Am J Epidemiol 2004; 159:1108.
Copyright © 2004 by the Johns
Hopkins Bloomberg School of Public Health
LETTERS TO THE EDITOR |
THE AUTHORS REPLY
1 Division of Pharmacoepidemiology and Pharmacoeconomics, Division of Preventive Medicine, Brigham and Women’s Hospital, Harvard Medical School, Boston MA 02120
2 Department of Epidemiology, German Centre for Research on Ageing, University of Heidelberg, 69115 Heidelberg, Germany
We thank Drs. Schill and Wild for their comments (1) on our article (2). We welcome the interest in the flexible matching strategies that we promoted (2, 3), also evidenced by a recent article in the Journal (4).
We introduced the degree of matching (DM) only to parameterize flexible matching as a function of previously known study designs, that is, the unmatched case-control study (DM = 0) and the frequency-matched study (DM = 1). Using simulations, we could show that the optimal degree of matching with respect to power and relative efficiency to estimate main effects (3) and interactions (2) is rarely 1, but often between 0 and 1 or above 1, depending on the assumed scenario. Once the concept of flexible matching and its possible advantages with respect to power and relative efficiency have been accepted, the parameter we used to introduce the concept (DM) might not be ideal, a fact that we already acknowledged (2, 3).
Although we agree that the optimum flexible matching strategy for a given set of parameters is a function of balance of the four cells in sampled controls and therefore does not depend on the parameters of the disease model, we do not find this information very helpful from a practical or pragmatic point of view. In the planning phase of a case-control study, the first question is whether or not to adopt "biased control sampling," which decision should be based on an evaluation of the possible gain in efficiency compared with the increased complexity (and its potential costs) of the control sampling. Although flexible matching can help to improve efficiency compared with "traditional" frequency matching, the overall gain in efficiency by any form of matching is often marginal, is likely to be dependent on the expected cell frequencies in cases, and can therefore be assessed only by taking the parameters of the disease model (that are also needed to estimate the gain by "traditional" frequency matching) into account.
To do so, we developed a Statistical Analysis System (SAS; SAS Institute, Inc., Cary, North Carolina) macro calculating the power, relative efficiency, and expected cell frequencies for cases and controls selected over the whole range of possible (marginal) prevalences of the matching factor based on the large sample variance of the multiplicative interaction for any parameter constellation (5). The free program can be downloaded from the statistical archive network maintained by the Department of Medical Informatics, Biometry, and Epidemiology at the University of Erlangen-Nuremberg (http://www.imbe.med.uni-erlangen.de/issan/issan.htm) and will help epidemiologists to assess the benefits of flexible matching in the planning phase and during control sampling of case-control studies. Once "biased control sampling" has been decided upon, the optimal prevalence of the matching factor should be aimed at rather than the one observed in cases ("traditional" frequency matching), and losses in efficiency due to nonoptimal prevalences should be weighted against the costs of achieving the optimal prevalence.
We hope that the idea of flexible matching will stimulate further insights into "biased control sampling" strategies and thus help to improve our understanding of optimal efficiency of control sampling in case-control studies.
REFERENCES
- Schill W, Wild P. Re: "Flexible matching strategies to increase power and efficiency to detect and estimate gene-environment interactions in case-control studies." (Letter). Am J Epidemiol 2004;159:1107–8.
[Free Full Text] - Stürmer T, Brenner H. Flexible matching strategies to increase power and efficiency to detect and estimate gene-environment interactions in case-control studies. Am J Epidemiol 2002;155:593–602.
[Abstract/Free Full Text] - Stürmer T, Brenner H. Degree of matching and gain in power and efficiency in case-control studies. Epidemiology 2001;12:101–8.[CrossRef][ISI][Medline]
- Saunders CL, Barrett JH. Flexible matching in case-control studies of gene-environment interactions. Am J Epidemiol 2004;159:17–22.
[Abstract/Free Full Text] - Stürmer T, Gefeller O, Brenner H. A computer program to estimate power and relative efficiency to assess gene-environment interactions in flexibly matched case-control studies. Comput Methods Programs Biomed (in press). (doi:10.1016/j.cmpb.2003.08.003).
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