# Quasi-Experimental Design for Medical Studies with the Method of the Fuzzy Pseudo-Control Group
## 4 Annuloplasty Favorability Case Study  
We shall illustrate our proposed method with a case study from medical practice. Ischemic heart disease (IHD) (also known as coronary heart disease or coronary artery disease) is among the most common heart diseases worldwide. When IHD is additionally complicated with a secondary mitral regurgitation (\(MR\)), the mitral valve (MV) between the left heart chambers (the left atrium, LA, and the left ventricle, LV) does not fully close. Blood leaks backward across the valve and into the LA to form the regurgitation volume (RV). The prognosis for patients with ischemic \(MR\) (IMR) is worse than when the \(MR\) is caused by other conditions (e.g., primary \(MR\), which is caused by a primary abnormality of one or more components of the valve apparatus--leaflets, chordae tendineae, papillary muscles, annulus, etc.). Such patients suffer an abnormality of the myocardium of the LV of the heart that leads to the remodeling of the LV and dislocation of the papillary muscles. This complex mechanism is the leading cause of IMR, which deteriorates over time and can cause various levels of heart failure [41; 42; 43]. Patients with mild IMR (also called grade I) usually undergo an isolated coronary artery bypass graft (CABG). Patients with severe IMR traditionally undergo a combined operation that includes mitral valve repair (MVRepair) through annuloplasty or valve replacement, combined with a coronary artery bypass (MVRepair + CABG). These surgical recommendations are well-accepted in medical practice [44]. When patients have moderate or moderate-to-severe IMR, the optimal treatment is rigorously debated due to factors such as recurring IMR several months to several years after surgery, long-term survival rates, etc. Research in favor of the combined intervention is proposed in [45; 46; 47; 48; 49]. Research that outlined the shortcomings of anuloplasty in such patients is provided in [50; 51; 52]. The available studies included comparatively small groups of patients, and the results are hard to compare, as the studies used different diagnostic criteria and operation techniques. Our analysis aims to demonstrate if annuloplasty positively influences patients with moderate and moderate-to-severe IMR. Part of the patients with IMR in our study underwent MVRepair+CABG (group \(A\)), whereas the rest underwent only CABG (group \(B\)). The choice of surgical treatment in the case of IMR is not trivial, for the reasons outlined above. The choice of an approach faces the following difficulties:  
1. Traditionally, the classification of patients is based on subjective expertise. There is no specific measure of how typical a patient is to a given group. 2. The groups are not homogenous. Therefore, comparing them is complicated. Some patients are very suitable for a given procedure; others are clearly unsuitable for this procedure, but the decision is unclear and ambiguous for the remaining patients. A previous study offered two stratification algorithms to allocate the patients in each group into two comparatively more homogenous subgroups depending on the preoperative medical status of patients: comparatively preserved status (subgroups \(A_{1}\) and \(B_{1}\)) and comparatively deteriorated status (subgroups \(A_{2}\) and \(B_{2}\)) [53]. This allows us to avoid comparing the groups \(A\) and \(B\). Instead, we will compare \(A_{1}\) and \(B_{1}\) on one hand and \(A_{2}\) and \(B_{2}\) on the other. As a result, we can adequately assess the effect of the annuloplasty. We shall demonstrate the application of MFPCG to assess the effect of the annuloplasty (\(R\)) that acts in conjunction with the base intervention of revascularization (\(V\)) over two of the continuous parameters (\(X_{1}\) and \(X_{2}\)), described in Section 4.1, that characterize the condition of the target population (\(P\)) of patients with moderate and moderate-to-severe IMR subjected to a combined procedure (MVRepair + CABG).