Univariate and multivariate regression I found a research article Nurses’ reports of staffing adequacy and surgical site infections: A cross-sectional multi-centre study and I want to know the reason why they used regression for their research. 
The research is about the relationship of work environment with the emergence of surgical site infections.  They first performed Univariate mixed effects logistic regression to examine the associate between the independent and dependent variable. 
Independent variables that were significantly associated with the clinical outcome variable were then included in the multivariate mixed effects logistic regression. 
I want to know why they used two regression and if it is appropriate.    
 A: This is table 4 from the linked paper:
Table 4. Univariate mixed-effects logistic regression model for the associations between independent variables and surgical site infections (patients: level 1* and hospitals: level 2**).

 Variables  Surgical site infection after total hip arthroplasty
                                                    Odds ratio  95% confidence interval p-value
    Elective procedure* (reference: non-elective)   0.40    0.24, 0.67  p < 0.001
    Age group*                                      1.04    1.02, 1.07  p < 0.001
    Staffing adequacy**                             0.97    0.95, 0.99  p = 0.009
    Overall survival**                              0.81    0.46, 1.43  p = 0.476
    Nurses' reports on the quality system**         0.99    0.95, 1.05  p = 0.938
    Patient safety management**                     1.00    0.96, 1.04  p = 0.980
    Nurse-physician relationship**                  0.99    0.95, 1.05  p = 0.935
    Quality of nursing**                            1.00    0.96, 1.04  p = 0.984

Note how the odds ratios (even the significant ones) are mostly close to 1. These table is the uni-variate (that is, with only one predictor) (logistic) regressions, all with the same response surgical site infections. 
Then the multi-predictor (logistic) regression:

Table 5. Mixed-effects logistic regression model for the associations
  between independent variables and surgical site infections including
  the interaction between staffing adequacy and procedure type (n =
  2724) (patients: level 1* and hospital: level 2**).

Variables   Surgical site infection after total hip arthroplasty
                                                    Odds ratio  95% confidence interval p-value
Staffing adequacy                                   1.00    0.96, 1.02  0.670
Age group                                           1.03    1.01, 1.06  0.008
Non-elective procedure                              1   –   –
Elective procedure                                  5.4 1.34, 21.7  0.017
Interaction: elective procedure × staffing adequacy 0.94    0.91, 0.97  0.001

No other model validation is reported. I'm not sure this looks very convincing, looks like a pilot study. 
