Causal message-passing for experiments with unknown and general network interference.

Randomized experiments are a powerful methodology for data-driven evaluation of decisions or interventions. Yet, their validity may be undermined by network interference. This occurs when the treatment of one unit impacts not only its outcome but also that of connected units, biasing traditional treatment effect estimations. Our study introduces a framework to accommodate complex and unknown network interference, moving beyond specialized models in the existing literature. Our framework, termed causal message-passing, is grounded in high-dimensional approximate message-passing methodology. It is tailored for multiperiod experiments and is particularly effective in settings with many units and prevalent network interference. The framework models causal effects as a dynamic process where a treated unit's impact propagates through the network via neighboring units until equilibrium is reached. This approach allows us to approximate the dynamics of potential outcomes over time, enabling the extraction of valuable information before treatment effects reach equilibrium. Utilizing causal message-passing, we introduce a practical algorithm to estimate the total treatment effect, defined as the impact observed when all units are treated compared to the scenario where no unit receives treatment. We demonstrate the effectiveness of this approach across five numerical scenarios, each characterized by a distinct interference structure.

An encoding generative modeling approach to dimension reduction and covariate adjustment in causal inference with observational studies.

In this article, we develop CausalEGM, a deep learning framework for nonlinear dimension reduction and generative modeling of the dependency among covariate features affecting treatment and response. CausalEGM can be used for estimating causal effects in both binary and continuous treatment settings. By learning a bidirectional transformation between the high-dimensional covariate space and a low-dimensional latent space and then modeling the dependencies of different subsets of the latent variables on the treatment and response, CausalEGM can extract the latent covariate features that affect both treatment and response. By conditioning on these features, one can mitigate the confounding effect of the high dimensional covariate on the estimation of the causal relation between treatment and response. In a series of experiments, the proposed method is shown to achieve superior performance over existing methods in both binary and continuous treatment settings. The improvement is substantial when the sample size is large and the covariate is of high dimension. Finally, we established excess risk bounds and consistency results for our method, and discuss how our approach is related to and improves upon other dimension reduction approaches in causal inference.

Efficiently exploring the causal role of contextual moderators in behavioral science.

Behavioral science interventions have the potential to address longstanding policy problems, but their effects are typically heterogeneous across contexts (e.g., teachers, schools, and geographic regions). This contextual heterogeneity is poorly understood, however, which reduces the field's impact and its understanding of mechanisms. Here, we present an efficient way to interrogate heterogeneity and address these gaps in knowledge. This method a) presents scenarios that vividly represent different moderating contexts, b) measures a short-term behavioral outcome (e.g., an academic choice) that is known to relate to typical intervention outcomes (e.g., academic achievement), and c) assesses the causal effect of the moderating context on the link between the psychological variable typically targeted by interventions and this short-term outcome. We illustrated the utility of this approach across four experiments (total n = 3,235) that directly tested contextual moderators of the links between growth mindset, which is the belief that ability can be developed, and students' academic choices. The present results showed that teachers' growth mindset-supportive messages and the structural opportunities they provide moderated the link between students' mindsets and their choices (studies 1 to 3). This pattern was replicated in a nationally representative sample of adolescents and did not vary across demographic subgroups (study 2), nor was this pattern the result of several possible confounds (studies 3 to 4). Discussion centers on how this method of interrogating contextual heterogeneity can be applied to other behavioral science interventions and broaden their impact in other policy domains.

Estimating the total treatment effect in randomized experiments with unknown network structure.

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, and from public policy to the technology industry. 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 its neighbors' outcomes, an issue referred to as network interference or as nonindividualized treatment response. A key challenge in these situations is that the network is often unknown and difficult or costly to measure. We assume a potential outcomes model with heterogeneous additive network effects, encompassing a broad class of network interference sources, including spillover, peer effects, and contagion. First, we characterize the limitations in estimating the total treatment effect without knowledge of the network that drives interference. By contrast, we subsequently develop a simple estimator and efficient randomized design that outputs an unbiased estimate with low variance in situations where one is given access to average historical baseline measurements prior to the experiment. Our solution does not require knowledge of the underlying network structure, and it comes with statistical guarantees for a broad class of models. Due to their ease of interpretation and implementation, and their theoretical guarantees, we believe our results will have significant impact on the design of randomized experiments.

Heterogeneous treatment effect of dose-dense paclitaxel plus carboplatin therapy for advanced ovarian cancer.

