Showing papers by "Donald B. Rubin published in 2006"

Fully conditional specification in multivariate imputation

Abstract: The use of the Gibbs sampler with fully conditionally specified models, where the distribution of each variable given the other variables is the starting point, has become a popular method to create imputations in incomplete multivariate data. The theoretical weakness of this approach is that the specified conditional densities can be incompatible, and therefore the stationary distribution to which the Gibbs sampler attempts to converge may not exist. This study investigates practical consequences of this problem by means of simulation. Missing data are created under four different missing data mechanisms. Attention is given to the statistical behavior under compatible and incompatible models. The results indicate that multiple imputation produces essentially unbiased estimates with appropriate coverage in the simple cases investigated, even for the incompatible models. Of particular interest is that these results were produced using only five Gibbs iterations starting from a simple draw from observed marginal distributions. It thus appears that, despite the theoretical weaknesses, the actual performance of conditional model specification for multivariate imputation can be quite good, and therefore deserves further study. © 2006 Taylor & Francis.

Matched Sampling for Causal Effects

Abstract: Part I. The Early Years and the Influence of William G. Cochran: 1. William G. Cochran's contributions to the design, analysis, and evaluation of observational studies 2. Controlling bias in observational studies: a review William G. Cochran Part II. Univariate Matching Methods and the Dangers of Regression Adjustment: 3. Matching to remove bias in observational studies 4. The use of matched sampling and regression adjustment to remove bias in observational studies 5. Assignment to treatment group on the basis of a covariate Part III. Basic Theory of Multivariate Matching: 6. Multivariate matching methods that are equal percent bias reducing, I: Some examples 7. Multivariate matching methods that are equal percent bias reducing, II: Maximums on bias reduction for fixed sample sizes 8. Using multivariate matched sampling and regression adjustment to control bias in observational studies 9. Bias reduction using Mahalanobis-metric matching Part IV. Fundamentals of Propensity Score Matching: 10. The central role of the propensity score in observational studies for causal effects Paul R. Rosenbaum 11. Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome Paul R. Rosenbaum 12. Reducing bias in observational studies using subclassification on the propensity score Paul R. Rosenbaum 13. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score Paul Rosenbaum 14. The bias due to incomplete matching Paul R. Rosenbaum Part V: Affinely Invariant Matching Methods with Ellipsoidally Symmetric Distributions, Theory and Methodology: 15. Affinely invariant matching methods with ellipsoidal distributions Neal Thomas 16. Characterizing the effect of matching using linear propensity score methods with normal distributions Neal Thomas 17. Matching using estimated propensity scores: relating theory to practice Neal Thomas 18. Combining propensity score matching with additional adjustments for prognostic covariates Part VI. Some Applied Contributions: 19. Causal inference in retrospective studies Paul Holland 20. The design of the New York school choice scholarships program evaluation Jennifer Hill and Neal Thomas 21. Estimating and using propensity scores with partially missing data Ralph D'Agostino Jr. 22. Using propensity scores to help design observational studies: application to the tobacco litigation Part VII. Some Focused Applications: 23. Criminality, aggression and intelligence in XYY and XXY men H. A. Witkin 24. Practical implications of modes of statistical inference for causal effects and the critical role of the assignment mechanism 25. In utero exposure to phenobarbital and intelligence deficits in adult men June Reinisch, Stephanie Sanders, and Erik Mortensen 26. Estimating causal effects from large data sets using propensity scores 27. On estimating the causal effects of DNR orders Martin McIntosh.

Validation of Software for Bayesian Models Using Posterior Quantiles

Abstract: This article presents a simulation-based method designed to establish the computational correctness of software developed to fit a specific Bayesian model, capitalizing on properties of Bayesian posterior distributions. We illustrate the validation technique with two examples. The validation method is shown to find errors in software when they exist and, moreover, the validation output can be informative about the nature and location of such errors. We also compare our method with that of an earlier approach.

Causal Inference Through Potential Outcomes and Principal Stratification: Application to Studies with “Censoring” Due to Death

Abstract: Causal inference is best understood using potential out- comes. This use is particularly important in more complex settings, that is, observational studies or randomized experiments with compli- cations such as noncompliance. The topic of this lecture, the issue of estimating the causal effect of a treatment on a primary outcome that is "censored" by death, is another such complication. For example, sup- pose that we wish to estimate the effect of a new drug on Quality of Life (QOL) in a randomized experiment, where some of the patients die before the time designated for their QOL to be assessed. Another example with the same structure occurs with the evaluation of an ed- ucational program designed to increase final test scores, which are not defined for those who drop out of school before taking the test. A fur- ther application is to studies of the effect of job-training programs on wages, where wages are only defined for those who are employed. The analysis of examples like these is greatly clarified using potential out- comes to define causal effects, followed by principal stratification on the intermediated outcomes (e.g., survival).

