Matching and Design Efficiency in Retrospective Studies

In a recent article in Biometrics (1) I considered, among other matters, the efficiency of pairwise in experiments and in prospective nonexperimental studies. In a passing comment I cautioned against applying the statistical efficiency results to retrospective studies, pointing out that with the retrospective approach generally tends to reduce efficiency and would therefore have to be motivated by the pursuit of validity alone. That note has drawn a reaction in this journal from Bross (2), who attributes my view to the use of an unrealistic mathematical model, attempts to refute my position by presenting a simple hypothetical counterexample, and maintains that even in retrospective studies it is reasonable to seek design efficiency by matching out a strong factor in exploring the effect of a weaker factor. By reading my article (1), and possibly also the reference (3) given there and/or a subsequent discussion (4), the reader may verify that my reservations about the efficiency motive for in retrospective studies do not represent conclusions from any mathematical model but have a rather nonmathematical rationale. As to the refutation of the assertion at 1 Departments of Epidemiology and Biostatistics, Harvard School of Public Health, and Cardiology Division, Department of Medicine, Children's Hospital Medical Center, Boston, Mass. issue, in the counterexample Bross (2) does not actually compare the efficiency of the matched pairs design (involving constraints in the selection of control subjects together with a specific procedure of analysis) to that of using an independently selected control series. Instead, he merely compares two different ways of analyzing data from a study in which a matched control series was in fact used, an appropriate one (maintaining the original pairing) and a generally inappropriate one (with random repairing for analysis). Thus, Bross' counterexample illustrates the well-known analysis principle that efficiency is lost in hypothesistesting if is ignored in the analysis, but it has no bearing on the question of whether should be applied in the selection of the control series.