Controlling for time-varying confounding in the longitudinal fixed-effects model: A latent variable approach

Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal effects. Underlying this recent body of literature on Bayesian propensity score estimation is an implicit discordance between the goal of the propensity score and the use of Bayes’ theorem. The propensity score condenses multivariate covariate information into a scalar to allow estimation of causal effects without specifying a model for how each covariate relates to the outcome. Avoiding specification of a detailed model for the outcome response surface is valuable for robust estimation of causal effects, but this strategy is at odds with the use of Bayes’ theorem, which presupposes a full probability model for the observed data that adheres to the likelihood principle. The goal of this article is to explicate this fundamental feature of Bayesian estimation of causal effects with propensity scores to provide context for the existing literature and for future work on this important topic.[Received June 2014. Revised September 2015.]

BackgroundCausal inference has seen an increasing popularity in medical research. Estimation of causal effects from observational data allows to draw conclusions from data when randomized controlled trials cannot be conducted. Although the identification of structural causal models (SCM) and the calculation of structural coefficients has received much attention, a key requirement for valid causal inference is that conclusions are drawn based on the true data-generating model.MethodsIt remains widely unknown how large the probability is to reject the true structural causal model when observational data from it is sampled. The latter probability – the causal false-positive risk – is crucial, as rejection of the true causal model can induce bias in the estimation of causal effects. In this paper, the widely used causal models of confounders and colliders are studied regarding their causal false-positive risk in linear Markovian models. A simulation study is carried out which investigates the causal false-positive risk in Gaussian linear Markovian models. Therefore, the testable implications of the DAG corresponding to confounders and colliders are analyzed from a Bayesian perspective. Furthermore, the induced bias in estimating the structural coefficients and causal effects is studied.ResultsResults show that the false-positive risk of rejecting a true SCM of even simple building blocks like confounders and colliders is substantial. Importantly, estimation of average, direct and indirect causal effects can become strongly biased if a true model is rejected. The causal false-positive risk may thus serve as an indicator or proxy for the induced bias.ConclusionWhile the identification of structural coefficients and testable implications of causal models have been studied rigorously in the literature, this paper shows that causal inference also must develop new concepts for controlling the causal false-positive risk. Although a high risk cannot be equated with a substantial bias, it is indicative of the induced bias. The latter fact calls for the development of more advanced risk measures for committing a causal type I error in causal inference.

Nonrandom selection in one-sample Mendelian Randomization (MR) results in biased estimates and inflated type I error rates only when the selection effects are sufficiently large. In two-sample MR, the different selection mechanisms in two samples may more seriously affect the causal effect estimation. Firstly, we propose sufficient conditions for causal effect invariance under different selection mechanisms using two-sample MR methods. In the simulation study, we consider 49 possible selection mechanisms in two-sample MR, which depend on genetic variants (G), exposures (X), outcomes (Y) and their combination. We further compare eight pleiotropy-robust methods under different selection mechanisms. Results of simulation reveal that nonrandom selection in sample II has a larger influence on biases and type I error rates than those in sample I. Furthermore, selections depending on X+Y, G+Y, or G+X+Y in sample II lead to larger biases than other selection mechanisms. Notably, when selection depends on Y, bias of causal estimation for non-zero causal effect is larger than that for null causal effect. Especially, the mode based estimate has the largest standard errors among the eight methods. In the absence of pleiotropy, selections depending on Y or G in sample II show nearly unbiased causal effect estimations when the casual effect is null. In the scenarios of balanced pleiotropy, all eight MR methods, especially MR-Egger, demonstrate large biases because the nonrandom selections result in the violation of the Instrument Strength Independent of Direct Effect (InSIDE) assumption. When directional pleiotropy exists, nonrandom selections have a severe impact on the eight MR methods. Application demonstrates that the nonrandom selection in sample II (coronary heart disease patients) can magnify the causal effect estimation of obesity on HbA1c levels. In conclusion, nonrandom selection in two-sample MR exacerbates the bias of causal effect estimation for pleiotropy-robust MR methods.

We provide sufficient conditions for estimating from longitudinal data the causal effect of a time-dependent exposure or treatment on the marginal probability of response for a dichotomous outcome. We then show how one can estimate this effect under these conditions using the g-computation algorithm of Robins. We also derive the conditions under which some current approaches to the analysis of longitudinal data, such as the generalized estimating equations (GEE) approach of Zeger and Liang, the feedback model techniques of Liang and Zeger, and within-subject conditional methods, can provide valid tests and estimates of causal effects. We use our methods to estimate the causal effect of maternal stress on the marginal probability of a child's illness from the Mothers' Stress and Children's Morbidity data and compare our results with those previously obtained by Zeger and Liang using a GEE approach.

