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Test selection & reporting · ~4 min read

Logistic Regression

Adjusted for what, exactly? What that phrase in your results section actually has to mean.

Published

In short

An odds ratio from a multivariable logistic regression describes the association between one predictor and an outcome, holding every other predictor in the model constant. That last part, holding the others constant, is the entire point of running a multivariable model instead of several separate univariate ones, and it is also the part most often left out of the sentence reporting the result. A real three-predictor model below shows what "adjusted for" actually means in practice.

What "adjusted" means, precisely

A univariate odds ratio describes how an outcome's odds relate to a single predictor, ignoring everything else that might also be driving that relationship. A multivariable logistic regression estimates each predictor's odds ratio while mathematically holding the other predictors in the model fixed, which is what allows a sentence like "adjusted for age and BMI" to mean something specific rather than functioning as a stock phrase.

A real model: glucose, BMI, and age predicting diabetes

In 752 patients from a diabetes screening dataset with complete glucose and BMI measurements, a multivariable logistic regression modeled diabetes diagnosis as a function of fasting glucose, BMI, and age simultaneously.1

StatsPlease output: multivariable logistic regression

n = 752 · model converged
Glucose: OR = 1.036 (95% CI, 1.029–1.043), P < .001
BMI: OR = 1.094 (95% CI, 1.064–1.125), P < .001
Age: OR = 1.029 (95% CI, 1.013–1.045), P < .001

In a multivariable logistic regression, higher fasting glucose (adjusted OR, 1.04 per mg/dL; 95% CI, 1.03–1.04; P < .001), higher BMI (adjusted OR, 1.09 per unit; 95% CI, 1.06–1.13; P < .001), and older age (adjusted OR, 1.03 per year; 95% CI, 1.01–1.05; P < .001) were each independently associated with higher odds of a diabetes diagnosis, holding the other two predictors constant.

Figures computed with statsmodels from real data (diabetes screening dataset).

Example data: public diabetes screening dataset (Smith JW et al., 1988). Figures computed with statsmodels from real data.

Glucose's adjusted odds ratio of 1.04 per mg/dL looks modest next to BMI's 1.09 per unit, but the two aren't on comparable scales: glucose spans a range of roughly 50–200 mg/dL in this population, while BMI spans roughly 20–50. Comparing raw odds ratios across predictors measured in different units, without accounting for the range each one actually covers, is a common way to misjudge which predictor matters more in practical terms.

Writing the AMA sentence

Report each odds ratio with its own confidence interval and P value, and say explicitly what it was adjusted for. "Glucose was significantly associated with diabetes (OR = 1.04, P < .001)" is incomplete if the model also included BMI and age; a reader needs to know those were held constant to interpret the 1.04 correctly.

Try it yourself

Reproduce this result

In StatsPlease

  1. Upload the dataset as a CSV.
  2. Open the Analysis tab.
  3. Set diagnosis as the Outcome and mark the predictors — glucose, BMI, and age — as Group by variables.
  4. Press the Regression preset button. There is no separate run step; pressing the preset runs the analysis, detecting the binary outcome and routing to logistic regression.
  5. On the Results tab, the model convergence check, adjusted odds ratios with CIs, and the AMA sentence for the full model are shown together.

In SPSS

  1. Analyze → Regression → Binary Logistic
  2. Dependent: diagnosis. Covariates: glucose, BMI, age (entered together, not stepwise)
  3. Under Options, request confidence intervals for the exponentiated coefficients (Exp(B))
  4. Read Exp(B) as the adjusted odds ratio for each predictor, with its CI
  5. Report all three predictors together, naming which variables each was adjusted for

Frequently asked questions

What does "adjusted" mean in an adjusted odds ratio?

It means the odds ratio for one predictor was estimated while holding every other predictor in the same model mathematically constant, isolating that one variable's association with the outcome from the others included in the model.

Can odds ratios for different predictors be compared directly by their size?

Not without accounting for each predictor's scale. A predictor measured in units that span a wide range and one measured in units that span a narrow range can have very different-looking odds ratios per unit even if their practical importance is similar.

Does a univariate odds ratio give the same result as an adjusted one from a multivariable model?

Not necessarily. A univariate odds ratio ignores the influence of other variables that may also be associated with the outcome; the adjusted version from a multivariable model can differ meaningfully once those other predictors are held constant.

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References

  1. Smith JW, Everhart JE, Dickson WC, Knowler WC, Johannes RS. Using the ADAP learning algorithm to forecast the onset of diabetes mellitus. In: Proceedings of the Symposium on Computer Applications and Medical Care. IEEE Computer Society Press; 1988:261-265.

StatsPlease fits the multivariable model on your own uploaded predictors and reports every adjusted odds ratio with its confidence interval in AMA format.

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