# Quasi-Experimental Design for Medical Studies with the Method of the Fuzzy Pseudo-Control Group
## 4 Annuloplasty Favorability Case Study
### Summary  
In the annuloplasty favorability case study, the MFPCG Algorithm (Section 3.6) was applied two times. Let \(U\) be the super-population of patients diagnosed with IHD and moderate and moderate-to-severe IMR with indications for surgery. In both applications, \(X_{1}=RF\) and \(X_{2}=MR\). In the first application, \(P\) is the population from \(U\) consisting of patients with indications for combined surgery who have a relatively preserved medical state (subgroup \(A_{1}\) comprises patients from \(P\)); \(Q\) is the population of \(U\) consisting of patients with indications for an isolated intervention who have a relatively preserved medical state (subgroup \(B_{1}\) comprises patients from \(Q\)). In the second application, \(P\) is the population of \(U\) consisting of patients with indications for combined surgery who have \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline
**Modification Time** & \(\mathbf{C_{M}}\) & \(\mathbf{C_{MED}}\) & \(\mathbf{Cond_{1}}\) & \(\mathbf{Cond_{2}}\) & \(\mathbf{Cond_{3}}\) & \(\mathbf{C_{t}}\) & **Rule** &
\begin{tabular}{l} **Result of** \\ **MFPCG** \\ \end{tabular} & **Class** \\ \hline BM1 & Preop & \(M_{-1}\) & \(MED_{-1}\) & T & T & F & \(C_{-1}\) & 5 & \((C_{b},C_{e})=(C_{-1},C_{+1})\) & YES+ \\ \hline BM1 & Late\_Postop & \(M_{+1}\) & \(MED_{+1}\) & T & T & F & \(C_{+1}\) & 1 & \((C_{-1},C_{+1})\) & YES+ \\ \hline BM2 & Preop & \(M_{-1}\) & \(MED_{-1}\) & T & T & F & \(C_{-1}\) & 5 & \((C_{b},C_{e})=(C_{-1},C_{+1})\) & YES+ \\ \hline BM2 & Late\_Postop & \(M_{+1}\) & \(MED_{+1}\) & T & T & F & \(C_{+1}\) & 1 & \((C_{-1},C_{+1})\) & YES+ \\ \hline BM3 & Preop & \(M_{-1}\) & \(MED_{-1}\) & T & T & F & \(C_{+1}\) & 1 & \((C_{b},C_{e})=(C_{-1},C_{+1})\) & YES+ \\ \hline BM4 & Preop & \(M_{-1}\) & \(MED_{-1}\) & T & T & F & \(C_{+1}\) & 1 & \((C_{b},C_{e})=(C_{-1},C_{+1})\) & YES+ \\ \hline \hline \end{tabular}
\end{table} 
Table 13: The MFPCG diagnostics of the influence of \(R\) on a continuous parameter \(MR\), comparing subgroups \(A_{2}\) and \(B_{2}\). \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Sample** & \(\mathbf{E_{b}}\) & \(\mathbf{PC_{b}}\) & \(\mathbf{R}\) **Favorability** & \(\mathbf{E_{e}}\) & \(\mathbf{PC_{e}}\) & \(\mathbf{R}\) **Favorability** \\ \hline No. of observations & 53 & 38 & N/A & 44 & 32 & N/A \\ \hline Fuzzy mean & 5.7 & 3.92 & unfavorable & 0.827 & 2.92 & favorable \\ \hline Fuzzy median & 6 & 4 & unfavorable & 0 & 2.64 & favorable \\ \hline Fuzzy STD & 0.802 & 0.813 & N/A & 1.13 & 1.53 & N/A \\ \hline Fuzzy IQR & 1 & 0.101 & N/A & 2 & 2 & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The numerical characteristics and change favorability for the \(MR\) fuzzy samples for groups \(A_{2}\) and \(B_{2}\). \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline
**Modification Time** & **FBT1** & **FBT2** & **FBT3** & **FBT4** & **FBT5** & **FBT6** & **FBT7** & **FBT8** & **FBT9** \\ \hline BM1 & Preop & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.9650 & 0.4540 & 0.5010 & 0.4145 \\ \hline BM1 & Late\_Postop & 0.0000 & 0.0000 & 0.0000 & 0.0005 & 0.0000 & 0.1550 & 0.0915 & 1.0000 & 0.5060 \\ \hline BM2 & Preop & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.9675 & 0.6010 & 0.5290 & 0.3650 \\ \hline BM2 & Late\_Postop & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.1925 & 0.0775 & 1.0000 & 0.5125 \\ \hline BM3 & Preop & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.9690 & 0.4135 & 0.5175 & 0.4340 \\ \hline BM3 & Late\_Postop & 0.0000 & 0.0000 & 0.0000 & 0.0005 & 0.0000 & 0.1795 & 0.1165 & 1.0000 & 0.4925 \\ \hline BM4 & Preop & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.9690 & 0.6085 & 0.5365 & 0.3895 \\ \hline BM4 & Late\_Postop & 0.0000 & 0.0000 & 0.0000 & 0.0005 & 0.0000 & 0.1885 & 0.0860 & 1.0000 & 0.5335 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: The \(p\)-values of the fuzzy Bootstrap statistical tests in MFPCG for parameter \(MR\), comparing subgroups \(A_{2}\) and \(B_{2}\).