Inverse probability (IP) weighting of marginal structural models (MSMs) can provide consistent estimators of time-varying treatment effects under correct model specifications and identifiability assumptions, even in the presence of time-varying confounding. However, this method has two problems: (i) inefficiency due to IP-weights cumulating all time points and (ii) bias and inefficiency due to the MSM misspecification. To address these problems, we propose (i) new IP-weights for estimating parameters of the MSM that depends on partial treatment history and (ii) closed testing procedures for selecting partial treatment history (how far back in time the MSM depends on past treatments). We derive the theoretical properties of our proposed methods under known IP-weights and discuss their extension to estimated IP-weights. Although some of our theoretical results are derived under additional assumptions beyond standard identifiability assumptions, some of which can be checked empirically from the data. In simulation studies, our proposed methods outperformed existing methods both in terms of performance in estimating time-varying treatment effects and in selecting partial treatment history. Our proposed methods have also been applied to real data of hemodialysis patients with reasonable results.
Robins 1997 introduced marginal structural models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding. In his work, identification of MSM parameters is established under a sequential randomization assumption (SRA), which rules out unmeasured confounding of treatment assignment over time. We consider sufficient conditions for identification of the parameters of a subclass, Marginal Structural Mean Models (MSMMs), when sequential randomization fails to hold due to unmeasured c…
Estimating marginal treatment effects from observational studies and indirect treatment comparisons: When are standardization-based methods preferable to those based on propensity score weighting?
Objectives: Clinical prediction models (CPMs) can inform decision-making concerning treatment initiation. Here, one requires predicted risks assuming that no treatment is given. This is challenging since CPMs are often derived in datasets where patients receive treatment; moreover, treatment can commence post-baseline - treatment drop-ins. This study presents a novel approach of using marginal structural models (MSMs) to adjust for treatment drop-in. Study Design and Setting: We illustrate the use of MSMs in the CPM framework through simulation studies, representing randomised controlled trial…
In observational studies, treatments are typically not randomized and therefore estimated treatment effects may be subject to confounding bias. The instrumental variable (IV) design plays the role of a quasi-experimental handle since the IV is associated with the treatment and only affects the outcome through the treatment. In this paper, we present a novel framework for identification and inference using an IV for the marginal average treatment effect amongst the treated (ETT) in the presence of unmeasured confounding. For inference, we propose three different semiparametric approaches: (i) i…
Marginal structural models (MSMs) with inverse probability weighting offer an approach to estimating causal effects of treatment sequences on repeated outcome measures in the presence of time-varying confounding and dependent censoring. However, when weights are estimated by maximum likelihood, inverse probability weighted estimators (IPWEs) can be inefficient and unstable in practice. We propose a joint calibration approach for inverse probability of treatment and censoring weights to improve the efficiency and robustness of the IPWEs for MSMs with time-varying treatments of arbitrary (i.e., …
This paper studies treatment effect models in which individuals are classified into unobserved groups based on heterogeneous treatment rules. Using a finite mixture approach, we propose a marginal treatment effect (MTE) framework in which the treatment choice and outcome equations can be heterogeneous across groups. Under the availability of instrumental variables specific to each group, we show that the MTE for each group can be separately identified. Based on our identification result, we propose a two-step semiparametric procedure for estimating the group-wise MTE. We illustrate the usefuln…
Robins (1998) introduced marginal structural models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding. He established identification of MSM parameters under a sequential randomization assumption (SRA), which essentially rules out unmeasured confounding of treatment assignment over time. In this technical report, we consider sufficient conditions for identification of MSM parameters with the aid of a time-varying instrumental variable, when sequential randomization fails to…
The distribution of treatment effects (DTE) is often of interest in the context of welfare policy evaluation. In this paper, I consider partial identification of the DTE under known marginal distributions and support restrictions on the potential outcomes. Examples of such support restrictions include monotone treatment response, concave treatment response, convex treatment response, and the Roy model of self-selection. To establish informative bounds on the DTE, I formulate the problem as an optimal transportation linear program and develop a new dual representation to characterize the identi…
In this commentary, we highlight the importance of: (1) carefully considering and clarifying whether a marginal or conditional treatment effect is of interest in a population-adjusted indirect treatment comparison; and (2) developing distinct methodologies for estimating the different measures of effect. The appropriateness of each methodology depends on the preferred target of inference.
Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the population of …
In the statistical literature, a number of methods have been proposed to ensure valid inference about marginal effects of variables on a longitudinal outcome in settings with irregular monitoring times. However, the potential biases due to covariate-driven monitoring times and confounding have rarely been considered simultaneously, and never in a setting with an ordinal outcome and a continuous exposure. In this work, we propose and demonstrate a methodology for causal inference in such a setting, relying on a proportional odds model to study the effect of the exposure on the outcome. Irregula…
Propensity score methods are increasingly being used to reduce estimation bias of treatment effects for observational studies. Previous research has shown that propensity score methods consistently estimate the marginal hazard ratio for time to event data. However, recurrent data frequently arise in the biomedical literature and there is a paucity of research into the use of propensity score methods when data are recurrent in nature. The objective of this paper is to extend the existing propensity score methods to recurrent data setting. We illustrate our methods through a series of Monte Carl…
Marginal structural models are a popular tool for investigating the effects of time-varying treatments, but they require an assumption of no unobserved confounders between the treatment and outcome. With observational data, this assumption may be difficult to maintain, and in studies with panel data, many researchers use fixed effects models to purge the data of time-constant unmeasured confounding. Unfortunately, traditional linear fixed effects models are not suitable for estimating the effects of time-varying treatments, since they can only estimate lagged effects under implausible assumpti…
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 …
We provide sufficient conditions for the identification of the heterogeneous treatment effects, defined as the conditional expectation for the differences of potential outcomes given the untreated outcome, under the nonignorable treatment condition and availability of the information on the marginal distribution of the untreated outcome. These functions are useful both to identify the average treatment effects (ATE) and to determine the treatment assignment policy. The identification holds in the following two general setups prevalent in applied studies: (i) a randomized controlled trial with …
Treatment-induced confounders complicate analyses of time-varying treatment effects and causal mediation. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between treatment and the outcome, leading to bias. Although several methods for estimating marginal effects avoid these complications, including inverse-probability-of-treatment-weighted (IPTW) estimation of marginal structural models (MSMs) as well as g- and regression-with-residuals (RWR) estimation of highly constrained structural nested me…
Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is based on propensity score weighting, which is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average th…
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…
I analyze treatment effects in situations when agents endogenously select into the treatment group and into the observed sample. As a theoretical contribution, I propose pointwise sharp bounds for the marginal treatment effect (MTE) of interest within the always-observed subpopulation under monotonicity assumptions. Moreover, I impose an extra mean dominance assumption to tighten the previous bounds. I further discuss how to identify those bounds when the support of the propensity score is either continuous or discrete. Using these results, I estimate bounds for the MTE of the Job Corps Traini…
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…
When making causal inferences, post-treatment confounders complicate analyses of time-varying treatment effects. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between treatment and the outcome, leading to bias. To avoid such bias, researchers often use marginal structural models (MSMs) with inverse probability weighting (IPW). However, IPW requires models for the conditional distributions of treatment and is highly sensitive to their misspecification. Moreover, IPW is relatively inefficient, s…
Marginal structural models (MSMs) estimate the causal effect of a time-varying treatment in the presence of time-dependent confounding via weighted regression. The standard approach of using inverse probability of treatment weighting (IPTW) can lead to high-variance estimates due to extreme weights and be sensitive to model misspecification. Various methods have been proposed to partially address this, including truncation and stabilized-IPTW to temper extreme weights and covariate balancing propensity score (CBPS) to address treatment model misspecification. In this paper, we present Kernel O…
