Attributing Effects to Treatment in Matched Observational Studies

By Rosenbaum, Paul R. | Journal of the American Statistical Association, March 2002 | Go to article overview

Attributing Effects to Treatment in Matched Observational Studies


Rosenbaum, Paul R., Journal of the American Statistical Association


An effect is attributable to treatment if it would not have been observed had the individual been exposed to control instead. Extending earlier results on attributable effects in unmatched groups, a method of exact randomization inference and sensitivity analysis is developed for case-referent, case-crossover, and cohort studies with matched sets, and a large sample approximation to the exact inference is given. The unmatched case, considered previously, has certain symmetries that the matched case, considered here, does not have. As a result, approximation for the matched case requires the use of the recently developed method of asymptotic separability, which was not needed in the unmatched case. Several examples are presented, including a case-referent study of Helicobactre pylori infection as a cause of myocardial infarction, a case-crossover study of alcohol as a cause of injury, a cohort study of women who gave birth at home, and a study of the effects of cadmium exposure with a continuous outcome measur ing kidney function. Unlike tests of no effect, inference about attributable effects has a different form in case-referent and cohort studies.

KEY WORDS: Asymptotic separability; Attributable effect; Displacement effect; Randomization inference; Sensitivity analysis.

1. ATTRIBUTABLE EFFECTS IN EXPERIMENTS AND OBSERVATIONAL STUDIES

1.1 How Does Randomization Affect Inference?

In his 1935 book Design of Experiments, Fisher carefully argued that the random assignment of treatments in experiments justifies certain inferences about the effects caused by those treatments--that randomization forms the "reasoned basis for inference" in experiments--and that these same inferences would not be justified by identical data obtained in a nonrandomized study. In Fisher's view, causal inference depends partly on the observed data, but also partly on how the data were obtained. This view has two desirable consequences. First, it serves to encourage randomized experimentation when randomization is ethical and feasible. Second, it forces analyses of nonrandomized or observational studies of treatment effects to explicitly acknowledge, as part of the quantitative findings, greater uncertainty about causal effects than would be present had random assignment been used.

A limitation is that many randomization tests of the hypothesis of no treatment effect are not paired with confidence intervals. If the treatment has an additive effect, [tau], then a randomization test of no effect can be inverted to yield confidence intervals and point estimates for [tau] (see, e.g., Hodges and Lehmann 1963; Moses 1965; Lehmann 1963, 1975; Rosenbaum 1995a sec. 2). The model of an additive effect is useful in many settings but is inapplicable in many others- for instance, for binary responses, where inferences typically invoke distributional assumptions not derived from random assignment. This article extends a line of reasoning begun in earlier work (Rosenbaum 2001), in which attributable effects are used to substantially expand the collection of randomization tests that may be inverted to yield confidence intervals. The approach also yields sensitivity analyses that measure the added uncertainty present when treatments are not randomly assigned.

An attributable effect describes how treated subjects would have responded had they been spared exposure to the treatment. As a consequence, the attributable effect depends in part on the identity of the subjects exposed to treatment, and so different randomizations typically produce different attributable effects. In this sense, the attributable effect is not a parameter, but rather is an unobserved random variable. Nonetheless, inference proceeds along a relatively conventional path. Before embarking on that path, I present a useful illustration.

1.2 Example: Infection as a Possible Cause of Early Onset Myocardial Infarction

The example in this section is from an observational study and is intended to provide the simplest illustration of the general method developed in the current article.

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Attributing Effects to Treatment in Matched Observational Studies
Settings

Settings

Typeface
Text size Smaller Larger
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Full screen

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.