Bridging preference-based instrumental variable studies and cluster-randomized encouragement experiments: study design, noncompliance, and average cluster effect ratio
Instrumental variable methods are widely used in medical and social science research to draw causal conclusions when the treatment and outcome are confounded by unmeasured confounding variables. One important feature of such studies is that the instrumental variable is often applied at the cluster level, e.g., hospitals' or physicians' preference for a certain treatment where each hospital or physician naturally defines a cluster. This paper proposes to embed such observational instrumental variable data into a cluster-randomized encouragement experiment using statistical matching. Potential outcomes and causal assumptions underpinning the design are formalized and examined. Testing procedures for two commonly-used estimands, Fisher's sharp null hypothesis and the pooled effect ratio, are extended to the current setting. We then introduce a novel cluster-heterogeneous proportional treatment effect model and the relevant estimand: the average cluster effect ratio. This new estimand is advantageous over the structural parameter in a constant proportional treatment effect model in that it allows treatment heterogeneity, and is advantageous over the pooled effect ratio estimand in that it is immune to Simpson's paradox. We develop an asymptotically valid randomization-based testing procedure for this new estimand based on solving a mixed integer quadratically-constrained optimization problem. The proposed design and inferential methods are applied to a study of the effect of using transesophageal echocardiography during CABG surgery on patients' 30-day mortality rate.
It is common in instrumental variable studies for instrument values to be missing, for example when the instrument is a genetic test in Mendelian randomization studies. In this paper we discuss two apparent paradoxes that arise in so-called single consent designs where there is one-sided noncompliance, i.e., where unencouraged units cannot access treatment. The first paradox is that, even under a missing completely at random assumption, a complete-case analysis is biased when knowledge of one-sided noncompliance is taken into account; this is not the case when such information is disregarded. …
Generalized Encouragement-Based Instrumental Variables for Counterfactual Regression
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；Emory University（埃默里大学）；Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高瓴人工智能学院）；Carnegie Mellon University（卡内基梅隆大学）
Many policy evaluations occur in settings where treatment is randomized at the cluster level, and there is treatment noncompliance within each cluster. For example, villages might be assigned to treatment and control, but residents in each village may choose to comply or not with their assigned treatment status. When noncompliance is present, the instrumental variables framework can be used to identify and estimate causal effects. While a large literature exists on instrumental variables estimation methods, relatively little work has been focused on settings with clustered treatments. Here, we…
We investigate the efficacy of surgical versus non-surgical management for two gastrointestinal conditions, colitis and diverticulitis, using observational data. We deploy an instrumental variable design with surgeons' tendencies to operate as an instrument. Assuming instrument validity, we find that non-surgical alternatives can reduce both hospital length of stay and the risk of complications, with estimated effects larger for septic patients than for non-septic patients. The validity of our instrument is plausible but not ironclad, necessitating a sensitivity analysis. Existing sensitivity …
Cluster randomized trials (CRTs) are popular in public health and in the social sciences to evaluate a new treatment or policy where the new policy is randomly allocated to clusters of units rather than individual units. CRTs often feature both noncompliance, when individuals within a cluster are not exposed to the intervention, and individuals within a cluster may influence each other through treatment spillovers where those who comply with the new policy may affect the outcomes of those who do not. Here, we study the identification of causal effects in CRTs when both noncompliance and treatm…
Randomization inference for stepped-wedge designs with noncompliance with application to a palliative care pragmatic trial
University of Chicago（芝加哥大学）；Data Science Institute, University of Chicago（芝加哥大学数据科学研究所）；University of Pennsylvania（宾夕法尼亚大学）；Department of Medicine, University of Pennsylvania（宾夕法尼亚大学医学系）；Department of Mathematics and Statistics, Mississippi State University（密西西比州立大学数学与统计系）；Department of Statistics and Data Science, University of Pennsylvania（宾夕法尼亚大学统计与数据科学系）；Yale School of Public Health（耶鲁公共卫生学院）
I review recent work in the statistics literature on instrumental variables methods from an econometrics perspective. I discuss some of the older, economic, applications including supply and demand models and relate them to the recent applications in settings of randomized experiments with noncompliance. I discuss the assumptions underlying instrumental variables methods and in what settings these may be plausible. By providing context to the current applications, a better understanding of the applicability of these methods may arise.