Estimating the Causal Effects of Marketing Interventions Using Propensity Score Methodology

Abstract: Propensity score methods were proposed by Rosenbaum and Rubin (Biometrika 70 (1983) 41-55) as central tools to help assess the causal effects of interventions. Since their introduction more than two decades ago, they have found wide application in a variety of areas, including medical research, economics, epidemiology and education, es- pecially in those situations where randomized experiments are either difficult to perform, or raise ethical questions, or would require exten- sive delays before answers could be obtained. In the past few years, the number of published applications using propensity score methods to evaluate medical and epidemiological interventions has increased dra- matically. Nevertheless, thus far, we believe that there have been few applications of propensity score methods to evaluate marketing inter- ventions (e.g., advertising, promotions), where the tradition is to use generally inappropriate techniques, which focus on the prediction of an outcome from background characteristics and an indicator for the in- tervention using statistical tools such as least-squares regression, data mining, and so on. With these techniques, an estimated parameter in the model is used to estimate some global "causal" effect. This practice can generate grossly incorrect answers that can be self-perpetuating: polishing the Ferraris rather than the Jeeps "causes" them to continue to win more races than the Jeeps , visiting the high-prescribing doc- tors rather than the low-prescribing doctors "causes" them to continue to write more prescriptions. This presentation will take "causality" seri- ously, not just as a casual concept implying some predictive association in a data set, and will illustrate why propensity score methods are gen- erally superior in practice to the standard predictive approaches for estimating causal effects.

Affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributions

Abstract: In observational studies designed to estimate the effects of interventions or exposures, such as cigarette smoking, it is desirable to try to control background differences between the treated group (e.g., current smokers) and the control group (e.g., never smokers) on covariates X (e.g., age, education). Matched sampling attempts to effect this control by selecting subsets of the treated and control groups with similar distributions of such covariates. This paper examines the consequences of matching using affinely invariant methods when the covariate distributions are "discriminant mixtures of proportional ellipsoidally symmetric" (DMPES) distributions, a class herein defined, which generalizes the ellipsoidal symmetry class of Rubin and Thomas [Ann. Statist. 20 (1992) 1079-1093]. The resulting generalized results help indicate why earlier results hold quite well even when the simple assumption of ellipsoidal symmetry is not met [e.g., Biometrics 52 (1996) 249-264]. Extensions to conditionally affinely invariant matching with conditionally DMPES distributions are also discussed.

Matched Sampling for Causal Effects: William G. Cochran's Contributions to the Design, Analysis, and Evaluation of Observational Studies

Abstract: Bill Cochran was not only a wonderfully creative and insightful statistician, with major written contributions to many areas, including to the field of nonrandomized, observational studies, but personally was a fabulous teacher and PhD adviser, whose influence on many is still strongly felt. This brief presentation will describe some of the major themes of his work in this area, and how these permeate modern thinking on the design, analysis, and evaluation of observational studies.

Estimating the Causal Effects of Marketing Interventions Using Propensity Score Methodology

Abstract: Propensity score methods were proposed by Rosenbaum and Rubin [Biometrika 70 (1983) 41--55] as central tools to help assess the causal effects of interventions. Since their introduction more than two decades ago, they have found wide application in a variety of areas, including medical research, economics, epidemiology and education, especially in those situations where randomized experiments are either difficult to perform, or raise ethical questions, or would require extensive delays before answers could be obtained. In the past few years, the number of published applications using propensity score methods to evaluate medical and epidemiological interventions has increased dramatically. Nevertheless, thus far, we believe that there have been few applications of propensity score methods to evaluate marketing interventions (e.g., advertising, promotions), where the tradition is to use generally inappropriate techniques, which focus on the prediction of an outcome from background characteristics and an indicator for the intervention using statistical tools such as least-squares regression, data mining, and so on. With these techniques, an estimated parameter in the model is used to estimate some global ``causal'' effect. This practice can generate grossly incorrect answers that can be self-perpetuating: polishing the Ferraris rather than the Jeeps ``causes'' them to continue to win more races than the Jeeps $\Leftrightarrow$ visiting the high-prescribing doctors rather than the low-prescribing doctors ``causes'' them to continue to write more prescriptions. This presentation will take ``causality'' seriously, not just as a casual concept implying some predictive association in a data set, and will illustrate why propensity score methods are generally superior in practice to the standard predictive approaches for estimating causal effects.

24 Statistical Inference for Causal Effects, with Emphasis on Applications in Psychometrics and Education

Abstract: A central problem in statistics, psychometrics and education, is how to draw inferences about the causal effects of treatments (i.e., interventions) from randomized and nonrandomized data. For example, does the new job-training program really improve the quality of jobs for those trained relative to the jobs they would get without training, or does exposure to that chemical in drinking water increase cancer rates relative to drinking water without that chemical, or, of particular relevance in this volume, does that educational intervention improve the test scores of students relative to the standard program? This presentation provides an overview of the approach to the estimation of such causal effects based on the concept of potential outcomes, including a relatively detailed presentation of the Bayesian approach.

