Showing papers by "Donald B. Rubin published in 1983"

The central role of the propensity score in observational studies for causal effects

Abstract: : The results of observational studies are often disputed because of nonrandom treatment assignment. For example, patients at greater risk may be overrepresented in some treatment group. This paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies. The propensity score is the (estimated) conditional probability of assignment to a particular treatment given a vector of observed covariates. Both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates. Applications include: matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching, multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations, and visual representation of multivariate adjustment by a two-dimensional plot. (Author)

Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary Outcome

Abstract: This paper proposes a simple technique for assessing the range of plausible causal con- clusions from observational studies with a binary outcome and an observed categorical covariate. The technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response. A medical study of coronary artery disease is used to illustrate the technique. Inevitably, the results of clinical studies are subject to dispute. In observational studies, one basis for dispute is obvious: since patients were not assigned to treatments at random, patients at greater risk may be over-represented in some treatment groups. This paper proposes a method for assess- ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response. Despite their limitations, observational studies will continue to be a valuable source of information, and therefore it is prudent to develop appropriate methods of analysis for them. Our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u, under several sets of assumptions about u. Both Cornfield et al. (1959) and Bross (1966) have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment, that is, whether the treatment effect, after adjustment for u could be zero. Our method has two advantages: first, Cornfield et al. (1959) and Bross (1966) adjust only for the unmeasured binary covariate u, whereas we adjust for measured covariates in addition to the unmeasured covariate u. Second, Cornfield et al. (1959) and Bross (1966, 1967) only judge whether the effect of the treatment could be zero having adjusted for u, where Cornfield et al. (1959) employ an implicit yet extreme assumption about u. In contrast, we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u. In principle, the ith of the N patients under study has both a binary response r1i that would have resulted if he had received the new treatment, and a binary response ro0 that would have resulted if he had received the control treatment. In this formulation, treatment effects are comparisons of r1i and roi, such as r1i - roi. Since each patient receives only one treatment, either rli or ro0 is observed, but not both, and therefore comparisons of rli and roi imply some degree of speculation. Treatment effects defined as comparisons of the two potential responses, r1i and roi, of individual patients are implicit in Fisher's (1953) randomization test of the sharp null

The bias due to incomplete hatching

Abstract: Observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments. Matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group. In practice, there is a trade-off between the desires to find matches for all treated units and to obtain matched treated-control pairs that are extremely similar to each other. We derive expressions for the bias in the average matched pair difference due to (1) the failure to match all treated units—incomplete matching, and (2) the failure to obtain exact matches—inexact matching. A practical example shows that the bias due to incomplete matching can be severe, and moreover, can be avoided entirely by using an appropriate multivariate nearest available matching algorithm, which in the example, leaves only a small residual bias due to inexact matching.

On Jointly Estimating Parameters and Missing Data by Maximizing the Complete-Data Likelihood

Abstract: One approach to handling incomplete data occasionally encountered in the literature is to treat the missing data as parameters and to maximize the complete-data likelihood over the missing data and parameters. This article points out that although this approach can be useful in particular problems, it is not a generally reliable approach to the analysis of incomplete data. In particular, it does not share the optimal properties of maximum likelihood estimation, except under the trivial asymptotics in which the proportion of missing data goes to zero as the sample size increases.

Incomplete data in sample surveys. Vol. 2: theory and bibliographies

Abstract: This is one of three volumes that represent the results of work undertaken by the Panel on Incomplete Data. The panel was set up in 1977 by the Committee on National Statistics within the Commission on Behavioral and Social Sciences and Education of the National Research Council in order to undertake a comprehensive review of the literature on survey incompleteness in sample surveys and to explore ways of improving the methods of dealing with it. The second volume contains the papers on theory and two bibliographies. An initial paper considers the historical perspective. Five papers are then presented on data collection dealing with callbacks follow-ups and repeated telephone calls; the impact of substitution on survey estimates; quota sampling; randomized response techniques; and handling missing data by network sampling. The next two papers focus on non-response and double sampling covering the randomization approach and the Bayesian approach. A section on weighting and imputation methods covers conceptual issues in the presence of non-response weighting adjustment for unit non-response hot-deck procedures and the use of multiple imputations to handle non-response. Sections are also included on imputation methodology concerning total survey error and on superpopulation models for non-response including both the ignorable case and the non-ignorable case. A selected annotated bibliography is provided with keywords and phrases available as an index; a separate unannotated bibliography deals with non-response and related topics. The primary geographic focus is on the United States.

