38. Logistic Regression with Multiple Predictors (55 Patients)

In the Chaps. 36 and 37 logistic regression with a single binary or continuous predictor was explained. Just like linear regression, logistic regression can also be performed on data with multiple predictors. In this way the effects on the outcome of not only treatment modalities, but also of additional predictors like age, gender, comorbidities etc. can be tested simultaneously.

Do all of the predictors independently of one another predict the outcome.

The example of Chap. 35 is used once more. In 55 hospitalized patients the risk of falling out of bed was assessed. The question to be answered was: is there a significant difference between the risk of falling out of bed at the departments of surgery and internal medicine. The first 10 patients of the 55 patient file is underneath.

The entire data file is entitled “chapter35unpairedbinary” and is in extras.springer.com. We will start by opening the data file in SPSS. First, simple logistic regression with department as predictor and falloutofbed as outcome will be performed. For analysis the statistical model Binary Logistic Regression in the module Regression is required.

The above results table of the logistic regression shows that the department is a significant predictor at p = 0,025.

Next, we will test whether age is a significant predictor of falloutofbed.

Also age is a significant predictor of falling out of bed at p < 0,0001.

Subsequently, we will test all of the predictors simultaneously, and, in addition, will test the possibility of interaction between age and department on the outcome. Clinically, this could very well exist. Therefore, we will add an interaction-variable of the two as an additional predictor.

The above table shows the output of the multiple logistic regression. Interaction is not observed, and the significant effect of the department has disappeared, while age as single variable is a statistically significant predictor of falling out of bed with a p-value of 0,016 and an odds ratio of 1,069 per year.

The initial significant effect of the difference in department is, obviously, not caused by a real difference, but rather by the fact that at one department many more elderly patients had been admitted than those at the other department. After adjustment for age the significant effect of the department had disappeared.

In the Chaps. 36 and 37 logistic regression with a single binary or continuous predictor was explained. Just like linear regression, logistic regression can also be performed on data with multiple predictors. In this way the effects on the outcome of not only treatment modalities, but also of additional predictors like age, gender, comorbidities etc. can be tested simultaneously. If you have clinical arguments for interactions, then interaction variables can be added to the data. The above analysis shows that department was a confounder rather than a real effect (Confounding is reviewed in the Chap. 22).

More background, theoretical, and mathematical information about logistic regression is given in Statistics applied to clinical studies 5th edition, Chaps. 17 and 65, Springer Heidelberg Germany, 2012, from the same authors.