Two-stage randomized experiments are becoming an increasingly popular experimental design for causal inference when the outcome of one unit may be affected by the treatment assignments of other units in the same cluster. In this paper, we provide a methodological framework for general tools of statistical inference and power analysis for two-stage randomized experiments. Under the randomization-based framework, we consider the estimation of a new direct effect of interest as well as the average direct and spillover effects studied in the literature. We provide unbiased estimators of these causal quantities and their conservative variance estimators in a general setting. Using these results, we then develop hypothesis testing procedures and derive sample size formulas. We theoretically compare the two-stage randomized design with the completely randomized and cluster randomized designs, which represent two limiting designs. Finally, we conduct simulation studies to evaluate the empirical performance of our sample size formulas. For empirical illustration, the proposed methodology is applied to the randomized evaluation of the Indian national health insurance program. An open-source software package is available for implementing the proposed methodology.
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…
Causal mediation in cluster-randomized trials with multiple mediators: spillover-aware decomposition, identification, and semiparametric efficient inference
$P$-values that are derived from continuously distributed test statistics are typically uniformly distributed on $(0,1)$ under least favorable parameter configurations (LFCs) in the null hypothesis. Conservativeness of a $p$-value $P$ (meaning that $P$ is under the null hypothesis stochastically larger than a random variable which is uniformly distributed on $(0,1)$) can occur if the test statistic from which $P$ is derived is discrete, or if the true parameter value under the null is not an LFC. To deal with both of these sources of conservativeness, we present two approaches utilizing random…
When experimental subjects can interact with each other, the outcome of one individual may be affected by the treatment status of others. In many social science experiments, such spillover effects may occur through multiple networks, for example, through both online and offline face-to-face networks in a Twitter experiment. Thus, to understand how people use different networks, it is essential to estimate the spillover effect in each specific network separately. However, the unbiased estimation of these network-specific spillover effects requires an often-violated assumption that researchers o…
This paper shows how to use a randomized saturation experimental design to identify and estimate causal effects in the presence of spillovers--one person's treatment may affect another's outcome--and one-sided non-compliance--subjects can only be offered treatment, not compelled to take it up. Two distinct causal effects are of interest in this setting: direct effects quantify how a person's own treatment changes her outcome, while indirect effects quantify how her peers' treatments change her outcome. We consider the case in which spillovers occur within known groups, and take-up decisions ar…
We present current methods for estimating treatment effects and spillover effects under "interference", a term which covers a broad class of situations in which a unit's outcome depends not only on treatments received by that unit, but also on treatments received by other units. To the extent that units react to each other, interact, or otherwise transmit effects of treatments, valid inference requires that we account for such interference, which is a departure from the traditional assumption that units' outcomes are affected only by their own treatment assignment. Interference and associated …
Institute of Statistics, RWTH Aachen University（亚琛工业大学统计研究所）；Forschungszentrum Jülich, Institut für Energie- und Klimaforschung, IEK-5（于利希研究中心能源与气候研究所 IEK-5）
Randomized artificial neural networks such as extreme learning machines provide an attractive and efficient method for supervised learning under limited computing ressources and green machine learning. This especially applies when equipping mobile devices (sensors) with weak artificial intelligence. Results are discussed about supervised learning with such networks and regression methods in terms of consistency and bounds for the generalization and prediction error. Especially, some recent results are reviewed addressing learning with data sampled by moving sensors leading to non-stationary an…
Some patients benefit from a treatment while others may do so less or do not benefit at all. We have previously developed a two-stage network meta-regression prediction model that synthesized randomized trials and evaluates how treatment effects vary across patient characteristics. In this article, we extended this model to combine different sources of types in different formats: aggregate data (AD) and individual participant data (IPD) from randomized and non-randomized evidence. In the first stage, a prognostic model is developed to predict the baseline risk of the outcome using a large coho…
Truncated conditional expectation functions are objects of interest in a wide range of economic applications, including income inequality measurement, financial risk management, and impact evaluation. They typically involve truncating the outcome variable above or below certain quantiles of its conditional distribution. In this paper, based on local linear methods, a novel, two-stage, nonparametric estimator of such functions is proposed. In this estimation problem, the conditional quantile function is a nuisance parameter that has to be estimated in the first stage. The proposed estimator is …
