倾向得分区间匹配法用于非随机对照试验的探索与研究

目的探索研究倾向得分区间匹配法在非随机对照试验中用于均衡组间混杂因素的能力,并与logistic回归分析方法和倾向得分卡钳匹配进行比较。方法通过Monte Carlo模拟分析倾向得分区间匹配法处理二分类资料的能力,并与传统的logistic回归方法以及倾向得分卡钳匹配法进行比较,通过I类错误、检验效能、标准化差异以及匹配比例等指标进行综合评价。结果倾向得分区间匹配法与logistic回归法以及倾向得分卡钳匹配法的检验效能、I类错误、标准化差异和匹配比例四个评价指标无明显差异。结论在观察性研究和流行病学研究中,采用倾向得分区间匹配法均衡组间协变量得到真实的处理效应具有很高的实用价值。     

Estimating propensity scores with missing covariate data using general location mixture models

In many observational studies, analysts estimate causal effects using propensity scores, e.g. by matching, sub-classifying, or inverse probability weighting based on the scores. Estimation of propensity scores is complicated when some values of the covariates are missing. Analysts can use multiple imputation to create completed data sets from which propensity scores can be estimated. We propose a general location mixture model for imputations that assumes that the control units are a latent mixture of (i) units whose covariates are drawn from the same distributions as the treated units' covariates and (ii) units whose covariates are drawn from different distributions. This formulation reduces the influence of control units outside the treated units' region of the covariate space on the estimation of parameters in the imputation model, which can result in more plausible imputations. In turn, this can result in more reliable estimates of propensity scores and better balance in the true covariate distributions when matching or sub-classifying. We illustrate the benefits of the latent class modeling approach with simulations and with an observational study of the effect of breast feeding on children's cognitive abilities.     

倾向指数匹配法的模拟研究

目的 采用SAS程序模拟来研究倾向指数匹配法在处理非随机化试验数据中的效果.方法 利用蒙特-卡罗（Monte Carlo）模拟法产生有3个协变量（连续性变量X1,二分类变量X2,X3）的2组随机样本,以分组变量为因变量,以协变量为自变量建立logistic回归模型,并计算研究对象的倾向指数,然后按照倾向指数做组间无放回的卡钳匹配,得到一个各协变量均衡的处理组与对照组样本.用假设检验法和标准差异法分别评价匹配前后2组之间协变量的均衡性,并估计匹配前后2组间的处理效应.结果 假设检验法评价组间均衡性的结果为：匹配之前,协变量X1,X2,X3在2组间均有统计学差异,表明协变量X1,X2,X3在2组间不均衡;匹配之后,协变量X1,X2,X3在2组间均无统计学差异,表明协变量在2组间均衡.标准差异法评价组间均衡性的结果为：匹配之前,X1,X2,X3标准差异的均值分别为1 967.03%,117.29%,63.74%,均远远大于10%,表明协变量X1,X2,X3在处理组和对照组间都不均衡;匹配之后,X1,X2,X3标准差异的均值分别为19.46%,7.37%,6.85%,表明协变量X1,X2,X3在匹配后都基本变的均衡.可见使用基于倾向指数的卡钳匹配法对非随机化数据进行处理,协变量间不均衡的2个处理组在匹配以后达到了均衡.对处理效应的估计结果为：匹配之前,2组间的处理效应有统计学差异,但在匹配之后,2组间的处理效应变得没有统计学差异,表明匹配之前2组间的统计学差异是由协变量的不平衡引起的.结论 倾向指数法是一种有效的处理非随机化试验数据的方法,具有重要的应用价值.     

Subgroup finding via Bayesian additive regression trees

We provide a Bayesian decision theoretic approach to finding subgroups that have elevated treatment effects. Our approach separates the modeling of the response variable from the task of subgroup finding and allows a flexible modeling of the response variable irrespective of potential subgroups of interest. We use Bayesian additive regression trees to model the response variable and use a utility function defined in terms of a candidate subgroup and the predicted response for that subgroup. Subgroups are identified by maximizing the expected utility where the expectation is taken with respect to the posterior predictive distribution of the response, and the maximization is carried out over an a priori specified set of candidate subgroups. Our approach allows subgroups based on both quantitative and categorical covariates. We illustrate the approach using simulated data set study and a real data set. Copyright © 2017 John Wiley & Sons, Ltd.     

