the Wald test for testing the point effect of treatment. The simulation study illustrates that the Wald test achieves the nominal level of type I error and a low level of type II error. A real medical example illustrates how to conduct the Wald test in practice.
We investigate the problem of inferring the causal predictors of a response $Y$ from a set of $d$ explanatory variables $(X^1,\dots,X^d)$. Classical ordinary least squares regression includes all predictors that reduce the variance of $Y$. Using only the causal predictors instead leads to models that have the advantage of remaining invariant under interventions, loosely speaking they lead to invariance across different "environments" or "heterogeneity patterns". More precisely, the conditional distribution of $Y$ given its causal predictors remains invariant for all observations. Recent work e…
Construction of just-in-time adaptive interventions, such as prompts delivered by mobile apps to promote and maintain behavioral change, requires knowledge about time-varying moderated effects to inform when and how we deliver intervention options. Micro-randomized trials (MRT) have emerged as a sequentially randomized design to gather requisite data for effect estimation. The existing literature (Qian et al., 2020; Boruvka et al., 2018; Dempsey et al., 2020) has defined a general class of causal estimands, referred to as "causal excursion effects", to assess the time-varying moderated effect.…
Scientific researchers utilize randomized experiments to draw casual statements. Most early studies as well as current work on experiments with sequential intervention decisions has been focusing on estimating the causal effects among sequential treatments, ignoring the non-compliance issues that experimental units might not be compliant with the treatment assignments that they were originally allocated. A series of methodologies have been developed to address the non-compliance issues in randomized experiments with time-fixed treatment. However, to our best knowledge, there is little literatu…
Suppose that a sequence of treatments are assigned to influence an outcome of interest that occurs after the last treatment. Between treatments there exist time-dependent covariates that may be posttreatment variables of the earlier treatments and confounders of the subsequent treatments. In this article, we develop a parametric approach to inference of the causal effect of the treatment sequence on the outcome called the sequential causal effect. We construct a point parametrization for the conditional distribution of an outcome given all treatments and time-dependent covariates, in which the…
We study how to learn optimal interventions sequentially given causal information represented as a causal graph along with associated conditional distributions. Causal modeling is useful in real world problems like online advertisement where complex causal mechanisms underlie the relationship between interventions and outcomes. We propose two algorithms, causal upper confidence bound (C-UCB) and causal Thompson Sampling (C-TS), that enjoy improved cumulative regret bounds compared with algorithms that do not use causal information. We thus resolve an open problem posed by \cite{lattimore2016ca…
Causal mediation analysis is an important statistical method in social and medical studies, as it can provide insights about why an intervention works and inform the development of future interventions. Currently, most causal mediation methods focus on mediation effects defined on a mean scale. However, in health-risk studies, such as alcohol or risky sex, outcomes are typically count data and heavily skewed. Thus, mediation effects in these setting would be natural on a rate ratio scale, such as in Poisson and negative binomial regression methods. Existing methods also mainly rely on the assu…
Longitudinal observational patient data can be used to investigate the causal effects of time-varying treatments on time-to-event outcomes. Several methods have been developed for controlling for the time-dependent confounding that typically occurs. The most commonly used is inverse probability weighted estimation of marginal structural models (MSM-IPTW). An alternative, the sequential trials approach, is increasingly popular, in particular in combination with the target trial emulation framework. This approach involves creating a sequence of `trials' from new time origins, restricting to indi…
Goal-Oriented Sequential Bayesian Experimental Design for Causal Learning
Department of Computer Science and Engineering（计算机科学与工程系）；Department of Mechanical Engineering（机械工程系）；Gilbert S. Omenn Department of Computational Medicine and Bioinformatics（Gilbert S. Omenn 计算医学与生物信息学部门）
In comparative studies, such as in causal inference and clinical trials, balancing important covariates is often one of the most important concerns for both efficient and credible comparison. However, chance imbalance still exists in many randomized experiments. This phenomenon of covariate imbalance becomes much more serious as the number of covariates $p$ increases. To address this issue, we introduce a new randomization procedure, called pairwise sequential randomization (PSR). The proposed method allocates the units sequentially and adaptively, using information on the current level of imb…
Using observational data to estimate the effect of a treatment is a powerful tool for decision-making when randomized experiments are infeasible or costly. However, observational data often yields biased estimates of treatment effects, since treatment assignment can be confounded by unobserved variables. A remedy is offered by deconfounding methods that adjust for such unobserved confounders. In this paper, we develop the Sequential Deconfounder, a method that enables estimating individualized treatment effects over time in presence of unobserved confounders. This is the first deconfounding me…
Streaming data routinely generated by mobile phones, social networks, e-commerce, and electronic health records present new opportunities for near real-time surveillance of the impact of an intervention on an outcome of interest via causal inference methods. However, as data grow rapidly in volume and velocity, storing and combing data become increasingly challenging. The amount of time and effort spent to update analyses can grow exponentially, which defeats the purpose of instantaneous surveillance. Data sharing barriers in multi-center studies bring additional challenges to rapid signal det…
Causal mediation analysis is routinely conducted by applied researchers in a variety of disciplines. The goal of such an analysis is to investigate alternative causal mechanisms by examining the roles of intermediate variables that lie in the causal paths between the treatment and outcome variables. In this paper we first prove that under a particular version of sequential ignorability assumption, the average causal mediation effect (ACME) is nonparametrically identified. We compare our identification assumption with those proposed in the literature. Some practical implications of our identifi…
The micro-randomized trial (MRT) is a sequential randomized experimental design to empirically evaluate the effectiveness of mobile health (mHealth) intervention components that may be delivered at hundreds or thousands of decision points. MRTs have motivated a new class of causal estimands, termed "causal excursion effects", for which semiparametric inference can be conducted via a weighted, centered least squares criterion (Boruvka et al., 2018). Existing methods assume between-subject independence and non-interference. Deviations from these assumptions often occur. In this paper, causal exc…
In this paper we review the notion of direct causal effect as introduced by Pearl (2001). We show how it can be formulated without counterfactuals, using intervention indicators instead. This allows to consider the natural direct effect as a special case of sequential treatments discussed by Dawid and Didelez (2005) which immediately yields conditions for identifiability as well as a graphical way of checking identifiability. The results are contrasted with the criteria given by Pearl (2001) and Robins (2003).
Mediation analysis has been used in many disciplines to explain the mechanism or process that underlies an observed relationship between an exposure variable and an outcome variable via the inclusion of mediators. Decompositions of the total causal effect of an exposure variable into effects characterizing mediation pathways and interactions have gained an increasing amount of interest in the last decade. In this work, we develop decompositions for scenarios where the two mediators are causally sequential or non-sequential. Current developments in this area have primarily focused on either dec…
Consider the case that one observes a single time-series, where at each time t one observes a data record O(t) involving treatment nodes A(t), possible covariates L(t) and an outcome node Y(t). The data record at time t carries information for an (potentially causal) effect of the treatment A(t) on the outcome Y(t), in the context defined by a fixed dimensional summary measure Co(t). We are concerned with defining causal effects that can be consistently estimated, with valid inference, for sequentially randomized experiments without further assumptions. More generally, we consider the case whe…
Sequential Underspecified Instrument Selection for Cause-Effect Estimation
HelmholtzAI（亥姆霍兹人工智能研究所）；Helmholtz Munich（亥姆霍兹慕尼黑中心）；TUM School of Computation, Information and Technology, Technical University Munich（慕尼黑工业大学计算、信息与技术学院）；MILA - Quebec Artificial Intelligence Institute（MILA——魁北克人工智能研究所）；Recursion（Recursion公司）