Causal discovery and effect estimation for time series provide scientists with a way to extract causal information from observational studies when possible. But the high dimensionality of raw climate data causes computational problems for most analysis methods, and causal inference is no exception. To address this problem, climate scientists usually pre-process climate data using dimension reduction techniques (including seasonal and regional averaging and principle component analysis) that may result in the loss of valuable information before the true analysis even begins. For example, climate scientists often represent El Niño Southern Oscillation variability (ENSO) using the uni-variate Nino3.4 index, which cannot distinguish between central Pacific and eastern Pacific El Niño events, which are believed to impact global climate varaibility in different ways. This study introduces a method for avoiding premature data dimension reduction in causal effect estimation, implemented in tigramite. The method allows the researcher to define multi-variate climate indices, reducing the dimensionality of the causal inference problem via the causal assumptions instead of losing information from the data itself. To investigate the performance of this approach on climate data, we examine the effect of ENSO on the North Atlantic Oscillation (NAO) in simulated data from the Coupled Model Intercomparison Project, phase 6. We choose this as our case study because different types of El Nino are believed to have very different effects on NAO, to the extent that the impact may be completely undetectable in observations when no distinction between the types of ENSO is made. By comparing estimated effects using uni- and multi-variate climate indices, we demonstrate that this method retains valuable information that would be lost in uni-variate analysis, and make recommendations for best practices when using multi-variate climate indices in causal effect estimation.

In observational studies, covariates are often confounding factors for treatment assignment. Such covariates need to be adjusted to estimate the causal treatment effect. For observational studies with survival outcomes, it is usually more challenging to adjust for the confounding covariates for causal effect estimation because of censoring. The challenge becomes even thornier when there exists a nonignorable cure fraction in the population. In this paper, we propose a causal effect estimation approach in observational studies for survival data with a cure fraction. We extend the absolute treatment effects on survival outcomes-including the restricted average causal effect and SPCE-to survival outcomes with cure fractions, and construct the corresponding causal effect estimators based on propensity score stratification. We prove the asymptotic properties of the proposed estimators and conduct simulation studies to evaluate their performances. As an illustration, the method is applied to a stomach cancerstudy.

This paper discusses the problem of causal query in observational data with hidden variables, with the aim of seeking the change of an outcome when "manipulating" a variable while given a set of plausible confounding variables which affect the manipulated variable and the outcome. Such an "experiment on data" to estimate the causal effect of the manipulated variable is useful for validating an experiment design using historical data or for exploring confounders when studying a new relationship. However, existing data-driven methods for causal effect estimation face some major challenges, including poor scalability with high dimensional data, low estimation accuracy due to heuristics used by the global causal structure learning algorithms, and the assumption of causal sufficiency when hidden variables are inevitable in data. In this paper, we develop a theorem for using local search to find a superset of the adjustment (or confounding) variables for causal effect estimation from observational data under a realistic pretreatment assumption. The theorem ensures that the unbiased estimate of causal effect is included in the set of causal effects estimated by the superset of adjustment variables. Based on the developed theorem, we propose a data-driven algorithm for causal query. Experiments show that the proposed algorithm is faster and produces better causal effect estimation than an existing data-driven causal effect estimation method with hidden variables. The causal effects estimated by the proposed algorithm are as accurate as those by the state-of-the-art methods using domain knowledge.

پتانسیل تجاری اتحادیه اکو: کاربردی از رگرسیون فضایی پویا با در نظرگرفتن اثرات سرریز فضایی

Propensity score methods are an important tool to help reduce confounding in nonexperimental studies. Most propensity score methods assume that covariates are measured without error. However, covariates are often measured with error, which leads to biased causal effect estimates if the true underlying covariates are the actual confounders. Although some groups have investigated the impact of a single mismeasured covariate on estimating a causal effect and proposed methods for handling the measurement error, fewer have investigated the case where multiple covariates are mismeasured, and we found none that discussed correlated measurement errors. In this study, we examined the consequences of multiple error-prone covariates when estimating causal effects using propensity score-based estimators via extensive simulation studies and real data analyses. We found that causal effect estimates are less biased when the propensity score model includes mismeasured covariates whose true underlying values are strongly correlated with each other. However, when the measurement errors are correlated with each other, additional bias is introduced. In addition, it is beneficial to include correctly measured auxiliary variables that are correlated with confounders whose true underlying values are mismeasured in the propensity score model.

