Counterfactuals and the paired availability design
Stuart Baker, National Cancer Institute
19 October 2005
Professor Hofler has presented some good arguments for the use of counterfactuals in causal inference. I would like to draw attention to one area of observational analysis not mentioned in the paper in which the use of counterfactuals has had great success, namely the paired availability design for historical controls [1].
The paired availability design is a before-and-after study of many geographic areas which is designed to estimate the effect of treatment received. The paired availability design involves a potential outcomes model in which subjects are classified by the type of the treatment they would receive if the availability was that for a specified time period. Some of the potential outcomes are counterfactuals because they involve the treatment received if the availability were, contrary to fact, for a different time period.
For identifiability the paired availability design requires the often reasonable assumptions that (i) no subject would receive treatment during a period of less availability and not receive treatment during a period of more availability, and (ii) the probability of outcome among subjects who receive treatment or no treatment in either time period does not depend on time period. To the best of my knowledge the paired availability design was the first paper to explicitly introduce these subject types and assumptions which were later independently developed for noncompliance in randomized trials [2]. In an application to obstetric anesthesiology the paired availability design yielded the same qualitative results as a meta-analysis of randomized trials but different results from a propensity score analysis which likely omitted important confounders [3]. For more discussion and applications see [4-6].
[1] Baker SG, Lindeman KS. The paired availability design: a proposal for evaluating epidural analgesia during labor. Statistics in Medicine 1994;13:2269-2278.
[2] Angrist JD, Imbens GW, Rubin DB. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 1996; 92: 444-455
[5] Baker SG, Kramer BS, and Prorok PC. Comparing cancer mortality rates before-and-after a change in availability of screening in different regions: Extension of the paired availability design. BMC Medical Research Methodology 2004, 4:12.
Counterfactuals and the paired availability design
19 October 2005
Professor Hofler has presented some good arguments for the use of counterfactuals in causal inference. I would like to draw attention to one area of observational analysis not mentioned in the paper in which the use of counterfactuals has had great success, namely the paired availability design for historical controls [1].
The paired availability design is a before-and-after study of many geographic areas which is designed to estimate the effect of treatment received. The paired availability design involves a potential outcomes model in which subjects are classified by the type of the treatment they would receive if the availability was that for a specified time period. Some of the potential outcomes are counterfactuals because they involve the treatment received if the availability were, contrary to fact, for a different time period.
For identifiability the paired availability design requires the often reasonable assumptions that (i) no subject would receive treatment during a period of less availability and not receive treatment during a period of more availability, and (ii) the probability of outcome among subjects who receive treatment or no treatment in either time period does not depend on time period. To the best of my knowledge the paired availability design was the first paper to explicitly introduce these subject types and assumptions which were later independently developed for noncompliance in randomized trials [2]. In an application to obstetric anesthesiology the paired availability design yielded the same qualitative results as a meta-analysis of randomized trials but different results from a propensity score analysis which likely omitted important confounders [3]. For more discussion and applications see [4-6].
[1] Baker SG, Lindeman KS. The paired availability design: a proposal for evaluating epidural analgesia during labor. Statistics in Medicine 1994;13:2269-2278.
[2] Angrist JD, Imbens GW, Rubin DB. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 1996; 92: 444-455
[3] Baker, SG and Lindeman, K.L. Rethinking historical controls. Biostatistics 2001,2: 383-396.
[4] Baker SG, Lindeman KL, and Kramer, BS The paired availability design
for historical controls. BMC Medical Research Methodology 2001, 1:9.
http://www.biomedcentral.com/1471-2288/1/9http://www.biomedcentral.com/1471-2288/1/9
[5] Baker SG, Kramer BS, and Prorok PC. Comparing cancer mortality rates before-and-after a change in availability of screening in different regions: Extension of the paired availability design. BMC Medical Research Methodology 2004, 4:12.
http://www.biomedcentral.com/1471-2288/4/12http://www.biomedcentral.com/1471-2288/4/12
[6] Baker SG and Kramer BS. Simple maximum likelihood estimates of efficacy
in randomized trials and before-and-after studies, with implications for meta-analysis Statistical Methods in Medical Research 2005, 14:1-19.
Competing interests
None