# 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.

• Can you link to the article? A lot more context is needed before it can be determined why they used a particular type of analysis or whether it was appropriate. – syntonicC Sep 2 '17 at 4:16
• Using significance in univariate models to screen for predictors in multivariate models is just not valid. So simply, no, if that's the whole story, its not appropriate. – Matthew Drury Sep 2 '17 at 4:52
• In general I see what @MatthewDury is saying but perhaps they are doing a feature selection step first (haven't looked at the paper yet). As long as there show performance on hold out data i don't see a problem with that. – DataD'oh Sep 2 '17 at 18:43
• what you describe is not uncommon in medical research. For example, see the methods section in the following article, ie the 6 steps they list: nature.com/articles/7211492 – pau13rown Dec 30 '17 at 12:46

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.