This paper presents methods for analyzing spatial experiments when complex spillovers, displacement effects, and other types of "interference" are present. We present a robust, design-based approach to analyzing effects in such settings. The design-based approach derives inferential properties for causal effect estimators from known features of the experimental design, in a manner analogous to inference in sample surveys. The methods presented here target a quantity of interest called the "average marginalized response," which is equal to the average effect of activating a treatment at an inte…
Randomized experiments are widely used to estimate the causal effects of a proposed treatment in many areas of science, from medicine and healthcare to the physical and biological sciences, from the social sciences to engineering, to public policy and to the technology industry at large. Here, we consider situations where classical methods for estimating the total treatment effect on a target population are considerably biased due to confounding network effects, i.e., the fact that the treatment of an individual may impact their neighbors' outcomes, an issue referred to as network interference…
Estimating Causal Treatment Effects in Placebo-Controlled Randomized Clinical Trials When High Placebo Response is Anticipated
Smith Center for Outcomes Research in Cardiology, Beth Israel Deaconess Medical Center（贝斯以色列女医生医疗中心心脏结局研究史密斯中心）；Department of Statistics, SungKyunKwan University（成均馆大学统计系）；Biostatistics Department, Boston University（波士顿大学生物统计学系）
A small n, sequential, multiple assignment, randomized trial (snSMART) is a small sample, two-stage design where participants receive up to two treatments sequentially, but the second treatment depends on response to the first treatment. The treatment effect of interest in an snSMART is the first-stage response rate, but outcomes from both stages can be used to obtain more information from a small sample. A novel way to incorporate the outcomes from both stages applies power prior models, in which first stage outcomes from an snSMART are regarded as the primary data and second stage outcomes a…
University of Cambridge（剑桥大学）；Newcastle University（纽卡斯尔大学）
High-dimensional biomarkers such as genomics are increasingly being measured in randomized clinical trials. Consequently, there is a growing interest in developing methods that improve the power to detect biomarker-treatment interactions. We adapt recently proposed two-stage interaction detecting procedures in the setting of randomized clinical trials. We also propose a new stage 1 multivariate screening strategy using ridge regression to account for correlations among biomarkers. For this multivariate screening, we prove the asymptotic between-stage independence, required for family-wise erro…
Cluster-based randomized experiments are popular designs for mitigating the bias of standard estimators when interference is present and classical causal inference and experimental design assumptions (such as SUTVA or ITR) do not hold. Without an exact knowledge of the interference structure, it can be challenging to understand which partitioning of the experimental units is optimal to minimize the estimation bias. In the paper, we introduce a monotonicity condition under which a novel two-stage experimental design allows us to determine which of two cluster-based designs yields the least bias…
Clinicians and researchers alike are increasingly interested in how best to personalize interventions. A dynamic treatment regimen (DTR) is a sequence of pre-specified decision rules which can be used to guide the delivery of a sequence of treatments or interventions that are tailored to the changing needs of the individual. The sequential multiple-assignment randomized trial (SMART) is a research tool which allows for the construction of effective DTRs. We derive easy-to-use formulae for computing the total sample size for three common two-stage SMART designs in which the primary aim is to co…
To generalize inferences from a randomized trial to the target population of all trial-eligible individuals, investigators can use nested trial designs, where the randomized individuals are nested within a cohort of trial-eligible individuals, including those who are not offered or refuse randomization. In these designs, data on baseline covariates are collected from the entire cohort, and treatment and outcome data need only be collected from randomized individuals. In this paper, we describe nested trial designs that improve research economy by collecting additional baseline covariate data a…
We are interested in the distribution of treatment effects for an experiment where units are randomized to a treatment but outcomes are measured for pairs of units. For example, we might measure risk sharing links between households enrolled in a microfinance program, employment relationships between workers and firms exposed to a trade shock, or bids from bidders to items assigned to an auction format. Such a double randomized experimental design may be appropriate when there are social interactions, market externalities, or other spillovers across units assigned to the same treatment. Or it …
Cluster randomized trials (CRTs) randomly assign an intervention to groups of individuals (e.g., clinics or communities) and measure outcomes on individuals in those groups. While offering many advantages, this experimental design introduces challenges that are only partially addressed by existing analytic approaches. First, outcomes are often missing for some individuals within clusters. Failing to appropriately adjust for differential outcome measurement can result in biased estimates and inference. Second, CRTs often randomize limited numbers of clusters, resulting in chance imbalances on b…
Evaluating causal effects in the presence of interference is challenging in network-based studies of hard-to-reach populations. Like many such populations, people who inject drugs (PWID) are embedded in social networks and often exert influence on others in their network. In our setting, the study design is observational with a non-randomized network-based HIV prevention intervention. Information is available on each participant and their connections that confer possible HIV risk through injection and sexual behaviors. We considered two inverse probability weighted (IPW) estimators to quantify…
