We extend Robins' theory of causal inference for complex longitudinal data to the case of continuously varying as opposed to discrete covariates and treatments. In particular we establish versions of the key results of the discrete theory: the g-computation formula and a collection of powerful characterizations of the g-null hypothesis of no treatment effect. This is accomplished under natural continuity hypotheses concerning the conditional distributions of the outcome variable and of the covariates given the past. We also show that our assumptions concerning counterfactual variables place no restriction on the joint distribution of the observed variables: thus in a precise sense, these assumptions are "for free," or if you prefer, harmless.
Causal effects may vary among individuals and can even be of opposite signs. When significant effect heterogeneity exists, the population average causal effect might be uninformative for an individual. Due to the fundamental problem of causality, individual causal effects (ICEs) cannot be retrieved from cross-sectional data. However, in crossover studies, it is accepted that ICEs can be estimated under the assumptions of no carryover effects and time invariance of potential outcomes. A generic potential-outcome formulation with appropriate statistical assumptions to identify ICEs is lacking fo…
A new class of Marginal Structural Models (MSMs), History-Restricted MSMs (HRMSMs), was recently introduced for longitudinal data for the purpose of defining causal parameters which may often be better suited for public health research or at least more practicable than MSMs \citejoffe,feldman. HRMSMs allow investigators to analyze the causal effect of a treatment on an outcome based on a fixed, shorter and user-specified history of exposure compared to MSMs. By default, the latter represent the treatment causal effect of interest based on a treatment history defined by the treatments assigned …
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…
Many causal models of interest in epidemiology involve longitudinal exposures, confounders and mediators. However, repeated measurements are not always available or used in practice, leading analysts to overlook the time-varying nature of exposures and work under over-simplified causal models. Our objective is to assess whether - and how - causal effects identified under such misspecified causal models relates to true causal effects of interest. We derive sufficient conditions ensuring that the quantities estimated in practice under over-simplified causal models can be expressed as weighted av…
Questions concerning mediated causal effects are of great interest in psychology, cognitive science, medicine, social science, public health, and many other disciplines. For instance, about 60% of recent papers published in leading journals in social psychology contain at least one mediation test (Rucker, Preacher, Tormala, & Petty, 2011). Standard parametric approaches to mediation analysis employ regression models, and either the "difference method" (Judd & Kenny, 1981), more common in epidemiology, or the "product method" (Baron & Kenny, 1986), more common in the social sciences. In this pa…
Analyses of biomedical studies often necessitate modeling longitudinal causal effects. The current focus on personalized medicine and effect heterogeneity makes this task even more challenging. Towards this end, structural nested mean models (SNMMs) are fundamental tools for studying heterogeneous treatment effects in longitudinal studies. However, when outcomes are binary, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal parameters and the non-causal nuisance parameters. This leads to a series of difficulties in int…
In this paper we propose a new template for empirical studies intended to assess causal effects: the outcome-wide longitudinal design. The approach is an extension of what is often done to assess the causal effects of a treatment or exposure using confounding control, but now, over numerous outcomes. We discuss the temporal and confounding control principles for such outcome-wide studies, metrics to evaluate robustness or sensitivity to potential unmeasured confounding for each outcome, and approaches to handle multiple testing. We argue that the outcome-wide longitudinal design has numerous a…
In animal behavior studies, a common goal is to investigate the causal pathways between an exposure and outcome, and a mediator that lies in between. Causal mediation analysis provides a principled approach for such studies. Although many applications involve longitudinal data, the existing causal mediation models are not directly applicable to settings where the mediators are measured on irregular time grids. In this paper, we propose a causal mediation model that accommodates longitudinal mediators on arbitrary time grids and survival outcomes simultaneously. We take a functional data analys…