A Japanese clinical trial (JGOG3016) showed that dose-dense weekly paclitaxel in combination with carboplatin extensively prolonged overall survival (OS) in patients with advanced ovarian cancer. However, in other clinical trials, dose-dense paclitaxel regimens were not superior to triweekly paclitaxel regimens. In this study, causal tree analysis was applied to explore subpopulations with different treatment effects of dose-dense paclitaxel in a data-driven approach. The 587 participants with stage II-IV ovarian cancer in the JGOG3016 trial were used for model development. The primary endpoint was treatment effect in terms of 3-year OS in patients receiving dose-dense vs. conventional paclitaxel therapies. In patients <50 years, the 3-year OS was similar in both groups; however, it was higher in the dose-dense group in patients ≥50 years. Dose-dense paclitaxel showed strong positive treatment effects in patients ≥50 years with stage II/III disease, BMI <23 kg/m2, non-CC/MC, and residual tumor ≥1 cm. In contrast, although there was no significant difference in OS; the 3-year OS rate was 23% lower in dose-dense paclitaxel than conventional paclitaxel in patients ≥60 years with stage IV cancer. Patients in this group had a particularly lower performance status than other groups. Our causal tree analysis suggested that poor prognosis groups represented by residual tumor tissue ≥1 cm benefit from dose-dense paclitaxel, whereas elderly patients with advanced disease and low-performance status are negatively impacted by dose-dense paclitaxel. These subpopulations will be of interest to future validation studies. Personalized treatments based on clinical features are expected to improve advanced ovarian cancer prognosis.

High-dimensional Iterative Causal Forest (hdiCF) for Subgroup Identification Using Health Care Claims Data.

We recently developed a machine-learning subgrouping algorithm, iterative causal forest (iCF), to identify subgroups with heterogeneous treatment effects (HTEs) using predefined covariates. However, such predefined covariates may miss or poorly define important features leading to inaccurate subgrouping. To address such limitations, we developed a new semi-automatic subgrouping algorithm, hdiCF, which adapts methodology from high-dimensional propensity score for feature recognition in claims data. The hdiCF algorithm has 3 steps: 1) high-dimensional feature identification by International Classification of Diseases, Current Procedural Terminology, and Anatomical Therapeutic Chemical codes (in/outpatient diagnoses, procedures, prescriptions) and creation of ordinal variables by frequency of occurrence; 2) propensity score trimming and high-dimensional feature preparation; 3) iCF implementation to identify subgroups. We applied hdiCF in a 20% random sample of fee-for-service Medicare beneficiaries who initiated sodium-glucose cotransporter-2 inhibitors (SGLT2i) or glucagon-like peptide-1 receptor agonists to identify subgroups with HTEs for incidence of hospitalized heart failure. HdiCF findings were consistent with studies suggesting SGLT2i to be more beneficial for patients with pre-existing heart failure or chronic kidney disease. HdiCF is not dependent on prior hypotheses about HTEs and identifies subgroups with markers for potential HTEs in real-world evidence studies where active-comparator, new-user study designs limit the potential for unmeasured confounding.

A generalizability score for aggregate causal effect.

Scientists frequently generalize population level causal quantities such as average treatment effect from a source population to a target population. When the causal effects are heterogeneous, differences in subject characteristics between the source and target populations may make such a generalization difficult and unreliable. Reweighting or regression can be used to adjust for such differences when generalizing. However, these methods typically suffer from large variance if there is limited covariate distribution overlap between the two populations. We propose a generalizability score to address this issue. The score can be used as a yardstick to select target subpopulations for generalization. A simplified version of the score avoids using any outcome information and thus can prevent deliberate biases associated with inadvertent access to such information. Both simulation studies and real data analysis demonstrate convincing results for such selection.

Doubly robust nonparametric instrumental variable estimators for survival outcomes.

Instrumental variable (IV) methods allow us the opportunity to address unmeasured confounding in causal inference. However, most IV methods are only applicable to discrete or continuous outcomes with very few IV methods for censored survival outcomes. In this article, we propose nonparametric estimators for the local average treatment effect on survival probabilities under both covariate-dependent and outcome-dependent censoring. We provide an efficient influence function-based estimator and a simple estimation procedure when the IV is either binary or continuous. The proposed estimators possess double-robustness properties and can easily incorporate nonparametric estimation using machine learning tools. In simulation studies, we demonstrate the flexibility and double robustness of our proposed estimators under various plausible scenarios. We apply our method to the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial for estimating the causal effect of screening on survival probabilities and investigate the causal contrasts between the two interventions under different censoring assumptions.

Doubly robust evaluation of high-dimensional surrogate markers.

