A Tutorial and Case Study in Propensity Score Analysis: An Application to Estimating the Effect of In-Hospital Smoking Cessation Counseling on Mortality

Propensity score methods allow investigators to estimate causal treatment effects using observational or nonrandomized data. In this article we provide a practical illustration of the appropriate steps in conducting propensity score analyses. For illustrative purposes, we use a sample of current smokers who were discharged alive after being hospitalized with a diagnosis of acute myocardial infarction. The exposure of interest was receipt of smoking cessation counseling prior to hospital discharge and the outcome was mortality with 3 years of hospital discharge. We illustrate the following concepts: first, how to specify the propensity score model; second, how to match treated and untreated participants on the propensity score; third, how to compare the similarity of baseline characteristics between treated and untreated participants after stratifying on the propensity score, in a sample matched on the propensity score, or in a sample weighted by the inverse probability of treatment; fourth, how to estimate the effect of treatment on outcomes when using propensity score matching, stratification on the propensity score, inverse probability of treatment weighting using the propensity score, or covariate adjustment using the propensity score. Finally, we compare the results of the propensity score analyses with those obtained using conventional regression adjustment.     

A Tutorial and Case Study in Propensity Score Analysis: An Application to Estimating the Effect of In-Hospital Smoking Cessation Counseling on Mortality

Propensity score methods allow investigators to estimate causal treatment effects using observational or nonrandomized data. In this article we provide a practical illustration of the appropriate steps in conducting propensity score analyses. For illustrative purposes, we use a sample of current smokers who were discharged alive after being hospitalized with a diagnosis of acute myocardial infarction. The exposure of interest was receipt of smoking cessation counseling prior to hospital discharge and the outcome was mortality with 3 years of hospital discharge. We illustrate the following concepts: first, how to specify the propensity score model; second, how to match treated and untreated participants on the propensity score; third, how to compare the similarity of baseline characteristics between treated and untreated participants after stratifying on the propensity score, in a sample matched on the propensity score, or in a sample weighted by the inverse probability of treatment; fourth, how to estimate the effect of treatment on outcomes when using propensity score matching, stratification on the propensity score, inverse probability of treatment weighting using the propensity score, or covariate adjustment using the propensity score. Finally, we compare the results of the propensity score analyses with those obtained using conventional regression adjustment.     

A Propensity Score Analysis of Homework Adherence-Outcome Relations in Cognitive Behavioral Therapy for Depression

Little is known about whether or not a consistently high level of homework adherence over the course of therapy benefits patients. This question was examined in two samples of patients who were receiving individual Cognitive Behavioral Therapy (CBT) for depression (Ns = 128 [Sequenced Treatment Alternatives to Relieve Depression: STAR-D] and 183 [Continuation Phase Cognitive Therapy Relapse Prevention: C-CT-RP]). Logistic and linear regression and propensity score models were used to identify whether or not clinician assessments of homework adherence differentiated symptom reduction and remission, as assessed by the Hamilton Depression Rating Scale-17 (HDRS-17), the Quick Inventory of Depressive Symptomatology–Self-Reported Scale (QIDS-SR), and the QIDS–Clinician Scale (QIDS-C). CBT-related response and remission were equally likely between both high and low homework adherers in both studies and in all models. But in propensity adjusted models that adjusted for session attendance, for both the STAR-D and C-CT-RP samples, greater homework adherence was significantly associated with greater response and remission from depression in the first and last 8 sessions of CBT. Our results suggest that homework adherence can account for response and remission early and late in treatment, with adequate session attendence.     

A Propensity Score Adjustment for Multiple Group Structural Equation Modeling

In the behavioral and social sciences, quasi-experimental and observational studies are used due to the difficulty achieving a random assignment. However, the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates. To estimate average treatment effects when the treatment variable is binary, Rosenbaum and Rubin (1983a) proposed adjustment methods for pretreatment variables using the propensity score. However, these studies were interested only in estimating the average causal effect and/or marginal means. In the behavioral and social sciences, a general estimation method is required to estimate parameters in multiple group structural equation modeling where the differences of covariates are adjusted. We show that a Horvitz–Thompson-type estimator, propensity score weighted M estimator (PWME) is consistent, even when we use estimated propensity scores, and the asymptotic variance of the PWME is shown to be less than that with true propensity scores. Furthermore, we show that the asymptotic distribution of the propensity score weighted statistic under a null hypothesis is a weighted sum of independent χ² ₁ variables. We show the method can compare latent variable means with covariates adjusted using propensity scores, which was not feasible by previous methods. We also apply the proposed method for correlated longitudinal binary responses with informative dropout using data from the Longitudinal Study of Aging (LSOA). The results of a simulation study indicate that the proposed estimation method is more robust than the maximum likelihood (ML) estimation method, in that PWME does not require the knowledge of the relationships among dependent variables and covariates.     

Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction

Abstract

Extended redundancy analysis (ERA) combines linear regression with dimension reduction to explore the directional relationships between multiple sets of predictors and outcome variables in a parsimonious manner. It aims to extract a component from each set of predictors in such a way that it accounts for the maximum variance of outcome variables. In this article, we extend ERA into the Bayesian framework, called Bayesian ERA (BERA). The advantages of BERA are threefold. First, BERA enables to make statistical inferences based on samples drawn from the joint posterior distribution of parameters obtained from a Markov chain Monte Carlo algorithm. As such, it does not necessitate any resampling method, which is on the other hand required for (frequentist’s) ordinary ERA to test the statistical significance of parameter estimates. Second, it formally incorporates relevant information obtained from previous research into analyses by specifying informative power prior distributions. Third, BERA handles missing data by implementing multiple imputation using a Markov Chain Monte Carlo algorithm, avoiding the potential bias of parameter estimates due to missing data. We assess the performance of BERA through simulation studies and apply BERA to real data regarding academic achievement.     

