This paper reviews a theory of causal inference based on the Structural Causal Model (SCM) described in (Pearl, 2000a). The theory unifies the graphical, potential-outcome (Neyman-Rubin), decision analytical, and structural equation approaches to causation, and provides both a mathematical foundation and a friendly calculus for the analysis of causes and counterfactuals. In particular, the paper establishes a methodology for inferring (from a combination of data and assumptions) the answers to three types of causal queries: (1) queries about the effect of potential interventions, (2) queries about counterfactuals, and (3) queries about the direct (or indirect) effect of one event on another.

What is Causal Inference

Propensity score-based analysis is increasingly being used in observational studies to estimate the effects of treatments, interventions, and exposures. We introduce the concept of the propensity score and how it can be used in observational research. We describe four different ways of using the propensity score: matching on the propensity score, inverse probability of treatment weighting using the propensity score, stratification on the propensity score, and covariate adjustment on the propensity score (with a focus on the first two). We provide recommendations for the use and reporting of propensity score methods for the conduct of observational studies in neurological research.

https://n.neurology.org/content/neurology/97/18/856.full.pdf

Applying Propensity Score Methods in Clinical Research in Neurology.

http://www.amjtransplant.org/article/S1600613522082090/pdf

Outcome of liver transplantation with grafts from brain‐dead donors treated with dual hypothermic oxygenated machine perfusion, with particular reference to elderly donors

Propensity score weighting is an important tool for comparative effectiveness research.Besides the inverse probability of treatment weights (IPW), recent development has introduced a general class of balancing weights, corresponding to alternative target populations and estimands. In particular, the overlap weights (OW) lead to optimal covariate balance and estimation efficiency, and a target population of scientific and policy interest. We develop the R package PSweight to provide a comprehensive design and analysis platform for causal inference based on propensity score weighting. PSweight supports (i) a variety of balancing weights, (ii) binary and multiple treatments,(iii) simple and augmented weighting estimators, (iv) nuisance-adjusted sandwich variances, and(v) ratio estimands. PSweight also provides diagnostic tables and graphs for covariate balance assessment. We demonstrate the functionality of the package using a data example from the NationalChild Development Survey (NCDS), where we evaluate the causal effect of educational attainment on income.

PSweight: An R Package for Propensity Score Weighting Analysis

To extend previous simulations on the performance of propensity score (PS) weighting and trimming methods to settings without and with unmeasured confounding, Poisson outcomes, and various strengths of treatment prediction (PS c statistic), we simulated studies with a binary intended treatment T as a function of 4 measured covariates. We mimicked treatment withheld and last-resort treatment by adding 2 "unmeasured" dichotomous factors that directed treatment to change for some patients in both tails of the PS distribution. The number of outcomes Y was simulated as a Poisson function of T and confounders. We estimated the PS as a function of measured covariates and trimmed the tails of the PS distribution using 3 strategies ("Crump," "Sturmer," and "Walker"). After trimming and reestimation, we used alternative PS weights to estimate the treatment effect (rate ratio): inverse probability of treatment weighting, standardized mortality ratio (SMR)-treated, SMR-untreated, the average treatment effect in the overlap population (ATO), matching, and entropy. With no unmeasured confounding, the ATO (123%) and "Crump" trimming (112%) improved relative efficiency compared with untrimmed inverse probability of treatment weighting. With unmeasured confounding, untrimmed estimates were biased irrespective of weighting method, and only Sturmer and Walker trimming consistently reduced bias. In settings where unmeasured confounding (e.g., frailty) may lead physicians to withhold treatment, Sturmer and Walker trimming should be considered before primary analysis.

Propensity Score Weighting and Trimming Strategies for Reducing Variance and Bias of Treatment Effect Estimates: A Simulation Study.

Propensity score (PS) weighting methods are often used in non-randomized studies to adjust for confounding and assess treatment effects. The most popular among them, the inverse probability weighting (IPW), assigns weights that are proportional to the inverse of the conditional probability of a specific treatment assignment, given observed covariates. A key requirement for IPW estimation is the positivity assumption, i.e., the PS must be bounded away from 0 and 1. In practice, violations of the positivity assumption often manifest by the presence of limited overlap in the PS distributions between treatment groups. When these practical violations occur, a small number of highly influential IPW weights may lead to unstable IPW estimators, with biased estimates and large variances. To mitigate these issues, a number of alternative methods have been proposed, including IPW trimming, overlap weights (OW), matching weights (MW), and entropy weights (EW). Because OW, MW, and EW target the population for whom there is equipoise (and with adequate overlap) and their estimands depend on the true PS, a common criticism is that these estimators may be more sensitive to misspecifications of the PS model. In this paper, we conduct extensive simulation studies to compare the performances of IPW and IPW trimming against those of OW, MW, and EW under limited overlap and misspecified propensity score models. Across the wide range of scenarios we considered, OW, MW, and EW consistently outperform IPW in terms of bias, root mean squared error, and coverage probability.

Propensity score weighting under limited overlap and model misspecification.