When launching a new product, historical sales data are often not available, leaving price as a crucial experimental instrument for sellers to gauge market response. When designing pricing experiments, there are three fundamental objectives: estimating the causal effect of price (i.e., price elasticity), maximizing the expected revenue through the experiment, and controlling the tail risk that, if not controlled, may lead to significant financial losses. In this paper, we reveal the relationship among such three objectives. Under a linear structural model, we investigate the trade-offs between causal effect estimation and expected revenue maximization, as well as between expected revenue maximization and tail risk control. Furthermore, we propose an optimal pricing experimental design, which can flexibly adapt to different desired levels of trade-offs. Through the optimal design, we also explore the relationship between causal effect estimation and tail risk control. Moreover, we establish an always-valid confidence sequence and a central limit theorem for the inference of the causal effect. Finally, we extend our results and the design to a misspecified setting, where the structural model is not necessarily linear but the seller still runs our design for linear structural models. The results demonstrate the robustness of our design and the wide existence of the relationships among the three objectives. This paper was accepted by George Shanthikumar, data science. Funding: The authors thank the Massachusetts Institute of Technology (MIT)-IBM partnership in Artificial Intelligence and the MIT Data Science Laboratory for support. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.03209 .

We study identification and estimation of causal effects in settings with panel data. Traditionally researchers follow model-based identification strategies relying on assumptions governing the relation between the potential outcomes and the unobserved confounders. We focus on a novel, complementary, approach to identification where assumptions are made about the relation between the treatment assignment and the unobserved confounders. We introduce different sets of assumptions that follow the two paths to identification, and develop a double robust approach. We propose estimation methods that build on these identification strategies.

SummaryWe study identification and estimation of causal effects in settings with panel data. Traditionally, researchers follow model-based identification strategies relying on assumptions governing the relation between the potential outcomes and the observed and unobserved confounders. We focus on a different, complementary approach to identification, where assumptions are made about the connection between the treatment assignment and the unobserved confounders. Such strategies are common in cross-section settings, but rarely used with panel data. We introduce different sets of assumptions that follow the two paths to identification and develop a double robust approach. We propose estimation methods that build on these identification strategies.

BackgroundConfounders can produce spurious associations between exposure and outcome in observational studies. For majority of epidemiologists, adjusting for confounders using logistic regression model is their habitual method, though it has some problems in accuracy and precision. It is, therefore, important to highlight the problems of logistic regression and search the alternative method.MethodsFour causal diagram models were defined to summarize confounding equivalence. Both theoretical proofs and simulation studies were performed to verify whether conditioning on different confounding equivalence sets had the same bias-reducing potential and then to select the optimum adjusting strategy, in which logistic regression model and inverse probability weighting based marginal structural model (IPW-based-MSM) were compared. The “do-calculus” was used to calculate the true causal effect of exposure on outcome, then the bias and standard error were used to evaluate the performances of different strategies.ResultsAdjusting for different sets of confounding equivalence, as judged by identical Markov boundaries, produced different bias-reducing potential in the logistic regression model. For the sets satisfied G-admissibility, adjusting for the set including all the confounders reduced the equivalent bias to the one containing the parent nodes of the outcome, while the bias after adjusting for the parent nodes of exposure was not equivalent to them. In addition, all causal effect estimations through logistic regression were biased, although the estimation after adjusting for the parent nodes of exposure was nearest to the true causal effect. However, conditioning on different confounding equivalence sets had the same bias-reducing potential under IPW-based-MSM. Compared with logistic regression, the IPW-based-MSM could obtain unbiased causal effect estimation when the adjusted confounders satisfied G-admissibility and the optimal strategy was to adjust for the parent nodes of outcome, which obtained the highest precision.ConclusionsAll adjustment strategies through logistic regression were biased for causal effect estimation, while IPW-based-MSM could always obtain unbiased estimation when the adjusted set satisfied G-admissibility. Thus, IPW-based-MSM was recommended to adjust for confounders set.

Synthesizing Subject-matter Expertise for Variable Selection in Causal Effect Estimation: A Case Study.

Causal effects estimation is one of the central problems in real clinical data analysis. Outcome regression and inverse probability weighting are two basic strategies to estimate causal effects in observational studies. The former suffers the problem of implicitly making extrapolation and the latter encounters the problem of volatility in the presence of extreme weights (some propensity score values are close to 0 or 1), which sometimes occurs in clinical data. In this work, we propose two asymptotically equivalent semiparametric estimators of average causal effects based on propensity score. The proposed approaches apply machine learning techniques to estimate propensity score and can circumvent the problem of model extrapolation. It is easy to implement and robust to extreme weights. The proposed estimators are shown to be consistent and asymptotically normal, and the asymptotic variances can also be estimated. In addition, the proposed estimators enjoy the property of quasi-oracle: the resulting estimators of average causal effects based on estimated propensity score are asymptotically indistinguishable from the estimators with true propensity score. Simulation studies and empirical applications further demonstrate the advantages of the proposed methods compared with competing ones.