Causal mediation analysis seeks to investigate how the treatment effect of an exposure on outcomes is mediated through intermediate variables. Although many applications involve longitudinal data, the existing methods are not directly applicable to settings where the mediator and outcome are measured on sparse and irregular time grids. We extend the existing causal mediation framework from a functional data analysis perspective, viewing the sparse and irregular longitudinal data as realizations of underlying smooth stochastic processes. We define causal estimands of direct and indirect effects…
A Bayesian semi-parametric approach to causal mediation for longitudinal mediators and time-to-event outcomes with application to a cardiovascular disease cohort study
The use of observational time series data to assess the impact of multi-time point interventions is becoming increasingly common as more health and activity data are collected and digitized via wearables, social media, and electronic health records. Such time series may involve hundreds or thousands of irregularly sampled observations. One common analysis approach is to simplify such time series by first discretizing them into sequences before applying a discrete-time estimation method that adjusts for time-dependent confounding. In certain settings, this discretization results in sequences wi…
Single-subject health data are becoming increasingly available thanks to advances in self-tracking technology (e.g., wearable devices, mobile apps, sensors, implants). Many users and health caregivers seek to use such observational time series data to recommend changing health practices in order to achieve desired health outcomes. However, there are few available causal inference approaches that are flexible enough to analyze such idiographic data. We develop a recently introduced causal-analysis framework based on n-of-1 randomized trials, and implement a flexible random-forests g-formula app…
Causal mediation analysis for zero-inflated longitudinal data in the presence of treatment non-compliance and multiple mediators
University of Chicago（芝加哥大学）；Smeal College of Business, The Pennsylvania State University（宾夕法尼亚州立大学斯米尔商学院）；University of Florida（佛罗里达大学）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
Centre for Big Data Research in Health (CBDRH)（健康大数据研究中心）
Causal inference for observational longitudinal studies often requires the accurate estimation of treatment effects on time-to-event outcomes in the presence of time-dependent patient history and time-dependent covariates. To tackle this longitudinal treatment effect estimation problem, we have developed a time-variant causal survival (TCS) model that uses the potential outcomes framework with an ensemble of recurrent subnetworks to estimate the difference in survival probabilities and its confidence interval over time as a function of time-dependent covariates and treatments. Using simulated …
Participant noncompliance, in which participants do not follow their assigned treatment protocol, often obscures the causal relationship between treatment and treatment effect in randomized trials. In the longitudinal setting, the G-computation algorithm can adjust for confounding to estimate causal effects. Typically, G-computation assumes that both 1) compliance is observed; and 2) the densities of the confounders can be correctly specified. We aim to develop a G-computation estimator in the setting where both assumptions are violated. For 1), in place of unobserved compliance, we substitute…
Operationalizing Longitudinal Causal Discovery Under Real-World Workflow Constraints
Kyoto University Graduate School of Medicine（京都大学医学研究科）；SANKEN The University of Osaka（SANKEN 大阪大学）；Faculty of Data Science Shiga University（Shiga大学数据科学学部）；AIP RIKEN；Faculty of Medicine, University of Miyazaki（Miyazaki大学医学部）；Hiroshima University Graduate School of Biomedical and Health Sciences（广岛大学生物医学和健康科学研究生院）
Causal Diffusion Models for Counterfactual Outcome Distributions in Longitudinal Data
Department of Economics, Northeastern University（东北大学经济学系）；Center for Health Policy and Healthcare Research, Northeastern University（东北大学健康政策与医疗研究中心）；Department of Public Health and Health Sciences, Bouvé College of Health Sciences, Northeastern University（东北大学布维健康科学学院公共卫生与健康科学系）