Near/far matching: a study design approach to instrumental variables

Classic instrumental variable techniques involve the use of structural equation modeling or other forms of parameterized modeling. In this paper we use a nonparametric, matching-based instrumental variable methodology that is based on a study design approach. Similar to propensity score matching, though unlike classic instrumental variable approaches, near/far matching is capable of estimating causal effects when the outcome is not continuous. Unlike propensity score matching, though similar to instrumental variable techniques, near/far matching is also capable of estimating causal effects even when unmeasured covariates produce selection bias. We illustrate near/far matching by using Medicare data to compare the effectiveness of carotid arterial stents with cerebral protection versus carotid endarterectomy for the treatment of carotid stenosis.     

Semiparametric Bayesian analysis of structural equation models with fixed covariates

Latent variables play the most important role in structural equation modeling. In almost all existing structural equation models (SEMs), it is assumed that the distribution of the latent variables is normal. As this assumption is likely to be violated in many biomedical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of SEMs with covariates, we provide a general Bayesian framework in which a semiparametric hierarchical modeling with an approximate truncation Dirichlet process prior distribution is specified for the latent variables. The stick-breaking prior and the blocked Gibbs sampler are used for efficient simulation in the posterior analysis. The developed methodology is applied to a study of kidney disease in diabetes patients. A simulation study is conducted to reveal the empirical performance of the proposed approach. Supplementary electronic material for this paper is available in Wiley InterScience at http://www.mrw.interscience.wiley.com/suppmat/1097-0258/suppmat/.     

Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity‐score matched samples

The propensity score is a subject's probability of treatment, conditional on observed baseline covariates. Conditional on the true propensity score, treated and untreated subjects have similar distributions of observed baseline covariates. Propensity‐score matching is a popular method of using the propensity score in the medical literature. Using this approach, matched sets of treated and untreated subjects with similar values of the propensity score are formed. Inferences about treatment effect made using propensity‐score matching are valid only if, in the matched sample, treated and untreated subjects have similar distributions of measured baseline covariates. In this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified: comparing means and prevalences of baseline characteristics using standardized differences; ratios comparing the variance of continuous covariates between treated and untreated subjects; comparison of higher order moments and interactions; five‐number summaries; and graphical methods such as quantile–quantile plots, side‐by‐side boxplots, and non‐parametric density plots for comparing the distribution of baseline covariates between treatment groups. We describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero, thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified. We highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity‐score model. In particular, methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative. Copyright © 2009 John Wiley & Sons, Ltd.     

非随机化医学研究中风险比的一种估计方法

目的提出一种适用于非随机化医学研究的,结合倾向指数与非参数生存分析估计风险比的方法.方法首先对倾向指数进行估计,然后对倾向指数分布分层以消除比较两组间协变量分布的不均衡.其次对分层样本用非参数生存分析的方法估计两组间发病或死亡的风险比.最后比较本法与常用的Cox模型方法并探讨其适用性.结果将本法应用于一项评价某降血脂新药效果的4期临床试验数据后显示:(1)对倾向指数分布分层后基本上消除了由于随机分组方案失败导致的新药组与传统药物组之间协变量分布的不均衡性,使得非参数生存分析方法得以应用;(2)由本法得到的新药效果的估计-风险比与由Cox模型得到的结果基本一致.结论对于非随机化医学研究,结合倾向指数进行非参数生存分析是一种新的可选择的统计方法.     

Stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure

Stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure. A more traditional alternative technique is the direct adjustment for confounding in regression models.This paper discusses fundamental differences between the two approaches, with a focus on linear regression and propensity score stratification, and identifies points to be considered for an adequate comparison. The treatment estimators are examined for unbiasedness and efficiency. This is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models. We demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model, even if it is built on coarser covariate strata than the linear model. As a consequence the coarsening property of the propensity score-adjustment for a one-dimensional confounder instead of a high-dimensional covariate-may be viewed as a way to implement a pre-specified, richly parametrized linear model. We conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome.     

Addressing missing data in confounders when estimating propensity scores for continuous exposures

Propensity score models are frequently used to estimate causal effects in observational studies. One unresolved issue in fitting these models is handling missing values in the propensity score model covariates. As these models usually contain a large set of covariates, using only individuals with complete data significantly decreases the sample size and statistical power. Several missing data imputation approaches have been proposed, including multiple imputation (MI), MI with missingness pattern (MIMP), and treatment mean imputation. Generalized boosted modeling (GBM), which is a nonparametric approach to estimate propensity scores, can automatically handle missingness in the covariates. Although the performance of MI, MIMP, and treatment mean imputation have previously been compared for binary treatments, they have not been compared for continuous exposures or with single imputation and GBM. We compared these approaches in estimating the generalized propensity score (GPS) for a continuous exposure in both a simulation study and in empirical data. Using GBM with the incomplete data to estimate the GPS did not perform well in the simulation. Missing values should be imputed before estimating propensity scores using GBM or any other approach for estimating the GPS.     

Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group

In observational studies, investigators have no control over the treatment assignment. The treated and non-treated (that is, control) groups may have large differences on their observed covariates, and these differences can lead to biased estimates of treatment effects. Even traditional covariance analysis adjustments may be inadequate to eliminate this bias. The propensity score, defined as the conditional probability of being treated given the covariates, can be used to balance the covariates in the two groups, and therefore reduce this bias. In order to estimate the propensity score, one must model the distribution of the treatment indicator variable given the observed covariates. Once estimated the propensity score can be used to reduce bias through matching, stratification (subclassification), regression adjustment, or some combination of all three. In this tutorial we discuss the uses of propensity score methods for bias reduction, give references to the literature and illustrate the uses through applied examples. © 1998 John Wiley & Sons, Ltd.     

Bias associated with using the estimated propensity score as a regression covariate

The use of propensity score methods to adjust for selection bias in observational studies has become increasingly popular in public health and medical research. A substantial portion of studies using propensity score adjustment treat the propensity score as a conventional regression predictor. Through a Monte Carlo simulation study, Austin and colleagues. investigated the bias associated with treatment effect estimation when the propensity score is used as a covariate in nonlinear regression models, such as logistic regression and Cox proportional hazards models. We show that the bias exists even in a linear regression model when the estimated propensity score is used and derive the explicit form of the bias. We also conduct an extensive simulation study to compare the performance of such covariate adjustment with propensity score stratification, propensity score matching, inverse probability of treatment weighted method, and nonparametric functional estimation using splines. The simulation scenarios are designed to reflect real data analysis practice. Instead of specifying a known parametric propensity score model, we generate the data by considering various degrees of overlap of the covariate distributions between treated and control groups. Propensity score matching excels when the treated group is contained within a larger control pool, while the model‐based adjustment may have an edge when treated and control groups do not have too much overlap. Overall, adjusting for the propensity score through stratification or matching followed by regression or using splines, appears to be a good practical strategy. Copyright © 2013 John Wiley & Sons, Ltd.     

Collaborative targeted learning using regression shrinkage

Causal inference practitioners are routinely presented with the challenge of model selection and, in particular, reducing the size of the covariate set with the goal of improving estimation efficiency. Collaborative targeted minimum loss‐based estimation (CTMLE) is a general framework for constructing doubly robust semiparametric causal estimators that data‐adaptively limit model complexity in the propensity score to optimize a preferred loss function. This stepwise complexity reduction is based on a loss function placed on a strategically updated model for the outcome variable through which the error is assessed using cross‐validation. We demonstrate how the existing stepwise variable selection CTMLE can be generalized using regression shrinkage of the propensity score. We present 2 new algorithms that involve stepwise selection of the penalization parameter(s) in the regression shrinkage. Simulation studies demonstrate that, under a misspecified outcome model, mean squared error and bias can be reduced by a CTMLE procedure that separately penalizes individual covariates in the propensity score. We demonstrate these approaches in an example using electronic medical data with sparse indicator covariates to evaluate the relative safety of 2 similarly indicated asthma therapies for pregnant women with moderate asthma.     

