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Why logistic regression
Many outcomes in nursing research are binary: a patient dies or survives, a nurse reports burnout or doesn't, a fall happens or it doesn't. Logistic regression models the relationship between one or more explanatory variables and the odds of such an outcome. Its main advantage is that it estimates each variable's association with the outcome while adjusting for the others, which helps reduce confounding (Sperandei, 2014).
Key concepts
- Odds are the probability that an event occurs divided by the probability that it doesn't. A probability of 0.20 gives odds of 0.20 ÷ 0.80 = 0.25.
- The model estimates coefficients on the log-odds scale. Exponentiating a coefficient gives an odds ratio (OR): the multiplicative change in the odds for a one-unit increase in that variable, holding the other variables constant.
- An OR of 1 means no association; above 1, higher odds; below 1, lower odds. A 95% confidence interval that excludes 1 indicates statistical significance at the .05 level.
A worked example from nursing research
Aiken et al. (2002) linked surveys of 10,184 nurses with outcomes for 232,342 surgical patients in 168 Pennsylvania hospitals. After adjusting for patient characteristics and hospital size, teaching status and technology, each additional patient per nurse was associated with:
| Outcome | Adjusted odds ratio (95% CI) | Interpretation |
|---|---|---|
| Death within 30 days of admission | 1.07 (1.03–1.12) | 7% higher odds for each additional patient per nurse |
| Failure to rescue | 1.07 (1.02–1.11) | 7% higher odds |
| Nurse burnout | 1.23 (1.13–1.34) | 23% higher odds |
| Nurse job dissatisfaction | 1.15 (1.07–1.25) | 15% higher odds |
Interpreting larger differences. Because odds ratios multiply, the difference between 4 and 8 patients per nurse is not 4 × 7% = 28%. It is 1.07⁴ ≈ 1.31, or about 31% higher odds of death. This is how the results translate into staffing scenarios.
Odds are not risks. An OR of 1.07 means the odds rise by 7%. When the outcome is uncommon, as 30-day surgical mortality is, the OR approximates the relative risk, but for common outcomes, such as burnout, the OR overstates the relative change in risk. Reports should say "odds" when presenting odds ratios.
Checking the model
A sound logistic regression analysis reports:
- how variables were selected and coded, including whether continuous variables like staffing were assumed to have a linear effect on the log-odds;
- enough outcome events for the number of variables in the model;
- checks for multicollinearity among explanatory variables;
- measures of model fit and discrimination;
- how clustering was handled, since patients in the same hospital are not independent.
What the analysis can't show
The Aiken et al. (2002) study was cross-sectional, so its results show associations, not proof that staffing caused deaths. Hospitals with better staffing may also differ in ways that weren't measured, such as leadership or physician staffing. Adjustment reduces but doesn't remove confounding. Later longitudinal studies and natural experiments, such as ratio legislation, strengthened the causal case.
Application to a DNP project
A DNP project comparing fall rates before and after a staffing change could use logistic regression with "fall during stay" as the outcome and adjust for age, fall-risk score and length of stay. The DNP-prepared nurse should report adjusted odds ratios with confidence intervals and interpret them in plain language for clinical leaders.
References
Aiken, L. H., Clarke, S. P., Sloane, D. M., Sochalski, J., & Silber, J. H. (2002). Hospital nurse staffing and patient mortality, nurse burnout, and job dissatisfaction. JAMA, 288(16), 1987–1993. https://doi.org/10.1001/jama.288.16.1987
Sperandei, S. (2014). Understanding logistic regression analysis. Biochemia Medica, 24(1), 12–18. https://doi.org/10.11613/BM.2014.003