When evaluating the effectiveness of a treatment, policy, or intervention, the desired measure of efficacy may be expensive to collect, not routinely available, or may take a long time to occur. In these cases, it is sometimes possible to identify a surrogate outcome that can more easily, quickly, or cheaply capture the effect of interest. Theory and methods for evaluating the strength of surrogate markers have been well studied in the context of a single surrogate marker measured in the course of a randomized clinical study. However, methods are lacking for quantifying the utility of surrogate markers when the dimension of the surrogate grows. We propose a robust and efficient method for evaluating a set of surrogate markers that may be high-dimensional. Our method does not require treatment to be randomized and may be used in observational studies. Our approach draws on a connection between quantifying the utility of a surrogate marker and the most fundamental tools of causal inference-namely, methods for robust estimation of the average treatment effect. This connection facilitates the use of modern methods for estimating treatment effects, using machine learning to estimate nuisance functions and relaxing the dependence on model specification. We demonstrate that our proposed approach performs well, demonstrate connections between our approach and certain mediation effects, and illustrate it by evaluating whether gene expression can be used as a surrogate for immune activation in an Ebola study.

Designing three-level cluster randomized trials to assess treatment effect heterogeneity.

Cluster randomized trials often exhibit a three-level structure with participants nested in subclusters such as health care providers, and subclusters nested in clusters such as clinics. While the average treatment effect has been the primary focus in planning three-level randomized trials, interest is growing in understanding whether the treatment effect varies among prespecified patient subpopulations, such as those defined by demographics or baseline clinical characteristics. In this article, we derive novel analytical design formulas based on the asymptotic covariance matrix for powering confirmatory analyses of treatment effect heterogeneity in three-level trials, that are broadly applicable to the evaluation of cluster-level, subcluster-level, and participant-level effect modifiers and to designs where randomization can be carried out at any level. We characterize a nested exchangeable correlation structure for both the effect modifier and the outcome conditional on the effect modifier, and generate new insights from a study design perspective for conducting analyses of treatment effect heterogeneity based on a linear mixed analysis of covariance model. A simulation study is conducted to validate our new methods and two real-world trial examples are used for illustrations.

Bayesian multiregional clinical trials using model averaging.

Multiregional clinical trials (MRCTs) provide the benefit of more rapidly introducing drugs to the global market; however, small regional sample sizes can lead to poor estimation quality of region-specific effects when using current statistical methods. With the publication of the International Conference for Harmonisation E17 guideline in 2017, the MRCT design is recognized as a viable strategy that can be accepted by regional regulatory authorities, necessitating new statistical methods that improve the quality of region-specific inference. In this article, we develop a novel methodology for estimating region-specific and global treatment effects for MRCTs using Bayesian model averaging. This approach can be used for trials that compare two treatment groups with respect to a continuous outcome, and it allows for the incorporation of patient characteristics through the inclusion of covariates. We propose an approach that uses posterior model probabilities to quantify evidence in favor of consistency of treatment effects across all regions, and this metric can be used by regulatory authorities for drug approval. We show through simulations that the proposed modeling approach results in lower MSE than a fixed-effects linear regression model and better control of type I error rates than a Bayesian hierarchical model.

Prediction of the treatment effect of FLASH radiotherapy with synchrotron radiation from the Circular Electron-Positron Collider (CEPC).

The Circular Electron-Positron Collider (CEPC) in China can also work as an excellent powerful synchrotron light source, which can generate high-quality synchrotron radiation. This synchrotron radiation has potential advantages in the medical field as it has a broad spectrum, with energies ranging from visible light to X-rays used in conventional radiotherapy, up to several megaelectronvolts. FLASH radiotherapy is one of the most advanced radiotherapy modalities. It is a radiotherapy method that uses ultra-high dose rate irradiation to achieve the treatment dose in an instant; the ultra-high dose rate used is generally greater than 40 Gy s-1, and this type of radiotherapy can protect normal tissues well. In this paper, the treatment effect of CEPC synchrotron radiation for FLASH radiotherapy was evaluated by simulation. First, a Geant4 simulation was used to build a synchrotron radiation radiotherapy beamline station, and then the dose rate that the CEPC can produce was calculated. A physicochemical model of radiotherapy response kinetics was then established, and a large number of radiotherapy experimental data were comprehensively used to fit and determine the functional relationship between the treatment effect, dose rate and dose. Finally, the macroscopic treatment effect of FLASH radiotherapy was predicted using CEPC synchrotron radiation through the dose rate and the above-mentioned functional relationship. The results show that the synchrotron radiation beam from the CEPC is one of the best beams for FLASH radiotherapy.

Time-dependent efficacy analysis of first-line immunotherapies for advanced non-small cell lung cancer.

