In sequential experiments, subjects become available for the study over a period of time, and covariates are often measured at the time of arrival. We consider the setting where the sample size is fixed but covariate values are unknown until subjects enrol. Given a model for the outcome, a sequential optimal design approach can be used to allocate treatments to minimize the variance of the treatment effect. We extend existing optimal design methodology so it can be used within a nonmyopic framework, where treatment allocation for the current subject depends not only on the treatments and covariates of the subjects already enrolled in the study, but also the impact of possible future treatment assignments. The nonmyopic approach is computationally expensive as it requires recursive formulae. We propose a pseudo-nonmyopic approach which has a similar aim to the nonmyopic approach, but does not involve recursion and instead relies on simulations of future possible decisions. Our simulation studies show that the myopic approach is the most efficient for the logistic model case with a single binary covariate and binary treatment.
Washington University in Saint Louis（圣路易斯华盛顿大学）；Amazon Research Cambridge（亚马逊剑桥研究院）
Finite-horizon sequential experimental design (SED) arises naturally in many contexts, including hyperparameter tuning in machine learning among more traditional settings. Computing the optimal policy for such problems requires solving Bellman equations, which are generally intractable. Most existing work resorts to severely myopic approximations by limiting the decision horizon to only a single time-step, which can underweight exploration in favor of exploitation. We present BINOCULARS: Batch-Informed NOnmyopic Choices, Using Long-horizons for Adaptive, Rapid SED, a general framework for deri…
We propose a dynamic allocation procedure that increases power and efficiency when measuring an average treatment effect in sequential randomized trials exploiting some subjects' previous assessed responses. Subjects arrive sequentially and are either randomized or paired to a previously randomized subject and administered the alternate treatment. The pairing is made via a dynamic matching criterion that iteratively learns which specific covariates are important to the response. We develop estimators for the average treatment effect as well as an exact test. We illustrate our method's increase…
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…
In randomized trials, researchers are often interested in mediation analysis to understand how a treatment works, in particular how much of a treatment's effect is mediated by an intermediated variable and how much the treatment directly affects the outcome not through the mediator. The standard regression approach to mediation analysis assumes sequential ignorability of the mediator, that is that the mediator is effectively randomly assigned given baseline covariates and the randomized treatment. Since the experiment does not randomize the mediator, sequential ignorability is often not plausi…
Mobile health is a rapidly developing field in which behavioral treatments are delivered to individuals via wearables or smartphones to facilitate health-related behavior change. Micro-randomized trials (MRT) are an experimental design for developing mobile health interventions. In an MRT the treatments are randomized numerous times for each individual over course of the trial. Along with assessing treatment effects, behavioral scientists aim to understand between-person heterogeneity in the treatment effect. A natural approach is the familiar linear mixed model. However, directly applying lin…
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 present an optimized rerandomization design procedure for a non-sequential treatment-control experiment. Randomized experiments are the gold standard for finding causal effects in nature. But sometimes random assignments result in unequal partitions of the treatment and control group visibly seen as imbalance in observed covariates. There can additionally be imbalance on unobserved covariates. Imbalance in either observed or unobserved covariates increases treatment effect estimator error inflating the width of confidence regions and reducing experimental power. "Rerandomization" is a strat…
In clinical trials, a covariate-adjusted response-adaptive (CARA) design allows a subject newly entering a trial a better chance of being allocated to a superior treatment regimen based on cumulative information from previous subjects, and adjusts the allocation according to individual covariate information. Since this design allocates subjects sequentially, it is natural to apply a sequential method for estimating the treatment effect in order to make the data analysis more efficient. In this paper, we study the sequential estimation of treatment effect for a general CARA design. A stopping c…
We propose the instrumental variable regime (IVR) method to estimate the causal effects of multiple sequential treatments. This method serves to address the problem of endogenous selections of sequential treatments. An IVR is a sequence of instrumental variables in which each IV instruments for an endogenous treatment variable. Our proposed method generalizes the LATE model in Imbens and Angrist (1994) from a single treatment to many treatments applied sequentially. More precisely, with the IVR this model allows for estimating the local average treatment regime effects (LATRE), possibly condit…
The first step towards investigating the effectiveness of a treatment via a randomized trial is to split the population into control and treatment groups then compare the average response of the treatment group receiving the treatment to the control group receiving the placebo. In order to ensure that the difference between the two groups is caused only by the treatment, it is crucial that the control and the treatment groups have similar statistics. Indeed, the validity and reliability of a trial are determined by the similarity of two groups' statistics. Covariate balancing methods increase …
A standard assumption for causal inference about the joint effects of time-varying treatment is that one has measured sufficient covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values, also known as "sequential randomization assumption (SRA)". SRA is often criticized as it requires one to accurately measure all confounders. Realistically, measured covariates can rarely capture all confounders with certainty. Often covariate measurements are at best proxies of confounders, thus invalidating inferences under SRA. In this paper, we extend the…
In sequential causal inference, one estimates the causal net effect of treatment in treatment sequence on an outcome after last treatment in the presence of time-dependent covariates between treatments, improves the estimation by the untestable assumption of strongly ignorable treatment assignment, and obtains consistent but non-genuine likelihood-based estimate. In this article, we introduce the net effect of treatment as parameter for the conditional distribution of outcome given all treatments and time-dependent covariates and show that it is equal to the causal net effect of treatment unde…
