How to Read Logistic Regression Results | A Simple Guide to Odds Ratios, 95% CIs, and p-Values
A practical guide to the order in which to read odds ratios, 95% CIs, and p-values in SPSS output and paper tables.
Logistic regression result tables often include odds ratios, 95% confidence intervals, p-values, regression coefficients, standard errors, and related statistics. For those unfamiliar with the method, it can be difficult to know which values matter and how they should be reported in a paper.
Logistic regression is used when the outcome is binary, such as recurrence yes/no, complication yes/no, purchase yes/no, or satisfied/not satisfied. A central point in reading the result iswhether the odds ratio is greater than or less than 1..
A basic approach is to examine, in order,the odds ratio, 95% confidence interval, p-value, adjustment variables, and reference category.These elements should be interpreted together.
What is logistic regression?
Logistic regression evaluates associations between explanatory variables and a binary outcome. In medical research it is used for outcomes such as disease onset, recurrence, death, and complications; in business it may be used for purchase, retention, and churn.
Results are commonly expressed as odds ratios. The odds ratio indicates whether the presence or level of a factor is associated with higher or lower odds of the outcome.
How to interpret an odds ratio
| Odds ratio = 1 | No difference in the odds of the outcome |
|---|---|
| Odds ratio > 1 | Association in the direction of higher odds of the outcome |
| Odds ratio < 1 | Association in the direction of lower odds of the outcome |
For example, an odds ratio of 2.0 means that the odds of the outcome are twice those of the reference group. However, an odds ratio is not the same as a risk ratio, so caution is required when the outcome is common.
How to interpret a 95% confidence interval
A 95% confidence interval expresses uncertainty around the estimate. In logistic regression, whether the interval includes 1 is particularly important.
For example, an odds ratio of 2.0 with a 95% CI of 1.2–3.4 does not include 1 and therefore suggests a statistically significant association. A 95% CI of 0.8–5.0 includes 1, making statistical significance less supportable.
How to interpret a p-value
The p-value indicates how unusual the observed result would be under the null hypothesis of no association. Conventionally, p < 0.05 is treated as statistically significant.
However, conclusions should not be based on the p-value alone; the magnitude of the odds ratio, 95% confidence interval, sample size, and study design should also be considered.
What is an adjusted odds ratio?
An adjusted odds ratio is estimated after including potential confounders such as age, sex, disease severity, or medical history in the model. Medical papers may distinguish univariable odds ratios from adjusted odds ratios estimated in a multivariable analysis.
The variables adjusted for should be clearly stated in the Methods. Including too many explanatory variables can destabilize the model, so the number of events relative to model complexity is also important.
Categorical variables and reference categories
When including categorical variables, it is necessary to confirm which category is the reference. For example, an odds ratio for women using men as the reference has the opposite interpretation from an odds ratio for men using women as the reference.
In paper tables, labels such as Reference, Ref, or equivalent notation should be checked so readers are not misled.
How to report results in a paper
When reporting logistic regression results, state the outcome, explanatory variables, adjustment variables, odds ratios, 95% confidence intervals, and p-values.
For example: “In logistic regression adjusted for age, smoking was significantly associated with complications (adjusted OR 2.10, 95% CI 1.20–3.65, p = 0.009).”
Frequently Asked Questions
Q1. Are odds ratios and risk ratios the same?
No. An odds ratio is a ratio of odds. When the outcome is rare it may approximate the risk ratio, but the difference can become substantial when the outcome is common.
Q2. What does it mean when a 95% confidence interval includes 1?
It means that the interval includes an odds ratio of 1, which corresponds to no association, so the result is generally not considered statistically significant at the corresponding level.
Q3. Is it better to include more adjustment variables?
Not necessarily. Variables should be selected based on the research objective, prior literature, clinical or substantive validity, and the number of outcome events.
Summary | Read logistic regression using the odds ratio, 95% CI, and p-value together
In logistic regression, check whether the odds ratio is above or below 1, whether the 95% confidence interval includes 1, and whether the p-value is statistically significant.
Reviewing the adjusted odds ratio, reference categories, adjustment variables, and model stability as well allows the findings to be described more clearly in papers and reports.