BACKGROUND: Many randomized controlled trials (RCTs) and network meta-analyses have demonstrated that the progression-free survival (PFS) and overall survival (OS) of advanced non-small cell lung cancer (NSCLC) patients can be improved through combination immunotherapy or monotherapies. However, time-dependent analysis of the treatment effect is currently lacking. Thus, we aimed to evaluate the efficacy of first-line immunotherapy, and establish a hazard ratio function to reflect the time-varying progression or mortality risk of patients with NSCLC. METHODS: Seventeen clinical trials were selected based on search strategy. Baseline characteristics, including the age, sex, smoking status, geographical region, and Eastern Cooperative Oncology Group (ECOG) performance status of patients, were balanced, resulting in ten immunotherapies from nine appropriate clinical trials to conduct treatment effect comparison. RESULTS: We found that nivolumab plus ipilimumab (nivo + ipi) improved the PFS and OS over time. The hazard ratio of nivo + ipi, relative to that of pembrolizumab, decreased from 1.11 to 0.36 for PFS, and from 0.93 to 0.49 for OS over a 10-year period. In terms of the response to immunotherapy in patients with different PD-L1 expression levels, patients with PD-L1 > = 50% experienced lower rates of progression and a reduced mortality risk over time. The hazard ratio of patients with PD-L1 > = 50% relative to all of the patients decreased from 0.73 to 0.69 for PFS, and from 0.78 to 0.67 for OS. CONCLUSIONS: Based on the fact that time-dependent progression and mortality risk existed during the treatment duration, physicians should select a suitable treatment regimen for patients based on the hazard ratio.

Sequential covariate-adjusted randomization via hierarchically minimizing Mahalanobis distance and marginal imbalance.

In comparative studies, covariate balance and sequential allocation schemes have attracted growing academic interest. Although many theoretically justified adaptive randomization methods achieve the covariate balance, they often allocate patients in pairs or groups. To better meet the practical requirements where the clinicians cannot wait for other participants to assign the current patient for some economic or ethical reasons, we propose a method that randomizes patients individually and sequentially. The proposed method conceptually separates the covariate imbalance, measured by the newly proposed modified Mahalanobis distance, and the marginal imbalance, that is the sample size difference between the 2 groups, and it minimizes them with an explicit priority order. Compared with the existing sequential randomization methods, the proposed method achieves the best possible covariate balance while maintaining the marginal balance directly, offering us more control of the randomization process. We demonstrate the superior performance of the proposed method through a wide range of simulation studies and real data analysis, and also establish theoretical guarantees for the proposed method in terms of both the convergence of the imbalance measure and the subsequent treatment effect estimation.

Confounder-dependent Bayesian mixture model: Characterizing heterogeneity of causal effects in air pollution epidemiology.

Several epidemiological studies have provided evidence that long-term exposure to fine particulate matter (pm2.5) increases mortality rate. Furthermore, some population characteristics (e.g., age, race, and socioeconomic status) might play a crucial role in understanding vulnerability to air pollution. To inform policy, it is necessary to identify groups of the population that are more or less vulnerable to air pollution. In causal inference literature, the group average treatment effect (GATE) is a distinctive facet of the conditional average treatment effect. This widely employed metric serves to characterize the heterogeneity of a treatment effect based on some population characteristics. In this paper, we introduce a novel Confounder-Dependent Bayesian Mixture Model (CDBMM) to characterize causal effect heterogeneity. More specifically, our method leverages the flexibility of the dependent Dirichlet process to model the distribution of the potential outcomes conditionally to the covariates and the treatment levels, thus enabling us to: (i) identify heterogeneous and mutually exclusive population groups defined by similar GATEs in a data-driven way, and (ii) estimate and characterize the causal effects within each of the identified groups. Through simulations, we demonstrate the effectiveness of our method in uncovering key insights about treatment effects heterogeneity. We apply our method to claims data from Medicare enrollees in Texas. We found six mutually exclusive groups where the causal effects of pm2.5 on mortality rate are heterogeneous.

Multiply robust estimation of marginal structural models in observational studies subject to covariate-driven observations.

Electronic health records and other sources of observational data are increasingly used for drawing causal inferences. The estimation of a causal effect using these data not meant for research purposes is subject to confounding and irregularly-spaced covariate-driven observation times affecting the inference. A doubly-weighted estimator accounting for these features has previously been proposed that relies on the correct specification of two nuisance models used for the weights. In this work, we propose a novel consistent multiply robust estimator and demonstrate analytically and in comprehensive simulation studies that it is more flexible and more efficient than the only alternative estimator proposed for the same setting. It is further applied to data from the Add Health study in the United States to estimate the causal effect of therapy counseling on alcohol consumption in American adolescents.

How to achieve model-robust inference in stepped wedge trials with model-based methods?

