*2.5. Analysis*

Descriptive statistics were derived from retrospective data found in the demographic section of the EMR for program graduates. Paired *t*-tests were used to compare dataset means from psychological questionnaires pre- and post-LTOT cessation. Prior to paired comparison, principal component analysis (PCA) was used to compare individual SF-36 subcategory results for the pre- and posttests. The SF-36 is typically reported as 8 individual scores—one for each category. However, since running multiple *t*-tests for all SF-36 subcategories might inflate the Type I error rate and result in false findings, dimension reduction was employed to minimize the number of variables to be tested. In PCA, data visualization techniques, including the loading plot [44,45] and the scree plot, were utilized in order to identify the proper number of principal components.

#### **3. Results**

#### *3.1. Descriptive Statistics*

The study began with 109 clinical program participants; 11 left the clinical program and were lost to the follow-up. Thus, 98 subjects (representing 90% of the program participants) remained under observation after the successful cessation of LTOT during the 10-week program [30] and were included in the present study. Of those who successfully graduated, 95 subjects (97%) chose to use buprenorphine as an LTOT cessation tool. Program participants were 27 to 88 years old; 69% were identified as female. A broad range of payer sources were noted: 30% Medicare, 25% industrial insurance, 10% Medicaid, 44% commercial insurance, and <1% no insurance.

#### *3.2. Principal Component Analysis and Scree Plot for the SF-36*

The reliability index, as measured by the standardized Cronbach's alpha of the pretest of SF-36 is 0.8899, compared with 0.846 at the posttest, implying that the response patterns to these questions are internally consistent. In the loading plot, the axes of the plots are the principal components, while the variables are symbolized by vectors radiating from the center. Vectors pointing in the same direction, with a small angle between them, implies a positive and close relationship between the variables. Due to this characteristic, they could be loaded into the same component. Figure 1a indicates that all observed variables in the pretest of SF-36, as depicted by the vectors, pointed in the same direction and are close to each other. Figure 1b suggests that the observed items in the posttest of SF-36 could be classified into two groups, based on the clustering patterns.

(**a**) Loading plot of pretest vectors. (**b**) Loading plot of posttest vectors.

**Figure 1.** Loading plots of SF-36 vectors.

In the scree plot (Figure 2a,b), the y-axis represents the eigenvalue, which is the sum of the squares of the loadings, whereas the x-axis denotes the number of potential components. Although the loading plot of the posttest indicates a 2-component model, both scree plots suggest that one single component is sufficient to yield the highest eigenvalue. Considering this finding, the average pretest and posttest scores of all SF-36 items were used for paired *t*-tests.

**Figure 2.** Scree plot of SF-36 variables.