Pollutant emissions from coal-burning power plants have been deemed to adversely impact ambient air quality and public health conditions. Despite the noticeable reduction in emissions and the improvement of air quality since the Clean Air Act (CAA) became the law, the public-health benefits from changes in emissions have not been widely evaluated yet. In terms of the chain of accountability (HEI Accountability Working Group, 2003), the link between pollutant emissions from the power plants (SO2) and public health conditions (respiratory diseases) accounting for changes in ambient air quality (…
Most causal inference methods consider counterfactual variables under interventions that set the treatment deterministically. With continuous or multi-valued treatments or exposures, such counterfactuals may be of little practical interest because no feasible intervention can be implemented that would bring them about. Furthermore, violations to the positivity assumption, necessary for identification, are exacerbated with continuous and multi-valued treatments and deterministic interventions. In this paper we propose longitudinal modified treatment policies (LMTPs) as a non-parametric alternat…
Dynamic prediction of causal effects under different treatment regimes conditional on an individual's characteristics and longitudinal history is an essential problem in precision medicine. This is challenging in practice because outcomes and treatment assignment mechanisms are unknown in observational studies, an individual's treatment efficacy is a counterfactual, and the existence of selection bias is often unavoidable. We propose a Bayesian framework for identifying subgroup counterfactual benefits of dynamic treatment regimes by adapting Bayesian g-computation algorithm (J. Robins, 1986; …
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…
Université Paris-Saclay（巴黎-萨克雷大学）；CentraleSupélec（中央理工-高等电力学院）；Saint-Gobain（圣戈班）；Université de Lorraine（洛林大学）；Sorbonne Université（索邦大学）；CEA（法国原子能和替代能源委员会）
Correcting for confounding in longitudinal experiments: positioning non-linear mixed effects modeling as implementation of standardization using latent conditional exchangeability
Most work in causal inference considers deterministic interventions that set each unit's treatment to some fixed value. However, under positivity violations these interventions can lead to non-identification, inefficiency, and effects with little practical relevance. Further, corresponding effects in longitudinal studies are highly sensitive to the curse of dimensionality, resulting in widespread use of unrealistic parametric models. We propose a novel solution to these problems: incremental interventions that shift propensity score values rather than set treatments to fixed values. Incrementa…
Doubly Robust Functional Representation Learning for Longitudinal Causal Inference with Irregular Histories
Academy of Life and Natural Sciences, Xi’an Jiaotong-Liverpool University（西交利物浦大学生命与自然科学学院）；Aerospace Information Research Institute, Chinese Academy of Sciences（中国科学院空天信息研究院）
Causal inference with observational longitudinal data and time-varying exposures is often complicated by time-dependent confounding and attrition. The G-computation formula is one approach for estimating a causal effect in this setting. The parametric modeling approach typically used in practice relies on strong modeling assumptions for valid inference, and moreover depends on an assumption of missing at random, which is not appropriate when the missingness is missing not at random (MNAR) or due to death. In this work we develop a flexible Bayesian semi-parametric G-computation approach for as…
Living forwards or understanding backwards? A comparison of Inverse Probability of Treatment Weighting and G-estimation methods for targeting hypothetical full adherence estimands in longitudinal cohort studies
A sensitivity analysis approach to principal stratification with a continuous longitudinal intermediate outcome: Applications to a cohort stepped wedge trial
Observational longitudinal data on treatments and covariates are increasingly used to investigate treatment effects, but are often subject to time-dependent confounding. Marginal structural models (MSMs), estimated using inverse probability of treatment weighting or the g-formula, are popular for handling this problem. With increasing development of advanced causal inference methods, it is important to be able to assess their performance in different scenarios to guide their application. Simulation studies are a key tool for this, but their use to evaluate causal inference methods has been lim…
Evaluating treatment effects on longitudinal outcomes with attrition due to death: Methods for a two-dimentional estimand with a case study in Quality of Life
Ghent University（根特大学）；Leiden University Medical Center（莱顿大学医学中心）；Pfizer Inc（辉瑞公司）；Oslo University Hospital（奥斯陆大学医院）；European Organisation for Research and Treatment of Cancer (EORTC) Headquarters（欧洲癌症研究与治疗组织（EORTC）总部）；University of Freiburg（弗赖堡大学）
