Showing papers by "Donald B. Rubin published in 2005"

Causal inference using potential outcomes: Design, modeling, decisions

Abstract: Causal effects are defined as comparisons of potential outcomes under different treatments on a common set of units. Observed values of the potential outcomes are revealed by the assignment mechanism—a probabilistic model for the treatment each unit receives as a function of covariates and potential outcomes. Fisher made tremendous contributions to causal inference through his work on the design of randomized experiments, but the potential outcomes perspective applies to other complex experiments and nonrandomized studies as well. As noted by Kempthorne in his 1976 discussion of Savage's Fisher lecture, Fisher never bridged his work on experimental design and his work on parametric modeling, a bridge that appears nearly automatic with an appropriate view of the potential outcomes framework, where the potential outcomes and covariates are given a Bayesian distribution to complete the model specification. Also, this framework crisply separates scientific inference for causal effects and decisions based on s...

Bayesian Inference for Causal Effects

Abstract: A central problem in statistics 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, or does exposure to that chemical in drinking water increase cancer rates? This presentation provides a brief overview of the Bayesian approach to the estimation of such causal effects based on the concept of potential outcomes.

Statistical issues: a roundtable discussion

Abstract: Dr Alderson: I am Norris Alderson. I am Associate Commissioner for Science at FDA, and I had the privilege of working with a Planning Committee to arrange for this workshop. I was the only non-statistician in the group, I must tell you, and this was really an experience for me. I want to introduce this panel because I think it is unique from the perspective that it has representatives from FDA, industry, and academia. They are Dr Susan Ellenberg from CBER, Dr Jay Siegel from Centocor, Professor Don Rubin from Harvard University, Dr Gregory Campbell from CBER, Dr Stacy Lindborg from Eli Lilly, Dr Robert O’Neill from CDER, and Professor Ralph D’Agostino, Boston University. Our task when we set up this panel was to give this group the opportunity to summarize, from their perspective, what they have heard, and also think about what is next. Speaking on behalf of the Planning Committee, we are interested in questions, as well as comments from the audience, as related to the use of Bayesian methods as a tool, particularly in the context of the critical path initiative, reduce the time for review and approval of new public health products.

Three contributions to statistical computing

Abstract: This thesis contains three papers (which may be read independently) on statistical computing. Paper 1 deals with improving the expectation-maximization (EM) algorithm using vector sequence transformations (VSTs). VSTs, such as reduced rank extrapolation and minimal polynomial extrapolation, are popular in numerical analysis but almost unknown to statisticians. For a vector sequence {sn, n ≥ 1} that converges linearly to s∞ these methods achieve increased speed of convergence by making a guess at s∞ based on several consecutive values of the sequence. These accelerators are easy to implement, take little computer time, and often result in considerably improved speed, although they do not automatically preserve the monotone increase in the likelihood function, which is a great advantage of EM. When fitting hierarchical models such as generalized linear mixed models (GLMMs) using EM or the data augmentation (DA) algorithm, the computing efficiency may depend crucially on the choice of the augmentation scheme. The efficient data augmentation idea of Meng and van Dyk (1997, 1999, 2001) chooses a DA scheme that is both quick to converge and easy to implement. Papers 2 and 3 both deal with finding efficient DA schemes. Paper 2 first studies the convergence rates of EM under two special augmentation schemes, the sufficient augmentation (SA) and the ancillary augmentation (AA), and then proceeds to design, using results on EM, certain optimal conditional augmentation (OCA) schemes, to speed up the DA algorithm. On the theoretical side, we derive general formulas for the OCA, which are often easily obtained or approximated; in the empirical comparisons, we extend the use of efficient DA to complicated situations such as GLMMs, and show that OCA results in considerable gain in efficiency. Paper 3 proposes a combined augmentation approach, which utilizes simultaneously the SA and the AA. Using a Poisson time series model as a realistic example, we demonstrate that, by utilizing both sufficient and ancillary augmentation schemes, considerable computational efficiency is gained with limited extra human effort, and the improved algorithm is fast for various data configurations. In the theoretical study that complements the empirical investigations, we show that, in addition to being robust, under certain conditions this combined approach is also optimal among a broad class of DA schemes.