Latent Class Analysis: An Alternative Perspective on Subgroup Analysis in Prevention and Treatment

The overall goal of this study is to introduce latent class analysis (LCA) as an alternative approach to latent subgroup analysis. Traditionally, subgroup analysis aims to determine whether individuals respond differently to a treatment based on one or more measured characteristics. LCA provides a way to identify a small set of underlying subgroups characterized by multiple dimensions which could, in turn, be used to examine differential treatment effects. This approach can help to address methodological challenges that arise in subgroup analysis, including a high Type I error rate, low statistical power, and limitations in examining higher-order interactions. An empirical example draws on N?=?1,900 adolescents from the National Longitudinal Survey of Adolescent Health. Six characteristics (household poverty, single-parent status, peer cigarette use, peer alcohol use, neighborhood unemployment, and neighborhood poverty) are used to identify five latent subgroups: Low Risk, Peer Risk, Economic Risk, Household & Peer Risk, and Multi-Contextual Risk. Two approaches for examining differential treatment effects are demonstrated using a simulated outcome: 1) a classify-analyze approach and, 2) a model-based approach based on a reparameterization of the LCA with covariates model. Such approaches can facilitate targeting future intervention resources to subgroups that promise to show the maximum treatment response.     

Comparing the performance of propensity score methods in healthcare database studies with rare outcomes

Nonrandomized studies of treatments from electronic healthcare databases are critical for producing the evidence necessary to making informed treatment decisions, but often rely on comparing rates of events observed in a small number of patients. In addition, studies constructed from electronic healthcare databases, for example, administrative claims data, often adjust for many, possibly hundreds, of potential confounders. Despite the importance of maximizing efficiency when there are many confounders and few observed outcome events, there has been relatively little research on the relative performance of different propensity score methods in this context. In this paper, we compare a wide variety of propensity‐based estimators of the marginal relative risk. In contrast to prior research that has focused on specific statistical methods in isolation of other analytic choices, we instead consider a method to be defined by the complete multistep process from propensity score modeling to final treatment effect estimation. Propensity score model estimation methods considered include ordinary logistic regression, Bayesian logistic regression, lasso, and boosted regression trees. Methods for utilizing the propensity score include pair matching, full matching, decile strata, fine strata, regression adjustment using one or two nonlinear splines, inverse propensity weighting, and matching weights. We evaluate methods via a ‘plasmode’ simulation study, which creates simulated datasets on the basis of a real cohort study of two treatments constructed from administrative claims data. Our results suggest that regression adjustment and matching weights, regardless of the propensity score model estimation method, provide lower bias and mean squared error in the context of rare binary outcomes. Copyright © 2017 John Wiley & Sons, Ltd.     

Invited commentary: propensity scores.

The propensity score is the conditional probability of exposure to a treatment given observed covariates. In a cohort study, matching or stratifying treated and control subjects on a single variable, the propensity score, tends to balance all of the observed covariates; however, unlike random assignment of treatments, the propensity score may not also balance unobserved covariates. The authors review the uses and limitations of propensity scores and provide a brief outline of associated statistical theory. They also present a new result of using propensity scores in case-cohort studies.     

Methods for Constructing and Assessing Propensity Scores

Objectives

To model the steps involved in preparing for and carrying out propensity score analyses by providing step-by-step guidance and Stata code applied to an empirical dataset.

Study Design

Guidance, Stata code, and empirical examples are given to illustrate (1) the process of choosing variables to include in the propensity score; (2) balance of propensity score across treatment and comparison groups; (3) balance of covariates across treatment and comparison groups within blocks of the propensity score; (4) choice of matching and weighting strategies; (5) balance of covariates after matching or weighting the sample; and (6) interpretation of treatment effect estimates.

