2.5. Statistical Analysis

Categorical variables were reported as numbers and percentages. The distributions of quantitative variables were described by the mean value (M) and the standard deviation (SD) or median (Me), and lower (Q1) and upper quartiles (Q3). The Shapiro–Wilko test was used to assess conformity with a normal distribution.

Linear regression was used to assess the relationship between the values on the scale of depression risk (GDS-SF) and considered variables (age, gender, results of anthropometric measurements, laboratory tests and comorbidities). To find out whether age, gender, or examined comorbidities change the direction or the magnitude of the relationship between total protein concentration and the risk of depression, models with the interaction term between the total protein concentration and the considered variable (moderator) were performed. The significance of the given moderator was assessed according to the change of proportion concerning the explained variance (ΔR²).

To investigate the mechanism of the relationship between total protein concentration and the risk of depression, mediation analysis was used, taking into consideration the third variable (i.e., mediator). The scheme of the applied mediation analysis is shown in Figure 1. The process macro procedure was used [35]. Several models (steps) of linear regression were performed. The results of the mediation analysis were presented by giving three factors (effects) from models:

Model presenting the examined mediation effect. X, independent variable (protein concentration); M, mediator; Y, dependent variable (GDS-SF); a, association between X and M; b, association between M and Y after controlling for X; c`, direct effects.

Providing the coefficient for a given mediator (after controlling for total protein concentration) with 95% confidence interval (95% CI), path b.

Direct effect (c`), coefficient of regression model for the total protein concentration after controlling for mediating variable (mediator) with 95% CI.

Indirect effect with 95% CI, calculated taking into consideration “bias-corrected” and “accelerated” corrections. The effect is the product (a*b, on the attached scheme) of the coefficients (in regression model) between the total protein concentration and the studied mediating variable which examines the relationship between the coefficient (in the regression model) between the mediating variable and depression.

To establish the significance of the mediation effect, bootstrapping method was used (made for 5000 drawings). This procedure estimates the indirect effect using the bootstrapping technique (generating empirical representation of the sample distribution, treated as a population representation). All analyses were made with IBM SPPS v.22 software (Armonk, NY, USA); as a statistical significance for bilateral tests α = 0.05 was applied.