Statistical approaches for causal inference

In sequential causal inference, two types of causal effects are of practical interest, namely, the causal effect of the treatment regime (called the sequential causal effect) and the blip effect of treatmenton on the potential outcome after the last treatment. The well-known G-formula expresses these causal effects in terms of the standard paramaters. In this article, we obtain a new G-formula that expresses these causal effects in terms of the point observable effects of treatments similar to treatment in the framework of single-point causal inference. Based on the new G-formula, we estimate these causal effects by maximum likelihood via point observable effects with methods extended from single-point causal inference. We are able to increase precision of the estimation without introducing biases by an unsaturated model imposing constraints on the point observable effects. We are also able to reduce the number of point observable effects in the estimation by treatment assignment conditions.

Psychologists have long had interest in the processes through which antecedent variables produce their effects on the outcomes of ultimate interest (e.g., Wood-worth's Stimulus-Organism-Response model). Models involving such meditational processes have characterized many of the important psychological theories of the 20th century and continue to the present day. However, it was not until Judd and Kenny (1981) and Baron and Kenny (1986) combined ideas from experimental design and structural equation modeling that statistical methods for directly testing such models, now known as mediation analysis, began to be developed. Methodologists have improved these statistical methods, developing new, more efficient estimators for mediated effects. They have also extended mediation analysis to multilevel data structures, models involving multiple mediators, models in which interactions occur, and an array of noncontinuous outcome measures (see MacKinnon, 2008). This work nicely maps on to key questions of applied researchers and has led to an outpouring of research testing meditational models (As of August, 2011, Baron and Kenny's article has had over 24,000 citations according to Google Scholar).

This paper reviews recent research on causal inference with large-scale assessments in education from a Bayesian perspective. I begin by adopting the potential outcomes model of Rubin (J Educ Psychol 66:688–701, 1974) as a framework for causal inference that I argue is appropriate with large-scale educational assessments. I then discuss the elements of Bayesian inference arguing that methods and models of causal inference can benefit from the Bayesian approach to quantifying uncertainty. Next I outline one method of causal inference that I believe is fruitful for addressing causal questions with large-scale educational assessments within the potential outcomes framework— namely, propensity score analysis. I then discuss the quantification of uncertainty in propensity score analysis through a Bayesian approach. Next, I discuss a series of necessary conditions for addressing causal questions with large-scale educational assessments. The paper closes with a discussion of the implications for the design of large-scale educational assessments when the goal is in asking causal questions and warranting causal claims.

Although causal Bayes networks are applicable to examining causal inferences about different static objects and about a changing object with different states, previous studies investigated the former, but not the latter. We propose a situation-modulated minimal change account for causal inferences. It predicts that dynamic situations are more likely to elicit minimal revisions on causal networks and adherence to the Markov assumption than static situations. Two experiments were conducted to investigate qualitative causal inferences about causal networks with binary and numerical variables, respectively. It was found that qualitative causal inferences were more likely to adhere to the Markov assumption in dynamic situations than in static situations. This finding supports the situation-modulated minimal change account rather than the other alternative accounts. We conclude that dynamic situations are more likely to elicit minimal revisions on causal networks and adherence to the Markov assumption than static situations. This conclusion is beyond the previous predominant view that causal inferences are apt to violate the Markov assumption.

Based on benchmarking various methods and analyzing multiple real scRNA-seq datasets, a computational platform/workflow and a set of tips for best practices are developed for analyzing causal interactions or relationships in single cells.

The central thesis of this book is that causal inferences based on careful integrative multi-method research designs have advantages over similar inferences that rely on only one method. A necessary first step in making this argument is showing that many applications of qualitative and quantitative methods in the social sciences share an underlying notion of causation. If causation in these two methodological traditions is fundamentally not the same sort of relation, then there is good reason to worry that they cannot contribute to a joint causal project. Indeed, given such fundamentally divergent worldviews, it is unclear that the methods could even contribute to testing each others’ assumptions – the central theme of integrative multi-method research designs. I argue below that the potential-outcomes framework, in which causal effects are characterized as the difference between what actually happens in a given case and what would have happened had that case been assigned to a different treatment category, can serve as that notion. After introducing this concept, I argue that stereotypically qualitative and quantitative causal thinking can be seen as sharing an underlying conceptual structure. The potential-outcomes framework is used to explicate causal models and hypotheses throughout the book. Existing work on the potential-outcomes framework has produced clear insights into the challenges of causal inference. Most famously, authors have pointed to the fundamental problem of causal inference: because it is impossible to observe both what does happen to a case in reality and what would have happened to that case had the independent variable been assigned a different value, no direct empirical observation of causation at the case level is possible (Holland 1986). Prior research also provides detailed findings regarding the assumptions necessary to get around this problem and make causal inferences in experiments, natural experiments, and quantitative observational studies (e.g. Morgan and Winship 2007). The last segment of this chapter reviews those findings with respect to regression-type analysis of observational studies, paying special attention to the assumptions about control variables necessary for regression-based causal inference. In particular, this literature shows that scholars need independent evidence that the regression does not suffer from confounders, colliders, or post-treatment bias. While these assumptions are not sufficient for causal inference, they are necessary and provide key openings for integrative multi-method research design.

