Quasi-Experimental Design for Medical Studies with the Method of the Fuzzy Pseudo-Control Group

(1) Background: Let the continuous parameter X be a proxy variable for the outcome of an intervention R. Quasi-experimental studies are designed to evaluate the effect of R over X when forming a randomized control group (without the intervention) is impractical or/and unethical. The most popular quasi-experimental design, the difference-in-differences (DID) method, uses four samples of X values (pre- and post-intervention experimental and pseudo-control groups). DID always quantitatively evaluates the effect of R over X. However, its practical significance is restricted by several (often unprovable) assumptions and by the monotonic preference requirement over X. We propose a novel fuzzy quasi-experimental computational approach that addresses those limitations. (2) Methods: A novel method of the fuzzy pseudo-control group (MFPCG) is introduced and formalized. It uses four fuzzy samples as input, exactly the same as DID. We practically determine and statistically compare the favorability of the differences in X before and after the intervention for the experimental and the pseudo-control groups in case of the more general hill preferences over X. MFPCG applies four modifications of fuzzy Bootstrap procedures to perform each of the nine statistical tests used. The new method does not use the assumptions of DID, but it does not always produce a positive or a negative answer, as MFPCG results are qualitative. It is not a competing methodology; as such, it should be used alongside DID. (3) Results: We assess the effect of annuloplasty that acts in conjunction with revascularization over two continuous parameters that characterize the condition of patients with ischemic heart disease complicated by moderate and moderate-to-severe ischemic mitral regurgitation. (4) Conclusions: The statistical results proved the favorable effect of annuloplasty on two parameters, both for patients with a relatively preserved medical state and patients with a relatively deteriorated medical state. We validate the MFPCG solution of the case study by comparing them with those from the fuzzy DID. We discuss the limitations and adaptability of MFPCG, which should warrant its use in other case studies and domains.