Logistic regression is used whenever a medical outcome has two categories, such as infection or no infection. Many researchers can run the model in SPSS but find the output difficult to read. Logistic regression interpretation means translating the coefficients, odds ratios, confidence intervals and model fit statistics into clear clinical statements. A common mistake is to describe an odds ratio of 2 as “twice the risk”, which is not correct when the outcome is common. This guide explains logistic regression interpretation step by step, using one hypothetical clinical example.
Table of Contents
What Is Logistic Regression Interpretation?
Logistic regression models the probability of a binary outcome as a function of one or more explanatory variables. The main advantage of the method is that it gives odds ratios for each variable while adjusting for the other variables in the model, which reduces confounding (Sperandei, 2014). If you are new to the method, our introduction to logistic regression explains the basic idea.
Binary Logistic Regression
Binary logistic regression is used when the outcome has two categories, coded 1 (event) and 0 (no event). The explanatory variables can be continuous, such as age, or categorical, such as diabetes. The same logistic regression interpretation applies to ordinal and multinomial extensions.
Probability, Odds and Log Odds
The model works on the log odds (logit) scale. If p is the probability of the event, the odds are p ÷ (1 − p), and the logit is the natural logarithm of the odds. For example, a probability of 0.20 corresponds to odds of 0.25. Therefore, each coefficient (B) describes a change in log odds, and its exponent, eB, is the odds ratio (Bewick et al., 2005).
Crude and Adjusted Odds Ratios
A crude (univariable) odds ratio comes from a model with one explanatory variable. In contrast, an adjusted odds ratio comes from a multivariable model and describes the association of a variable when the other variables are held constant. Logistic regression interpretation in medical papers is almost always based on adjusted odds ratios (see multivariate vs multivariable analysis).
Importance of Logistic Regression Interpretation in Medical Research
Identification of Independent Risk Factors
Clinical outcomes usually have several related causes. Correct logistic regression interpretation shows which factors remain associated with the outcome after adjustment, and how strong each association is.
Clear Communication with Clinicians and Reviewers
Reviewers expect odds ratios with 95% confidence intervals, not only p-values. Moreover, clinicians need simple statements, such as “the odds of infection were 4.8 times higher in patients with diabetes”.
Avoiding Misleading Conclusions
An odds ratio is not a risk ratio, and an association is not proof of causation. Careful logistic regression interpretation keeps these errors out of the Discussion and the Abstract.
Applications of Logistic Regression in Clinical Studies
Risk Factor Studies
Most cohort studies and case-control studies with a binary outcome use logistic regression to identify independent risk factors. In case-control studies, the odds ratio is the main measure of association.
Clinical Trials
In randomized trials with a binary endpoint, logistic regression gives the treatment effect adjusted for baseline factors. In observational studies, it also estimates the propensity score in propensity score matching.
Prediction Models and Diagnostics
Clinical risk scores are often built with logistic regression. The predicted probabilities can be evaluated with ROC curve analysis.
Assumptions of Logistic Regression
The following conditions should be checked before logistic regression interpretation begins:
- A binary outcome: the dependent variable has two categories, and the event of interest is coded 1.
- Independent observations: each patient appears once. Repeated measurements or matched data need other methods, such as conditional logistic regression.
- Linearity of the logit: continuous variables have a linear relationship with the log odds of the outcome, which can be checked with the Box-Tidwell test.
- No strong multicollinearity: the explanatory variables are not highly correlated. A variance inflation factor (VIF) above 5 to 10 indicates a problem.
- An adequate number of events: a common rule is at least 10 events per variable (EPV) in the model. Our guide to sample size explains this planning step.
- No complete separation: no variable predicts the outcome perfectly. Otherwise, the coefficients and their standard errors become extremely large.
How to Interpret Logistic Regression Output: A Clinical Example
Consider a hypothetical cohort of 400 adults who underwent elective abdominal surgery. The outcome was surgical site infection (SSI) within 30 days, which occurred in 75 patients (18.8%). The explanatory variables were age (per 10 years), diabetes, current smoking and male sex. The data were simulated for teaching purposes, and every value below was calculated from these data.
