Statistical Science

The Role of a Second Control Group in an Observational Study

Paul R. Rosenbaum

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Abstract

An observational study is an attempt to estimate the effects of a treatment when subjects are not randomly assigned to treatment or control. The possibility of using more than one control group has often been briefly mentioned in general discussions of observational studies, and many observational studies have used two control groups. Here, the limited and dispersed literature on this subject is reviewed, and the topic is developed in several directions by using a formal notation for observational studies. The value of a second control group depends on the supplementary information that is available about unobserved biases that are suspected to exist. A second control group provides a test of the assumption that conventional adjustments for observed covariates suffice in estimating treatment effects. Under the best of circumstances, this test is consistent and unbiased, and its power exceeds the probability of falsely detecting a treatment effect. Indeed, under the best of circumstances, two control groups can yield consistent and unbiased estimates of bounds on the treatment effect when conventional adjustments fail. In contrast, however, in the worst of circumstances, a second control group can be of little value.

Article information

Source
Statist. Sci. Volume 2, Number 3 (1987), 292-306.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.ss/1177013232

Digital Object Identifier
doi:10.1214/ss/1177013232

JSTOR
links.jstor.org

Citation

Rosenbaum, Paul R. The Role of a Second Control Group in an Observational Study. Statist. Sci. 2 (1987), no. 3, 292--306. doi:10.1214/ss/1177013232. http://projecteuclid.org/euclid.ss/1177013232.


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See also

  • See Comment: Paul W. Holland. [The Role of a Second Control Group in an Observational Study]: Comment. Statist. Sci., Volume 2, Number 3 (1987), 306--308.
  • See Comment: Barry H. Margolin. [The Role of a Second Control Group in an Observational Study]: Comment: The Use of Multiple Control Groups in Designed Experiments. Statist. Sci., Volume 2, Number 3 (1987), 308--310.
  • See Comment: Richard G. Cornell. [The Role of a Second Control Group in an Observational Study]: Comment. Statist. Sci., Volume 2, Number 3 (1987), 310--311.
  • See Comment: Norman Breslow. [The Role of a Second Control Group in an Observational Study]: Comment. Statist. Sci., Volume 2, Number 3 (1987), 311--312.
  • See Comment: Paul R. Rosenbaum. [The Role of a Second Control Group in an Observational Study]: Rejoinder. Statist. Sci., Volume 2, Number 3 (1987), 313--316.