Empirical Application

We use data from the Palliative Care for Cancer Patients (PC4C) study, a multisite observational study of the effect of inpatient palliative care on patient health outcomes and health services use, to illustrate the development and use of a propensity score.

Conclusions

Propensity scores are one useful tool for accounting for observed differences between treated and comparison groups. Careful testing of propensity scores is required before using them to estimate treatment effects.     

A general semiparametric hazards regression model: efficient estimation and structure selection

We consider a general semiparametric hazards regression model that encompasses the Cox proportional hazards model and the accelerated failure time model for survival analysis. To overcome the nonexistence of the maximum likelihood, we derive a kernel‐smoothed profile likelihood function and prove that the resulting estimates of the regression parameters are consistent and achieve semiparametric efficiency. In addition, we develop penalized structure selection techniques to determine which covariates constitute the accelerated failure time model and which covariates constitute the proportional hazards model. The proposed method is able to estimate the model structure consistently and model parameters efficiently. Furthermore, variance estimation is straightforward. The proposed estimation performs well in simulation studies and is applied to the analysis of a real data set. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimating treatment effects on healthcare costs under exogeneity: is there a ��magic bullet��?

Methods for estimating average treatment effects, under the assumption of no unmeasured confounders, include regression models; propensity score adjustments using stratification, weighting, or matching; and doubly robust estimators (a combination of both). Researchers continue to debate about the best estimator for outcomes such as health care cost data, as they are usually characterized by an asymmetric distribution and heterogeneous treatment effects,. Challenges in finding the right specifications for regression models are well documented in the literature. Propensity score estimators are proposed as alternatives to overcoming these challenges. Using simulations, we find that in moderate size samples (n= 5000), balancing on propensity scores that are estimated from saturated specifications can balance the covariate means across treatment arms but fails to balance higher-order moments and covariances amongst covariates. Therefore, unlike regression model, even if a formal model for outcomes is not required, propensity score estimators can be inefficient at best and biased at worst for health care cost data. Our simulation study, designed to take a 'proof by contradiction' approach, proves that no one estimator can be considered the best under all data generating processes for outcomes such as costs. The inverse-propensity weighted estimator is most likely to be unbiased under alternate data generating processes but is prone to bias under misspecification of the propensity score model and is inefficient compared to an unbiased regression estimator. Our results show that there are no 'magic bullets' when it comes to estimating treatment effects in health care costs. Care should be taken before naively applying any one estimator to estimate average treatment effects in these data. We illustrate the performance of alternative methods in a cost dataset on breast cancer treatment.     

Evaluating the Impact of Unmeasured Confounding with Internal Validation Data: An Example Cost Evaluation in Type 2 Diabetes

The quantitative assessment of the potential influence of unmeasured confounders in the analysis of observational data is rare, despite reliance on the “no unmeasured confounders” assumption. In a recent comparison of costs of care between two treatments for type 2 diabetes using a health care claims database, propensity score matching was implemented to adjust for selection bias though it was noted that information on baseline glycemic control was not available for the propensity model. Using data from a linked laboratory file, data on this potential “unmeasured confounder” were obtained for a small subset of the original sample. By using this information, we demonstrate how Bayesian modeling, propensity score calibration, and multiple imputation can utilize this additional information to perform sensitivity analyses to quantitatively assess the potential impact of unmeasured confounding. Bayesian regression models were developed to utilize the internal validation data as informative prior distributions for all parameters, retaining information on the correlation between the confounder and other covariates. While assumptions supporting the use of propensity score calibration were not met in this sample, the use of Bayesian modeling and multiple imputation provided consistent results, suggesting that the lack of data on the unmeasured confounder did not have a strong impact on the original analysis, due to the lack of strong correlation between the confounder and the cost outcome variable. Bayesian modeling with informative priors and multiple imputation may be useful tools for unmeasured confounding sensitivity analysis in these situations. Further research to understand the operating characteristics of these methods in a variety of situations, however, remains.