The Impact of Home Ownership on Life Satisfaction in Urban China: A Propensity Score Matching Analysis

China has implemented a series of socioeconomic reforms since 1978. One of the reforms allows urban residents to purchase their own houses rather than renting houses from state institutions which has resulted in a rapid increase in home ownership. This paper estimates the impact of home ownership on life satisfaction in urban China on the basis of the 2010 wave of the China General Social Survey. Special attention is paid to the methodological problem of confoundedness between the determinants of home ownership and life satisfaction. Propensity score matching (PSM) is applied to control it. The results show that PSM reduces upward estimation bias caused by confoundedness and that it is more appropriate to control confoundedness than ordered probit regression. The estimates furthermore indicate that home ownership has a significant positive impact on life satisfaction of medium- and high income urban residents. For low income urban residents, the impact is also positive, though insignificant. The outcomes connect to the objectives of national development policy and thus have several important policy implications. First, the central and local governments, especially in provinces where it is still low, may want to continue stimulating home ownership as it enhances life satisfaction. Secondly, specific programs may be designed to make home ownership financially affordable for low income groups. Thirdly, local governments may want to initiate or intensify urban (renewal) programs to improve poor public facilities including public transportation, green space and sports accommodations in the immediate vicinity of depressing low income neighborhoods.     

Causality, Propensity, and Bayesian Networks

This paper investigates the relations between causality and propensity. Aparticular version of the propensity theory of probability is introduced, and it is argued that propensities in this sense are not causes. Some conclusions regarding propensities can, however, be inferred from causal statements, but these hold only under restrictive conditions which prevent cause being defined in terms of propensity. The notion of a Bayesian propensity network is introduced, and the relations between such networks and causal networks is investigated. It is argued that causal networks cannot be identified with Bayesian propensity networks, but that causal networks can be a valuable heuristic guide for the construction of Bayesian propensity networks.     

A Systematic Review of Propensity Score Methods in the Social Sciences

The use of propensity scores in psychological and educational research has been steadily increasing in the last 2 to 3 years. However, there are some common misconceptions about the use of different estimation techniques and conditioning choices in the context of propensity score analysis. In addition, reporting practices for propensity score analyses often lack important details that allow other researchers to confidently judge the appropriateness of reported analyses and potentially to replicate published findings. In this article we conduct a systematic literature review of a large number of published articles in major areas of social science that used propensity scores up until the fall of 2009. We identify common errors in estimation, conditioning, and reporting of propensity score analyses and suggest possible solutions.     

A Case Study and Balance Sheet Approach to Unemployment

The authors describe positive and negative aspects of employment and unemployment in a balance sheet framework. They also discuss the value of the balance sheet approach in understanding individual differences in reactions to unemployment.     

High-Stakes Testing Case Study: A Latent Variable Approach for Assessing Measurement and Prediction Invariance

Psychometrika - The existence of differences in prediction systems involving test scores across demographic groups continues to be a thorny and unresolved scientific, professional, and societal...     

Natural Selection: A Case for the Counterfactual Approach

This paper investigates the conception of causation required in order to make sense of natural selection as a causal explanation of changes in traits or allele frequencies. It claims that under a counterfactual account of causation, natural selection is constituted by the causal relevance of traits and alleles to the variation in traits and alleles frequencies. The “statisticalist” view of selection (Walsh, Matthen, Ariew, Lewens) has shown that natural selection is not a cause superadded to the causal interactions between individual organisms. It also claimed that the only causation at work is those aggregated individual interactions, natural selection being only predictive and explanatory, but it is implicitly committed to a process-view of causation. I formulate a counterfactual construal of the causal statements underlying selectionist explanations, and show that they hold because of the reference they make to ecological reliable factors. Considering case studies, I argue that this counterfactual view of causal relevance proper to natural selection captures more salient features of evolutionary explanations than the statisticalist view, and especially makes sense of the difference between selection and drift. I eventually establish equivalence between causal relevance of traits and natural selection itself as a cause.     

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types—continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.     

A Bayesian Approach for Estimating Mediation Effects With Missing Data

Methodologists have developed mediation analysis techniques for a broad range of substantive applications, yet methods for estimating mediating mechanisms with missing data have been understudied. This study outlined a general Bayesian missing data handling approach that can accommodate mediation analyses with any number of manifest variables. Computer simulation studies showed that the Bayesian approach produced frequentist coverage rates and power estimates that were comparable to those of maximum likelihood with the bias-corrected bootstrap. We share an SAS macro that implements Bayesian estimation and use 2 data analysis examples to demonstrate its use.     

A Bayesian Approach to Informal Argument Fallacies

We examine in detail three classic reasoning fallacies, that is, supposedly ``incorrect' forms of argument. These are the so-called argumentam ad ignorantiam, the circular argument or petitio principii, and the slippery slope argument. In each case, the argument type is shown to match structurally arguments which are widely accepted. This suggests that it is not the form of the arguments as such that is problematic but rather something about the content of those examples with which they are typically justified. This leads to a Bayesian reanalysis of these classic argument forms and a reformulation of the conditions under which they do or do not constitute legitimate forms of argumentation.     

A Bayesian Nonparametric Approach to Test Equating

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are compared through the analysis of data sets famous in the equating literature. Also, the classical percentile-rank, linear, and mean equating models are each proven to be a special case of a Bayesian model under a highly-informative choice of prior distribution.