This paper addresses causal inference and modeling over event streams where data have high throughput, are unbounded, and may arrive out of order. The availability of large amount of data with these characteristics presents several new challenges related to causal modeling, such as the need for fast causal inference operations while ensuring consistent and valid results. There is no existing work specifically for such a streaming environment. We meet the challenges by introducing a time-centric causal inference strategy which leverages temporal precedence information to decrease the number of conditional independence tests required to establish the causalities between variables in a causal network. (Dependency and temporal precedence of cause over effect are the two properties of a causal relationship.) Moreover, we employ change-driven causal network inference to safely reduce the running time further. In this paper we present the Order-Aware Temporal Network Inference algorithm to model the temporal precedence relationships into a temporal network and then propose the Enhanced Fast Causal Network Inference algorithm for learning a causal network faster using the temporal network. Experiments using synthetic and real datasets demonstrate the efficacy of the proposed algorithms.

A central problem in public health studies is how to make inferences about the causal effects of treatments or agents. In this article we review an approach to making such inferences via potential outcomes. In this approach, the causal effect is defined as a comparison of results from two or more alternative treatments, with only one of the results actually observed. We discuss the application of this approach to a number of data collection designs and associated problems commonly encountered in clinical research and epidemiology. Topics considered include the fundamental role of the assignment mechanism, in particular the importance of randomization as an unconfounded method of assignment; randomization-based and model-based methods of statistical inference for causal effects; methods for handling noncompliance and missing data; and methods for limiting bias in the analysis of observational data, including propensity score matching and sensitivity analysis.

Counterfactuals, graphical causal models and potential outcomes: Response to Lindquist and Sobel

Many scientific problems require that treatment comparisons be adjusted for posttreatment variables, but the estimands underlying standard methods are not causal effects. To address this deficiency, we propose a general framework for comparing treatments adjusting for posttreatment variables that yields principal effects based on principal stratification. Principal stratification with respect to a posttreatment variable is a cross-classification of subjects defined by the joint potential values of that posttreatment variable tinder each of the treatments being compared. Principal effects are causal effects within a principal stratum. The key property of principal strata is that they are not affected by treatment assignment and therefore can be used just as any pretreatment covariate. such as age category. As a result, the central property of our principal effects is that they are always causal effects and do not suffer from the complications of standard posttreatment-adjusted estimands. We discuss briefly that such principal causal effects are the link between three recent applications with adjustment for posttreatment variables: (i) treatment noncompliance, (ii) missing outcomes (dropout) following treatment noncompliance. and (iii) censoring by death. We then attack the problem of surrogate or biomarker endpoints, where we show, using principal causal effects, that all current definitions of surrogacy, even when perfectly true, do not generally have the desired interpretation as causal effects of treatment on outcome. We go on to forrmulate estimands based on principal stratification and principal causal effects and show their superiority.

Bayesian causal inference in randomized experiments usually imposes model-based structure on potential outcomes. Yet causal inferences from randomized experiments are especially credible because they depend on a known assignment process, not a probability model of potential outcomes. In this article, I derive a randomization-based procedure for Bayesian inference of causal effects in a finite population setting. I formally show that this procedure satisfies Bayesian analogues of unbiasedness and consistency under weak conditions on a prior distribution. Unlike existing model-based methods of Bayesian causal inference, my procedure supposes neither probability models that generate potential outcomes nor independent and identically distributed random sampling. Unlike existing randomization-based methods of Bayesian causal inference, my procedure does not suppose that potential outcomes are discrete and bounded. Consequently, researchers can reap the benefits of Bayesian inference without sacrificing the properties that make inferences from randomized experiments especially credible in the first place.

Researchers are increasingly using observational or nonrandomized data to estimate causal treatment effects. Essential to the production of high-quality evidence is the ability to reduce or minimize the confounding that frequently occurs in observational studies. When using the potential outcome framework to define causal treatment effects, one requires the potential outcome under each possible treatment. However, only the outcome under the actual treatment received is observed, whereas the potential outcomes under the other treatments are considered missing data. Some authors have proposed that parametric regression models be used to estimate potential outcomes. In this study, we examined the use of ensemble-based methods (bagged regression trees, random forests, and boosted regression trees) to directly estimate average treatment effects by imputing potential outcomes. We used an extensive series of Monte Carlo simulations to estimate bias, variance, and mean squared error of treatment effects estimated using different ensemble methods. For comparative purposes, we compared the performance of these methods with inverse probability of treatment weighting using the propensity score when logistic regression or ensemble methods were used to estimate the propensity score. Using boosted regression trees of depth 3 or 4 to impute potential outcomes tended to result in estimates with bias equivalent to that of the best performing methods. Using an empirical case study, we compared inferences on the effect of in-hospital smoking cessation counseling on subsequent mortality in patients hospitalized with an acute myocardial infarction.

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control. However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the potential outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes and is directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.

Further refinements to the organizational schema for causal effects.

In this article, we discuss both prospective and retrospective causal inferences, building on Neyman’s potential outcome framework. For prospective causal inference, we review criteria for confounders and surrogates to avoid the Yule–Simpson paradox and the surrogate paradox, respectively. For retrospective causal inference, we introduce the concepts of posterior causal effects given observed evidence to quantify the causes of effects. The posterior causal effects provide a unified framework for deducing both effects of causes in prospective causal inference and causes of effects in retrospective causal inference. We compare the medical diagnostic approaches based on Bayesian posterior probabilities and posterior causal effects for classification and attribution.