Empirical bayes estimation of coefficients in the general linear model from data of deficient rank

Abstract: Empirical Bayes methods are shown to provide a practical alternative to standard least squares methods in fitting high dimensional models to sparse data. An example concerning prediction bias in educational testing is presented as an illustration.

Ensemble-Adjusted p Values

Abstract: In many data analyses, multiple tests of significance are performed. For example, many correlations in a large correlation matrix may be examined for significance or a number of other contrasts may be of interest. As the number of such tests of significance increases, there is an increasing likelihood that one of them will be declared significant even when the null hypothesis is true. More precisely, let PJ be the p value for they'th test of significance or contrast, j = 1, . . . , C. If the 7th contrast is declared significant when PJ < a, then even if all C null hypotheses of no effects are true, the probability that some contrast will be declared significant increases with C. A standard simple technique to guard against this danger is to apply Bonferroni's inequality and declare the jth contrast significant ifp/ < a/C (Harris, 1975; Morrison, 1976; Myers, 1979; Snedecor & Cochran, 1980). This procedure can be shown to be conservative in the sense that under the null hypothesis, the probability that one or more contrasts will be declared significant is at most a. Note that the p value for the jth contrast, PJ, is essentially replaced by an "ensemble-adjusted p value," Cpj, and these ensemble-adjusted p values are compared with the fixed significance level for hypothesis testing (a). Since in many contexts it is more informative to report p values than the significant-nonsignificant dichotomy for some fixed a, we believe that the ensemble-adjusted

Rounding Error in Regression: The Appropriateness of Sheppard's Corrections,

Abstract: : We consider three simple approaches to rounding error in least squares regression. The first treats the rounded data as if they were unrounded, the second adds an adjustment to the diagonal of the covariance matrix of the variables, and the third subtracts an adjustment from the diagonal. The third, Sheppard's corrections, can be motivated as maximum likelihood with small rounding error and either (1) joint normal data or (2) normal residuals, regular independent variables, and large samples. Although an example and theory suggest that the third approach is usually preferable to the first two, a generally satisfactory attack on rounding error in regression requires the specification of the full distribution of variables, and convenient computational methods for this problem are not currently available. (Author)

More on EM for ML Factor Analysis.

Abstract: We address several issues that are raised by Bentler and Tanaka's [1983] discussion of Rubin and Thayer [1982]. Our conclusions are: standard methods do not completely monitor the possible existence of multiple local maxima; summarizing inferential precision by the standard output based on second derivatives of the log likelihood at a maximum can be inappropriate, even if there exists a unique local maximum; EM and LISREL can be viewed as complementary, albeit not entirely adequate, tools for factor analysis.

A Case Study of the Robustness of Bayesian Methods of Inference: Estimating the Total in a Finite Population Using Transformations to Normality

Abstract: Publisher Summary This chapter presents a case study of the robustness of Bayesian methods of inference estimating the total in a finite population using transformations to normality. Bayesian intervals provide interval estimates that can legitimately be interpreted as such or at least to offer guidance as to when the intervals that are provided can be safely interpreted in this manner. The potential application of the statistical methods is often demonstrated either theoretically, from artificial data generated following some convenient analytic form, or from real data without a known correct answer. The case study presented here uses a small, real data set with a known value for the quantity to be estimated. It is surprising and instructive to see the care that may be needed to arrive at satisfactory inferences with real data. Simulation techniques are not needed to estimate totals routinely in practice. If stratification variables were available, that is, categorizing the municipalities into villages, towns, cities, and boroughs of New York City, to estimate the population total from a sample of 100, oversampling the large municipalities would be highly desirable. Robustness is not a property of data alone or questions alone, but particular combinations of data, questions and families of models. In many problems, statisticians may be able to define the questions being studied so as to have robust answers.

Missing data in large data sets

Abstract: Publisher Summary This chapter explores those statistical issues that arise from missing data and uses current population surveys to illustrate these ideas. Many basic problems are introduced via simple examples. The chapter presents the taxonomy of these methods. The explicit modeling approach is a flexible but principled way to proceed in practice. The chapter discusses the computational methods for the analysis of incomplete data. It also outlines various methods for handling incomplete data and describes the modeling approach to incomplete data. A principled approach to the problem of missing data in large databases requires a plausible model for the missing data mechanism and estimation procedures that remove or minimize biases introduced by the incompleteness of the data.