Step 1: Describe the Outcome by Each Variable
Before fitting the model, the SSI rate is described in each group. Patients with SSI were older than patients without SSI (mean age 62.6, SD 11.7 vs 56.6, SD 11.9 years).
| Variable | Group | SSI, n/N (%) |
|---|---|---|
| Diabetes | Yes | 43/117 (36.8) |
| No | 32/283 (11.3) | |
| Current smoking | Yes | 32/123 (26.0) |
| No | 43/277 (15.5) | |
| Sex | Male | 38/205 (18.5) |
| Female | 37/195 (19.0) | |
| Total | 75/400 (18.8) |
With 75 events and four variables, the EPV was 18.8, which meets the rule of 10. In addition, all VIF values were close to 1, so multicollinearity was not a concern.
Step 2: Check the Overall Model Significance
The omnibus (likelihood ratio) test compares the full model with a constant-only model. The −2 log likelihood decreased from 386.06 to 332.01, which gives χ² = 54.06, df = 4, p < 0.001. Therefore, the four variables together predicted SSI significantly.
Step 3: Read the Coefficients Table
The main logistic regression output is the “Variables in the Equation” table in SPSS. Each row gives the coefficient (B), its standard error (SE), the Wald statistic, the p-value, Exp(B) and its 95% CI:
| Variable | B | SE | Wald | df | p | Exp(B) = OR | 95% CI for OR |
|---|---|---|---|---|---|---|---|
| Age (per 10 years) | 0.459 | 0.122 | 14.10 | 1 | < 0.001 | 1.58 | 1.25 to 2.01 |
| Diabetes (yes) | 1.561 | 0.280 | 31.06 | 1 | < 0.001 | 4.76 | 2.75 to 8.24 |
| Current smoking (yes) | 0.774 | 0.288 | 7.20 | 1 | 0.007 | 2.17 | 1.23 to 3.81 |
| Male sex | 0.024 | 0.278 | 0.01 | 1 | 0.931 | 1.02 | 0.59 to 1.77 |
| Constant | −5.098 | 0.822 | 38.46 | 1 | < 0.001 | 0.006 | – |
A positive B means higher odds of the outcome, and a negative B means lower odds. The Wald statistic equals (B ÷ SE)², and it tests whether B differs from zero. For diabetes, B ÷ SE = 5.57, so the Wald statistic is 5.57² = 31.06, p < 0.001.
Step 4: Interpret the Odds Ratios
For a binary variable, the odds ratio compares the two groups. The adjusted odds of SSI were 4.76 times higher in patients with diabetes than in patients without diabetes (95% CI, 2.75 to 8.24). Similarly, current smokers had 2.17 times higher odds of SSI than non-smokers, which is a 117% increase in the odds.
For a continuous variable, the odds ratio refers to one unit of the variable. Because age was entered per 10 years, each 10-year increase in age multiplied the odds of SSI by 1.58, which is a 58% increase. Per single year, the odds ratio is e0.0459 = 1.047.
For male sex, the confidence interval (0.59 to 1.77) includes 1, and p = 0.931, so sex was not significantly associated with SSI. Notably, the constant refers to a patient with all variables equal to zero (age 0), so it has no clinical meaning here. See also our article on confidence intervals.
Finally, the crude odds ratios were 4.56 for diabetes, 1.91 for smoking and 1.53 for age per 10 years. Because the adjusted values changed only slightly, there was little confounding between these variables.
Step 5: Calculate a Predicted Probability
Predicted probabilities make logistic regression interpretation easier for clinicians. For a 60-year-old non-smoking woman with diabetes, the logit is −5.098 + (0.459 × 6) + 1.561 = −0.78. The probability is 1 ÷ (1 + e0.78) = 0.314, or 31.4%.
For the same woman without diabetes, the logit is −2.34, and the predicted probability is 8.8%. Importantly, the ratio of these probabilities is 3.6, while the odds ratio is 4.76. This difference shows why an odds ratio should not be described as a risk ratio when the outcome is common, as explained in our guide to the odds ratio vs relative risk.
Step 6: Assess Goodness of Fit and Pseudo R²
The Hosmer-Lemeshow test compares observed and predicted numbers of events across 10 groups of predicted risk (Bewick et al., 2005). Here, χ² = 12.18, df = 8, p = 0.143. A non-significant result indicates no evidence of poor fit.
The Cox and Snell R² was 0.126, and the Nagelkerke R² was 0.204. The Nagelkerke R² is usually preferred because it ranges from 0 to 1 (Bewick et al., 2005). However, pseudo R² values are not the R² of linear regression and do not mean “variance explained”.