We propose a model-free framework for sensitivity analysis of individual treatment effects (ITEs), building upon ideas from conformal inference. For any unit, our procedure reports the $Γ$-value, a number which quantifies the minimum strength of confounding needed to explain away the evidence for ITE. Our approach rests on the reliable predictive inference of counterfactuals and ITEs in situations where the training data is confounded. Under the marginal sensitivity model of Tan (2006), we characterize the shift between the distribution of the observations and that of the counterfactuals. We f…
Due to unmeasured confounding, it is often not possible to identify causal effects from a postulated model. Nevertheless, we can ask for partial identification, which usually boils down to finding upper and lower bounds of a causal quantity of interest derived from all solutions compatible with the encoded structural assumptions. One appealing way to derive such bounds is by casting it in terms of a constrained optimization method that searches over all causal models compatible with evidence, as introduced in the classic work of Balke and Pearl (1994) for discrete data. Although by constructio…
Does your cost-effectiveness model answer the question of interest? Marginal versus conditional inputs and transportability across populations
University of California, San Francisco（旧金山加利福尼亚大学）；UCSF Helen Diller Family Comprehensive Cancer Center, University of California, San Francisco（旧金山加利福尼亚大学 UCSF 海伦·迪勒家庭综合癌症中心）；The Philip R. Lee Institute for Health Policy Studies, University of California, San Francisco（旧金山加利福尼亚大学菲利普·李卫生政策研究所）；Health Economics & Outcomes Research（健康经济学与结果研究）；University of British Columbia, Vancouver, Canada（不列颠哥伦比亚大学）；University of Bristol, UK（布里斯托大学）；Novo Nordisk Pharma, Madrid, Spain（诺和诺德制药）；University College London, UK（伦敦大学学院）
In cohort studies, non-random medication use can pose barriers to estimation of the natural history trend in a mean biomarker value (namely, the association between a predictor of interest and a biomarker outcome that would be observed in the absence of biomarker-specific treatment). Common causes of treatment and outcomes are often unmeasured, obscuring our ability to easily account for medication use with commonly invoked assumptions such as ignorability. Further, absent some variable satisfying the exclusion restriction, use of instrumental variable approaches may be difficult to justify. H…
Marginal structural models fit via inverse probability of treatment weighting are commonly used to control for confounding when estimating causal effects from observational data. When planning a study that will be analyzed with marginal structural modeling, determining the required sample size for a given level of statistical power is challenging because of the effect of weighting on the variance of the estimated causal means. This paper considers the utility of the design effect to quantify the effect of weighting on the precision of causal estimates. The design effect is defined as the ratio…
Randomized clinical trials (RCTs) are ideal for estimating causal effects, because the distributions of background covariates are similar in expectation across treatment groups. When estimating causal effects using observational data, matching is a commonly used method to replicate the covariate balance achieved in a RCT. Matching algorithms have a rich history dating back to the mid-1900s, but have been used mostly to estimate causal effects between two treatment groups. When there are more than two treatments, estimating causal effects requires additional assumptions and techniques. We propo…
Optimal treatment regimes are personalized policies for making a treatment decision based on subject characteristics, with the policy chosen to maximize some value. It is common to aim to maximize the mean outcome in the population, via a regime assigning treatment only to those whose mean outcome is higher under treatment versus control. However, the mean can be an unstable measure of centrality, resulting in imprecise statistical procedures, as well as unrobust decisions that can be overly influenced by a small fraction of subjects. In this work, we propose a new median optimal treatment reg…
Patients with end-stage kidney disease can expect to wait for several years before they receive a transplant, all the while their health deteriorates. How would the survival change if we managed to reduce these waiting times? To provide an answer, we present a continuous-time marginal structural model (MSM) of hypothetical scenarios in which the time until treatment is changed. In these scenarios, the treatment process is defined on a hypothetical time scale where time passes at a different rate compared to the time actually observed. Changing the time of the treatment process corresponds to c…
Contrasting marginal counterfactual survival curves across treatment arms is an effective and popular approach for inferring the causal effect of an intervention on a right-censored time-to-event outcome. A key challenge to drawing such inferences in observational settings is the possible existence of unmeasured confounding, which may invalidate most commonly used methods that assume no hidden confounding bias. In this paper, rather than making the standard no unmeasured confounding assumption, we extend the recently proposed proximal causal inference framework of Miao et al. (2018), Tchetgen …