The method of instrumental variables (IV) provides a framework to study causal effects in both randomized experiments with noncompliance and in observational studies where natural circumstances produce as-if random nudges to accept treatment. Traditionally, inference for IV relied on asymptotic approximations of the distribution of the Wald estimator or two-stage least squares, often with structural modeling assumptions and/or moment conditions. In this paper, we utilize the randomization inference approach to IV inference. First, we outline the exact method, which uses the randomized assignme…
Two problems that arise in making causal inferences for non-mortality outcomes such as bronchopulmonary dysplasia (BPD) are unmeasured confounding and censoring by death, i.e., the outcome is only observed when subjects survive. In randomized experiments with noncompliance, instrumental variable methods can be used to control for the unmeasured confounding without censoring by death. But when there is censoring by death, the average causal treatment effect cannot be identified under usual assumptions, but can be studied for a specific subpopulation by using sensitivity analysis with additional…
Clinical trials traditionally employ blinding as a design mechanism to reduce the influence of placebo effects. In practice, however, it can be difficult or impossible to blind study participants and unblinded trials are common in medical research. Here we show how instrumental variables can be used to quantify and disentangle treatment and placebo effects in randomized clinical trials comparing control and active treatments in the presence of confounders. The key idea is to use randomization to separately manipulate treatment assignment and psychological encouragement messages that increase t…
An important concern in an observational study is whether or not there is unmeasured confounding, i.e., unmeasured ways in which the treatment and control groups differ before treatment that affect the outcome. We develop a test of whether there is unmeasured confounding when an instrumental variable (IV) is available. An IV is a variable that is independent of the unmeasured confounding and encourages a subject to take one treatment level vs. another, while having no effect on the outcome beyond its encouragement of a certain treatment level. We show what types of unmeasured confounding can b…
Instrumental variable (IV) analyses are becoming common in health services research and epidemiology. IV analyses can be used both to analyze randomized trials with noncompliance and as a form of natural experiment. In these analyses, investigators often adopt a monotonicity assumption, which implies that the relevant effect only applies to a subset of the study population known as compliers. Since the estimated effect is not the average treatment effect of the study population, it is important to compare the characteristics of compliers and non-compliers. Profiling compliers and non-compliers…
Instrumental variable methods allow for inference about the treatment effect by controlling for unmeasured confounding in randomized experiments with noncompliance. However, many studies do not consider the observed compliance behavior in the testing procedure, which can lead to a loss of power. In this paper, we propose a novel nonparametric likelihood approach, referred to as the binomial likelihood (BL) method, that incorporates information on compliance behavior while overcoming several limitations of previous techniques and utilizing the advantages of likelihood methods. Our proposed meth…
Instrumental variables (IV) are a useful tool for estimating causal effects in the presence of unmeasured confounding. IV methods are well developed for uncensored outcomes, particularly for structural linear equation models, where simple two-stage estimation schemes are available. The extension of these methods to survival settings is challenging, partly because of the nonlinearity of the popular survival regression models and partly because of the complications associated with right censoring or other survival features. We develop a simple causal hazard ratio estimator in a proportional haza…
There is a fast-growing literature on estimating optimal treatment regimes based on randomized trials or observational studies under a key identifying condition of no unmeasured confounding. Because confounding by unmeasured factors cannot generally be ruled out with certainty in observational studies or randomized trials subject to noncompliance, we propose a general instrumental variable approach to learning optimal treatment regimes under endogeneity. Specifically, we establish identification of both value function $E[Y_{\mathcal{D}(L)}]$ for a given regime $\mathcal{D}$ and optimal regimes…
Manipulating a Continuous Instrumental Variable in an Observational Study of Premature Babies: Algorithm, Partial Identification Bounds, and Inference under Randomization and Biased Randomization Assumptions
Estimation and evaluation of individualized treatment rules have been studied extensively, but real-world treatment resource constraints have received limited attention in existing methods. We investigate a setting in which treatment is intervened upon based on covariates to optimize the mean counterfactual outcome under treatment cost constraints when the treatment cost is random. In a particularly interesting special case, an instrumental variable corresponding to encouragement to treatment is intervened upon with constraints on the proportion receiving treatment. For such settings, we first…
Estimating dynamic treatment regimes (DTRs) from retrospective observational data is challenging as some degree of unmeasured confounding is often expected. In this work, we develop a framework of estimating properly defined "optimal" DTRs with a time-varying instrumental variable (IV) when unmeasured covariates confound the treatment and outcome, rendering the potential outcome distributions only partially identified. We derive a novel Bellman equation under partial identification, use it to define a generic class of estimands (termed IV-optimal DTRs), and study the associated estimation prob…
Identification of complier and noncomplier average causal effects in the presence of latent missing-at-random (LMAR) outcomes: a unifying view and choices of assumptions
Johns Hopkins Bloomberg School of Public Health（约翰斯·霍普金斯大学布隆伯格公共卫生学院）
This study introduces a new approach to power analysis in the context of estimating a local average treatment effect (LATE), where the study subjects exhibit noncompliance with treatment assignment. As a result of distributional complications in the LATE context, compared to the simple ATE context, there is currently no standard method of power analysis for the LATE. Moreover, existing methods and commonly used substitutes - which include instrumental variable (IV), intent-to-treat (ITT), and scaled ATE power analyses - require specifying generally unknown variance terms and/or rely upon stron…
We revisit the problem of estimating the local average treatment effect (LATE) and the local average treatment effect on the treated (LATT) when control variables are available, either to render the instrumental variable (IV) suitably exogenous or to improve precision. Unlike previous approaches, our doubly robust (DR) estimation procedures use quasi-likelihood methods weighted by the inverse of the IV propensity score - so-called inverse probability weighted regression adjustment (IPWRA) estimators. By properly choosing models for the propensity score and outcome models, fitted values are ens…
Instituto de Ciencias Matemáticas, CSIC（西班牙科学研究所数学科学研究所）；Departamento de Matemáticas, Universidad Autónoma de Madrid（马德里自治大学数学系）；Division of Biostatistics, University of California, Berkeley（加州大学伯克利分校生物统计学部）
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…