A stepped wedge design is an unidirectional crossover design where clusters are randomized to distinct treatment sequences. While model-based analysis of stepped wedge designs is a standard practice to evaluate treatment effects accounting for clustering and adjusting for covariates, their properties under misspecification have not been systematically explored. In this article, we focus on model-based methods, including linear mixed models and generalized estimating equations with an independence, simple exchangeable, or nested exchangeable working correlation structure. We study when a potentially misspecified working model can offer consistent estimation of the marginal treatment effect estimands, which are defined nonparametrically with potential outcomes and may be functions of calendar time and/or exposure time. We prove a central result that consistency for nonparametric estimands usually requires a correctly specified treatment effect structure, but generally not the remaining aspects of the working model (functional form of covariates, random effects, and error distribution), and valid inference is obtained via the sandwich variance estimator. Furthermore, an additional g-computation step is required to achieve model-robust inference under non-identity link functions or for ratio estimands. The theoretical results are illustrated via several simulation experiments and re-analysis of a completed stepped wedge cluster randomized trial.

Evaluating individualized treatment effect predictions: A model-based perspective on discrimination and calibration assessment.

In recent years, there has been a growing interest in the prediction of individualized treatment effects. While there is a rapidly growing literature on the development of such models, there is little literature on the evaluation of their performance. In this paper, we aim to facilitate the validation of prediction models for individualized treatment effects. The estimands of interest are defined based on the potential outcomes framework, which facilitates a comparison of existing and novel measures. In particular, we examine existing measures of discrimination for benefit (variations of the c-for-benefit), and propose model-based extensions to the treatment effect setting for discrimination and calibration metrics that have a strong basis in outcome risk prediction. The main focus is on randomized trial data with binary endpoints and on models that provide individualized treatment effect predictions and potential outcome predictions. We use simulated data to provide insight into the characteristics of the examined discrimination and calibration statistics under consideration, and further illustrate all methods in a trial of acute ischemic stroke treatment. The results show that the proposed model-based statistics had the best characteristics in terms of bias and accuracy. While resampling methods adjusted for the optimism of performance estimates in the development data, they had a high variance across replications that limited their accuracy. Therefore, individualized treatment effect models are best validated in independent data. To aid implementation, a software implementation of the proposed methods was made available in R.

Assessing heterogeneity in surrogacy using censored data.

Determining whether a surrogate marker can be used to replace a primary outcome in a clinical study is complex. While many statistical methods have been developed to formally evaluate a surrogate marker, they generally do not provide a way to examine heterogeneity in the utility of a surrogate marker. Similar to treatment effect heterogeneity, where the effect of a treatment varies based on a patient characteristic, heterogeneity in surrogacy means that the strength or utility of the surrogate marker varies based on a patient characteristic. The few methods that have been recently developed to examine such heterogeneity cannot accommodate censored data. Studies with a censored outcome are typically the studies that could most benefit from a surrogate because the follow-up time is often long. In this paper, we develop a robust nonparametric approach to assess heterogeneity in the utility of a surrogate marker with respect to a baseline variable in a censored time-to-event outcome setting. In addition, we propose and evaluate a testing procedure to formally test for heterogeneity at a single time point or across multiple time points simultaneously. Finite sample performance of our estimation and testing procedure are examined in a simulation study. We use our proposed method to investigate the complex relationship between change in fasting plasma glucose, diabetes, and sex hormones using data from the diabetes prevention program study.

Flexible evaluation of surrogate markers with Bayesian model averaging.

When long-term follow up is required for a primary endpoint in a randomized clinical trial, a valid surrogate marker can help to estimate the treatment effect and accelerate the decision process. Several model-based methods have been developed to evaluate the proportion of the treatment effect that is explained by the treatment effect on the surrogate marker. More recently, a nonparametric approach has been proposed allowing for more flexibility by avoiding the restrictive parametric model assumptions required in the model-based methods. While the model-based approaches suffer from potential mis-specification of the models, the nonparametric method fails to give desirable estimates when the sample size is small, or when the range of the data does not follow certain conditions. In this paper, we propose a Bayesian model averaging approach to estimate the proportion of treatment effect explained by the surrogate marker. Our procedure offers a compromise between the model-based approach and the nonparametric approach by introducing model flexibility via averaging over several candidate models and maintains the strength of parametric models with respect to inference. We compare our approach with previous model-based methods and the nonparametric method. Simulation studies demonstrate the advantage of our method when surrogate supports are inconsistent and sample sizes are small. We illustrate our method using data from the Diabetes Prevention Program study to examine hemoglobin A1c as a surrogate marker for fasting glucose.