Propensity score weighting methods are often used in non-randomized studies to adjust for confounding and assess treatment effects. The most popular among them, the inverse probability weighting, assigns weights that are proportional to the inverse of the conditional probability of a specific treatment assignment, given observed covariates. A key requirement for inverse probability weighting estimation is the positivity assumption, i.e. the propensity score must be bounded away from 0 and 1. In practice, violations of the positivity assumption often manifest by the presence of limited overlap in the propensity score distributions between treatment groups. When these practical violations occur, a small number of highly influential inverse probability weights may lead to unstable inverse probability weighting estimators, with biased estimates and large variances. To mitigate these issues, a number of alternative methods have been proposed, including inverse probability weighting trimming, overlap weights, matching weights, and entropy weights. Because overlap weights, matching weights, and entropy weights target the population for whom there is equipoise (and with adequate overlap) and their estimands depend on the true propensity score, a common criticism is that these estimators may be more sensitive to misspecifications of the propensity score model. In this paper, we conduct extensive simulation studies to compare the performances of inverse probability weighting and inverse probability weighting trimming against those of overlap weights, matching weights, and entropy weights under limited overlap and misspecified propensity score models. Across the wide range of scenarios we considered, overlap weights, matching weights, and entropy weights consistently outperform inverse probability weighting in terms of bias, root mean squared error, and coverage probability.

Propensity score weighting under limited overlap and model misspecification

Cellular differentiation is associated with the acquisition of a unique protein signature which is essential to attain the ultimate cellular function and activity of the differentiated cell. This is predicted to result in unique biosynthetic demands that arise during differentiation. Using a bioinformatic approach, we discovered osteoblast differentiation is associated with increased demand for the amino acid proline. When compared to other differentiated cells, osteoblast-associated proteins including RUNX2, OSX, OCN and COL1A1 are significantly enriched in proline. Using a genetic and metabolomic approach, we demonstrate that the neutral amino acid transporter SLC38A2 acts cell autonomously to provide proline to facilitate the efficient synthesis of proline-rich osteoblast proteins. Genetic ablation of SLC38A2 in osteoblasts limits both osteoblast differentiation and bone formation in mice. Mechanistically, proline is primarily incorporated into nascent protein with little metabolism observed. Collectively, these data highlight a requirement for proline in fulfilling the unique biosynthetic requirements that arise during osteoblast differentiation and bone formation.

/pdf/slc38a2-provides-proline-to-fulfill-unique-synthetic-demands-28niuxme.pdf

SLC38A2 provides proline to fulfill unique synthetic demands arising during osteoblast differentiation and bone formation

In this paper, we consider recent progress in estimating the average treatment effect when extreme inverse probability weights are present and focus on methods that account for a possible violation of the positivity assumption. These methods aim at estimating the treatment effect on the subpopulation of patients for whom there is a clinical equipoise. We propose a systematic approach to determine their related causal estimands and develop new insights into the properties of the weights targeting such a subpopulation. Then, we examine the roles of overlap weights, matching weights, Shannon's entropy weights, and beta weights. This helps us characterize and compare their underlying estimators, analytically and via simulations, in terms of the accuracy, precision, and root mean squared error. Moreover, we study the asymptotic behaviors of their augmented estimators (that mimic doubly robust estimators), which lead to improved estimations when either the propensity or the regression models are correctly specified. Based on the analytical and simulation results, we conclude that overall overlap weights are preferable to matching weights, especially when there is moderate or extreme violations of the positivity assumption. Finally, we illustrate the methods using a real data example marked by extreme inverse probability weights.

A framework for causal inference in the presence of extreme inverse probability weights: the role of overlap weights

Common causal estimands include the average treatment effect, the average treatment effect of the treated, and the average treatment effect on the controls. Using augmented inverse probability weighting methods, parametric models are judiciously leveraged to yield doubly robust estimators, that is, estimators that are consistent when at least one the parametric models is correctly specified. Three sources of uncertainty are associated when we evaluate these estimators and their variances, that is, when we estimate the treatment and outcome regression models as well as the desired treatment effect. In this article, we propose methods to calculate the variance of the normalized, doubly robust average treatment effect of the treated and average treatment effect on the controls estimators and investigate their finite sample properties. We consider both the asymptotic sandwich variance estimation, the standard bootstrap as well as two wild bootstrap methods. For the asymptotic approximations, we incorporate the aforementioned uncertainties via estimating equations. Moreover, unlike the standard bootstrap procedures, the proposed wild bootstrap methods use perturbations of the influence functions of the estimators through independently distributed random variables. We conduct an extensive simulation study where we vary the heterogeneity of the treatment effect as well as the proportion of participants assigned to the active treatment group. We illustrate the methods using an observational study of critical ill patients on the use of right heart catherization.

Yunji Zhou

Papers

Propensity score weighting under limited overlap and model misspecification.

Propensity score weighting under limited overlap and model misspecification

SLC38A2 provides proline to fulfill unique synthetic demands arising during osteoblast differentiation and bone formation

A framework for causal inference in the presence of extreme inverse probability weights: the role of overlap weights

Variance estimation for the average treatment effects on the treated and on the controls