Variable selection for optimal treatment regime in a clinical trial or an observational study is getting more attention. Most existing variable selection techniques focused on selecting variables that are important for prediction, therefore some variables that are poor in prediction but are critical for decision-making may be ignored. A qualitative interaction of a variable with treatment arises when treatment effect changes direction as the value of this variable varies. The qualitative interaction indicates the importance of this variable for decision-making. Gunter et al. (2011) proposed S-…
Sequential generalized kernel equating: Providing comparable scores across multiple test forms with nonequivalent groups and differently measured covariates
From personalised medicine to targeted advertising, it is an inherent task to provide a sequence of decisions with historical covariates and outcome data. This requires understanding of both the dynamics and heterogeneity of treatment effects. In this paper, we are concerned with detecting abrupt changes in the treatment effects in terms of the conditional average treatment effect (CATE) in a sequential fashion. To be more specific, at each time point, we consider a nonparametric model to allow for maximal flexibility and robustness. Along the time, we allow for temporal dependence on historic…
In clinical trials, there is potential to improve precision and reduce the required sample size by appropriately adjusting for baseline variables in the statistical analysis. This is called covariate adjustment. Despite recommendations by regulatory agencies in favor of covariate adjustment, it remains underutilized leading to inefficient trials. We address two obstacles that make it challenging to use covariate adjustment. A first obstacle is the incompatibility of many covariate adjusted estimators with commonly used boundaries in group sequential designs (GSDs). A second obstacle is the unc…
Due to patient heterogeneity in response to various aspects of any treatment program, biomedical and clinical research is gradually shifting from the traditional "one-size-fits-all" approach to the new paradigm of personalized medicine. An important step in this direction is to identify the treatment by covariate interactions. We consider the setting in which there are potentially a large number of covariates of interest. Although a number of novel machine learning methodologies have been developed in recent years to aid in treatment selection in this setting, few, if any, have adopted formal …
Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumpti…
Kernel-based estimators for functional causal effects
School of Mathematical Sciences, Horizon Digital Economy Institute, University of Nottingham, Nottingham, UK（数学科学学院，Horizon数字经济研究所，诺丁汉大学，诺丁汉，英国）；Department of Statistics, Rice University, USA（统计学系，里士满大学，美国；伯克利国家实验室，美国）；Lawrence Berkeley National Laboratory, USA（统计科学组，洛斯阿拉莫斯国家实验室，美国）；Statistical Sciences Group, Los Alamos National Laboratory, USA（数学科学学院，诺丁汉大学，诺丁汉，英国）；School of Mathematical Sciences, University of Nottingham, Nottingham, UK
High dimensional classification has been highlighted for last two decades and much research has been conducted in order to circumvent challenges encountered in high dimensions. While existing methods have focused mainly on developing classification rules assuming independence of covariates or using regularization on the sample covariance matrix or the sample mean vector or among others, we propose a novel approach that employs the "discriminatory power" of each covariate, selects a set of important variables yielding the lowest misclassification rate empirically, and constructs the optimal lin…
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…
We focus on causal inference for longitudinal treatments, where units are assigned to treatments at multiple time points, aiming to assess the effect of different treatment sequences on an outcome observed at a final point. A common assumption in similar studies is Sequential Ignorability (SI): treatment assignment at each time point is assumed independent of future potential outcomes given past observed outcomes and covariates. SI is questionable when treatment participation depends on individual choices, and treatment assignment may depend on unobservable quantities associated with future ou…
Precision medicine incorporates patient-level covariates to tailor treatment decisions, seeking to improve outcomes. In longitudinal studies with time-varying covariates and sequential treatment decisions, precision medicine can be formalized with dynamic treatment regimes (DTRs): sequences of covariate-dependent treatment rules. To date, the precision medicine literature has not addressed a ubiquitous concern in health research - measurement error - where observed data deviate from the truth. We discuss the consequences of ignoring measurement error in the context of DTRs, focusing on challen…
Biased sampling designs can be highly efficient when studying rare (binary) or low variability (continuous) endpoints. We consider longitudinal data settings in which the probability of being sampled depends on a repeatedly measured response through an outcome-related, auxiliary variable. Such auxiliary variable- or outcome-dependent sampling improves observed response and possibly exposure variability over random sampling, {even though} the auxiliary variable is not of scientific interest. {For analysis,} we propose a generalized linear model based approach using a sequence of two offsetted r…
The primary analysis in two-arm clinical trials usually involves inference on a scalar treatment effect parameter; e.g., depending on the outcome, the difference of treatment-specific means, risk difference, risk ratio, or odds ratio. Most clinical trials are monitored for the possibility of early stopping. Because ordinarily the outcome on any given subject can be ascertained only after some time lag, at the time of an interim analysis, among the subjects already enrolled, the outcome is known for only a subset and is effectively censored for those who have not been enrolled sufficiently long…
The sequential treatment decisions made by physicians to treat chronic diseases are formalized in the statistical literature as dynamic treatment regimes. To date, methods for dynamic treatment regimes have been developed under the assumption that observation times, i.e., treatment and outcome monitoring times, are determined by study investigators. That assumption is often not satisfied in electronic health records data in which the outcome, the observation times, and the treatment mechanism are associated with patients' characteristics. The treatment and observation processes can lead to spu…
Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. This risk, viewed as a function of thresholds and possibly adjusted for covariates, we call the threshold-response function. Extending the work of Donovan, Hudgens and Gilbert (2019), we propose a nonparametric efficient estimator for the covariate-adjusted threshold-response function, which utilizes machine learning and Targeted Minimum-Loss Estimation (TMLE). We additionally propose a more general estimator, based on sequential regression, that also…
Cluster-level dynamic treatment regimens can be used to guide sequential, intervention or treatment decision-making at the cluster level in order to improve outcomes at the individual or patient-level. In a cluster-level DTR, the intervention or treatment is potentially adapted and re-adapted over time based on changes in the cluster that could be impacted by prior intervention, including based on aggregate measures of the individuals or patients that comprise it. Cluster-randomized sequential multiple assignment randomized trials (SMARTs) can be used to answer multiple open questions preventi…