Step 7: Evaluate Discrimination and the Classification Table
The area under the ROC curve (AUC) of the predicted probabilities was 0.754 (95% CI, 0.694 to 0.814), which indicates fair discrimination. The classification table at a cut-off of 0.5 is shown below:
| Observed | Predicted no SSI | Predicted SSI | Percentage correct |
|---|---|---|---|
| No SSI (n = 325) | 318 | 7 | 97.8 |
| SSI (n = 75) | 62 | 13 | 17.3 |
| Overall | 82.8 |
The overall accuracy of 82.8% looks high. However, predicting “no SSI” for every patient would already be correct in 81.3% of cases, and the sensitivity was only 17.3%. Therefore, the AUC is a better summary of discrimination.
How to Report Logistic Regression Results in a Manuscript
The Methods section should state the outcome, the variables entered, the checks of assumptions and the software. The Results section presents the significant findings:
Factors Associated with Surgical Site Infection
The multivariable logistic regression model was significant (χ² = 54.06, df = 4, p < 0.001, Nagelkerke R² = 0.204). Diabetes was independently associated with higher odds of surgical site infection (OR = 4.76, 95% CI, 2.75 to 8.24, p < 0.001). Moreover, current smoking was associated with higher odds of infection (OR = 2.17, 95% CI, 1.23 to 3.81, p = 0.007). Additionally, each 10-year increase in age was associated with higher odds of infection (OR = 1.58, 95% CI, 1.25 to 2.01, p < 0.001). (Table 2)
Notably, the clinical explanation of these associations and the comparison with previous studies belong to the Discussion section, not to the Results.
Common Mistakes in Logistic Regression Interpretation
Describing Odds Ratios as Risk Ratios
This is the most frequent error in logistic regression interpretation. When the outcome is common (more than about 10%), the odds ratio is further from 1 than the risk ratio. Therefore, “4.76 times higher odds” should not be written as “4.76 times higher risk” (Step 5).
Ignoring the Unit of Continuous Variables
An odds ratio of 1.05 per year and 1.58 per 10 years describe the same effect, so the unit should always be stated.
Choosing the Wrong Reference Category
By default, SPSS uses the last category as the reference. If “yes” is coded 1, the odds ratio will be inverted unless the reference is changed to “First”.
Relying on the Classification Table
A high percentage correct can hide a very low sensitivity. The AUC and calibration are more informative (Step 7).
Interpreting Associations as Causal Effects
Unmeasured confounding can remain after adjustment, so the wording should be “associated with”, not “caused”. Similarly, a non-significant p-value does not prove that a variable has no effect.
Running Logistic Regression in SPSS and R
For logistic regression in SPSS, choose Analyze → Regression → Binary Logistic. Move the outcome (SSI) to Dependent and the explanatory variables to Covariates. Then click Categorical to define categorical variables and set the reference category to First. Under Options, select Hosmer-Lemeshow goodness-of-fit and CI for exp(B). In R, the model and the odds ratios with Wald confidence intervals are obtained with: m <- glm(ssi ~ age10 + diabetes + smoker + male, family = binomial, data = d); exp(cbind(OR = coef(m), confint.default(m))). Our beginner’s guide to R explains how to start.
Conclusion
Logistic regression interpretation follows a clear order: check the overall model, read B and its sign, translate it into an odds ratio with a 95% CI, calculate predicted probabilities, and then assess fit and discrimination. The odds ratio should be described as a change in odds, with the unit of continuous variables stated. For an unadjusted comparison, read our guide to the chi-square test.
If you need support in analyzing your data or writing your Results section, the StatisMed team of biostatisticians provides statistical analysis services for medical studies. You can request a free quote today.
Frequently Asked Questions
1. What does an odds ratio of less than 1 mean?
An odds ratio below 1 means lower odds of the outcome. For example, an odds ratio of 0.60 means that the odds are 40% lower in the exposed group than in the reference group, when the other variables are held constant.
2. Should I use B or Exp(B) in my manuscript?
Most medical journals expect Exp(B), the odds ratio, with its 95% CI and p-value. The coefficient B can be added to a table.
3. What if the Hosmer-Lemeshow test is significant?
A significant result (p < 0.05) suggests poor calibration, so check for non-linear effects, missing interactions or omitted predictors before logistic regression interpretation. However, in very large samples, the test can be significant even for small differences.
References
Bewick, V., Cheek, L., & Ball, J. (2005). Statistics review 14: Logistic regression. Critical Care, 9(1), 112–118. https://doi.org/10.1186/cc3045
Sperandei, S. (2014). Understanding logistic regression analysis. Biochemia Medica, 24(1), 12–18. https://doi.org/10.11613/BM.2014.003
