Showing papers by "Donald B. Rubin published in 1974"

Estimating causal effects of treatments in randomized and nonrandomized studies.

Abstract: A discussion of matching, randomization, random sampling, and other methods of controlling extraneous variation is presented. The objective is to specify the benefits of randomization in estimating causal effects of treatments. The basic conclusion is that randomization should be employed whenever possible but that the use of carefully controlled nonrandomized data to estimate causal effects is a reasonable and necessary procedure in many cases. Recent psychological and educational literature has included extensive criticism of the use of nonrandomized studies to estimate causal effects of treatments (e.g., Campbell & Erlebacher, 1970). The implication in much of this literature is that only properly randomized experiments can lead to useful estimates of causal effects. If taken as applying to all fields of study, this position is untenable. Since the extensive use of randomized experiments is limited to the last half century,8 and in fact is not used in much scientific investigation today,4 one is led to the conclusion that most scientific "truths" have been established without using randomized experiments. In addition, most of us successfully determine the causal effects of many of our everyday actions, even interpersonal behaviors, without the benefit of randomization. Even if the position that causal effects of treatments can only be well established from randomized experiments is taken as applying only to the social sciences in which

Controlling Bias in Observational Studies: A Review.

Abstract: : This paper reviews work on the effectiveness of different methods of matched sampling and statistical adjustment, alone and in combination, in reducing bias due to confounding x-variables when comparing two populations. The adjustment methods were linear regression adjustment for x continuous and direct standardization for x categorical.

Characterizing the Estimation of Parameters in Incomplete-Data Problems

Abstract: A framework is given for organizing and understanding the problems of estimating the parameters of a multivariate data set which contains blocks of missing observations. The basic technique is to decompose the original estimation problem into smaller estimation problems by factoring the likelihood of the observed data into a product of likelihoods. The result is summarized in a “factorization table,” which identifies the “complete-data” factors whose parameters may be estimated using standard, well-understood complete-data techniques, and the “incomplete-data” factors whose parameters must be estimated using special missing-data methods.

Multivariate matching methods that are equal percent bias reducing, i: some examples

Abstract: Multivariate matching methods are commonly used in the behavioral and medical sciences in an attempt to control bias when randomization is not feasible. Some examples of multivariate matching methods are discussed in Althauser and Rubin (1970) and Cochran and Rubin (1973), but otherwise seem to have received little attention in the literature. Here, we present examples of multivariate matching methods that will yield the same percent reduction in bias for each matching variable for a variety of underlying distributions. Eleven distributional cases are considered, and for each one, matching methods are defined which are equal percent bias reducing. Methods discussed in Section 8, which are based on the values of the estimated best linear discriminant or which define distance by a sample based inner-product, will probably be the most generally applicable in practice.

Multivariate matching methods that are equal percent bias reducing, ii: maximums on bias reduction for fixed sample sizes

Abstract: Matched sampling is a method of data collection designed to reduce bias and variability due to specific matching variables. Although often used to control for bias in studies in which randomization is practically impossible, there is virtually no statistical literature devoted to investigating the ability of matched sampling to control bias in the common case of many matching variables. An obvious problem in studying the multivariate matching situation is the variety of sampling plans, underlying distributions, and intuitively reasonable matching methods. This article considers one class of multivariate matching methods which yield the same percent reduction in expected bias for each of the matching variables. The primary result is the derivation of the expression for the maximum attainable percent reduction in bias given fixed distributions and fixed sample sizes. An examination of trends in this maximum leads to a procedure for estimating minimum ratios of sample sizes needed to obtain well-matched samples.

The variance of a linear combination of independent estimators using estimated weights

Abstract: Let t1,…,tk be independent unbiased estimators of a parameter τ. Let t* = Σαiti have minimum variance among unbiased linear estimators of τ, and let , be any linear combinations with () independent of t1,…,tk. We prove that is unbiased for τ and that the ratio of the variance of to the variance of t* is where is the mean square error of as an estimator of αi.

Noniterative least squares estimates, standard errors, and f-tests for any analysis of variance with missing data

Abstract: This article generalizes Rubin's method of least squares estimation of missing values in any analysis of variance. The general method produces not only least squares estimates of all parameters and the residual mean square, but also the correct least squares standard error and t-test of any contrast as well as the least squares sum of squares and F-test due to any collection of contrasts. The method is noniterative and requires only those subroutines designed to handle complete data plus a subroutine to find the inverse of an m x m symmetric matrix, where m is the number of missing values.

The assessment of a treatment effect when a covariate is observed on a subset of the units: i. simple estimators

Abstract: Consider a completely randomized experiment with two groups, say treatment and control, and a covariate X that has been observed on a subset of the units. The objective is to estimate τ, the treatment effect on the variable Y which is recorded for all units. Although the average Y difference in the two groups, , is unbiased for τ, it is common to try to use X to increase the precision of the estimate of τ by forming a covariance adjustment, especially if the correlation between X and Y, ρ, is large. If X is not fully observed it is not clear whether to and/or how to form the covariance adjusted estimate. In addition to , we consider two covariance adjusted estimates of τ, which ignores the units without X, and which fills in group means for the missing values. We compare the three estimators' variances and find the conditions under which each estimator is best.

An algorithm for the posterior distribution of the cell means in a two‐way unbalanced manova

Abstract: When the prior distributions for the grand mean, row effects, column effects and interaction effects are all independent, with that for the grand mean being flat, the posterior expectation and covariance matrix of the cell means (under a Gaussian model) in a 2-way MANOVA may be obtained via a special matrix inversion technique which offers a great saving in storage and computation time. An APL program and example are presented.