Conceptual, computational and inferential benefits of the missing data perspective in applied and theoretical statistical problems

Abstract: This article advocates the following perspective: When confronting a scientific problem, the field of statistics enters by viewing the problem as one where the scientific answer could be calculated if some missing data, hypothetical or real, were available. Thus, statistical effort should be devoted to three steps:

Control of confounding through secondary samples.

Abstract: The control of confounding is essential in many statistical problems, especially in those that attempt to estimate exposure effects. In some cases, in addition to the 'primary' sample, there is another 'secondary' sample which, though having no direct information about the exposure effect, contains information about the confounding factors. The purpose of this article is to study the influence of the secondary sample on likelihood inference for the exposure effect. In particular, we investigate the interplay between the efficiency improvement and the possible bias introduced by the secondary sample as a function of the degree of confounding in the primary sample and the sizes of the primary and secondary samples. In the case of weak confounding, the secondary sample can only little improve estimation of the exposure effect, whereas with strong confounding the secondary sample can be much more useful. On the other hand, it will be more important to consider possible biasing effects in the latter case. For illustration, we use a formal example of a generalized linear model and a real example with sparse data from a case-control study of the association between gastric cancer and HM-CAP/Band 120.

Affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributions

Abstract: In observational studies designed to estimate the effects of interventions or exposures, such as cigarette smoking, it is desirable to try to control background differences between the treated group (e.g., current smokers) and the control group (e.g., never smokers) on covariates $X$ (e.g., age, education). Matched sampling attempts to effect this control by selecting subsets of the treated and control groups with similar distributions of such covariates. This paper examines the consequences of matching using affinely invariant methods when the covariate distributions are ``discriminant mixtures of proportional ellipsoidally symmetric'' (DMPES) distributions, a class herein defined, which generalizes the ellipsoidal symmetry class of Rubin and Thomas [Ann. Statist. 20 (1992) 1079--1093]. The resulting generalized results help indicate why earlier results hold quite well even when the simple assumption of ellipsoidal symmetry is not met [e.g., Biometrics 52 (1996) 249--264]. Extensions to conditionally affinely invariant matching with conditionally DMPES distributions are also discussed.

Rejoinder to Causal Inference Through Potential Outcomes and Principal Stratification: Application to Studies with "Censoring" Due to Death

Abstract: Rejoinder on Causal Inference Through Potential Outcomes and Principal Stratification: Application to Studies with ``Censoring'' Due to Death by D. B. Rubin [math.ST/0612783]

Use of Multiple Imputation Models in Medical Device Trials

Abstract: Missing data are a common problem with data sets in most clinical trials, including those dealing with devices. Imputation, or filling in the missing values, is an intuitive and flexible way to handle the incomplete data sets that arise because of such missing data. Here we present several imputation strategies and their theoretical background, as well as some current examples and advice on computation. Our focus is on multiple imputation, which is a statistically valid strategy for handling missing data. The analysis of a multiply imputed data set is now relatively standard, for example in SAS and in Stata. The creation of multiply imputed data sets is more challenging but still straightforward relative to other valid methods of handling missing data. Singly imputed data sets almost always lead to invalid inferences and should be eschewed.

Performance assessment and league tables. Comparing like with like.

Abstract: We formulate performance assessment as a problem of causal analysis and outline an approach based on the missing data principle for its solution It is particularly relevant in the context of so-called league tables for educational, health-care and other public-service institutions The proposed solution avoids comparisons of institutions that have substantially different clientele (intake)

Performance assessment and league tables. Comparing like with like

Abstract: We formulate performance assessment as a problem of causal analysis and outline an approach based on the missing data principle for its solution. It is particularly relevant in the context of so-called league tables for educational, health-care and other public-service institutions. The proposed solution avoids comparisons of institutions that have substantially different clientele (intake).

Matched Sampling for Causal Effects: My Introduction to Matched Sampling

Abstract: This volume reprints my publications on matched sampling, or more succinctly, matching, produced during a period of over three decades. My work on matching began just after I graduated college in 1965 and has continued to the present, and beyond, in the sense that there are publications on matching subsequent to those collected here, and I have continuing work in progress on the topic. For most of the years during this period, I believe I was one of the few statistical researchers publishing in this area, and therefore this collection is, I hope, both interesting and historically relevant. In the introduction to each part, I attempt to set the stage for the particular articles in that part. When read together, the part introductions provide a useful overview of developments in matched sampling. In contrast to the earlier years, in the last few years, there have been many other researchers making important contributions to matching. Among these, ones by technically adroit economists and other social scientists are particularly notable, for example: Hahn (1998); Dehejia and Wahba (1999); Lechner (2002); Hansen (2004); Hill, Reiter, and Zanutto (2004); Hirano, Imbens, and Ridder (2004); Imbens (2004); Zhao (2004); Abadie and Imbens (2005); and Diamond and Sekon (2005). Some of these have had a direct or indirect connection to a course on causal inference I've taught at Harvard for over a decade, sometimes jointly with Guido Imbens.