A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for three methods of implementation: propensity score stratification, weighting, and optimal full matching. Three simulation studies and one case study are presented to elaborate the proposed two-step Bayesian propensity score approach. Results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist-based treatment effect. A slight advantage is shown for the Bayesian approach in small samples. Results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results. However, greater precision around the correct treatment effect parameter yields quite good results, with slight improvement seen with greater precision in the propensity score equation. A comparison of coverage rates for the conventional frequentist approach and proposed Bayesian approach is also provided. The case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non-informative.     

Bayesian Model Averaging for Propensity Score Analysis

This article considers Bayesian model averaging as a means of addressing uncertainty in the selection of variables in the propensity score equation. We investigate an approximate Bayesian model averaging approach based on the model-averaged propensity score estimates produced by the R package BMA but that ignores uncertainty in the propensity score. We also provide a fully Bayesian model averaging approach via Markov chain Monte Carlo sampling (MCMC) to account for uncertainty in both parameters and models. A detailed study of our approach examines the differences in the causal estimate when incorporating noninformative versus informative priors in the model averaging stage. We examine these approaches under common methods of propensity score implementation. In addition, we evaluate the impact of changing the size of Occam’s window used to narrow down the range of possible models. We also assess the predictive performance of both Bayesian model averaging propensity score approaches and compare it with the case without Bayesian model averaging. Overall, results show that both Bayesian model averaging propensity score approaches recover the treatment effect estimates well and generally provide larger uncertainty estimates, as expected. Both Bayesian model averaging approaches offer slightly better prediction of the propensity score compared with the Bayesian approach with a single propensity score equation. Covariate balance checks for the case study show that both Bayesian model averaging approaches offer good balance. The fully Bayesian model averaging approach also provides posterior probability intervals of the balance indices.     

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.     

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.     

留守对农村儿童青少年社会适应的影响:倾向值匹配的比较分析

以河南和陕西两省3812名4~9年级农村学生为研究样本, 考察其在抑郁、自尊、问题行为、幸福感、未来压力感知及人际关系方面的社会适应状况, 并运用倾向值匹配方法探讨了父母外出务工对其产生的影响。结果发现, 在倾向值匹配之前, 双亲外出务工的留守儿童在未来压力感知、抑郁和幸福感3方面的适应状况均比非留守儿童差, 在师生关系上得分高于非留守儿童;单亲外出务工的留守儿童感知到的未来压力及抑郁水平也显著高于非留守儿童。经过倾向值匹配处理后, 双亲外出留守儿童的幸福感仍显著低于非留守儿童, 单亲外出留守儿童的未来压力感知也高于非留守儿童, 但其他方面的差异不再显著。研究结果提示对于留守与非留守儿童存在的社会适应差异不能完全归咎于父母的外出务工状态。     

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.     

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.     

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.     

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.     

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.     

Case Report: A Systems Approach to Genetic Counseling for Albinism

A systems approach to family therapy assumes that a person and his/her problems do not operate in a social vacuum but instead are imbedded in a social context. This context includes fairly small social systems such as a nuclear family and larger social systems such as school systems and cultural beliefs. A case of a girl with albinism born to a couple from India will be used to discuss how a systems approach might be useful in a genetic counseling setting.