The outcome type dictates the model -- and clinical outcomes are rarely just continuous or binary
By now you know the first two rules: a continuous outcome (blood loss, length of stay) gets linear regression; a binary outcome (alive/dead, complication yes/no) gets logistic regression. But open any surgical chart and most outcomes refuse to fit either box.
A Clavien-Dindo grade is not a number you can average. The modified Rankin Scale (mRS) is ranked, not measured. The number of complications, ED visits, or harvested lymph nodes is a count -- bounded at zero, often skewed, frequently bunched. Forcing these into a linear or binary model produces estimates that look respectable and are quietly wrong.
Two outcome families dominate the gap between continuous and binary: ORDINAL outcomes (ordered categories like Clavien-Dindo, mRS, ASA, pain 0--10) and COUNTS (events per patient or per unit of time). Each has its own correct model. Choosing the wrong one biases your inferences, not just your wording.
When categories are ordered but the spacing between them is unknown, you need ordinal logistic regression.
The proportional odds model (ordinal logistic regression) treats the outcome as a series of ordered cut points. For a Clavien-Dindo scale (I, II, III, IV, V), it implicitly considers every threshold: I vs ≥II, ≤II vs ≥III, and so on.
It returns a single common odds ratio for being in a higher category versus a lower one, and assumes that OR is the same at every cut point. An OR of 1.8 for a treatment means the odds of being in a worse Clavien-Dindo grade are 1.8 times higher, and that this holds whether you slice the scale at II/III or at IV/V.
| Variable | OR | 95% CI | p-value |
|---|---|---|---|
| Open (vs laparoscopic) | 1.82 | 1.31 -- 2.53 | <0.001 |
| Age (per 10 years) | 1.27 | 1.09 -- 1.48 | 0.002 |
| ASA III+ (vs I/II) | 2.04 | 1.42 -- 2.93 | <0.001 |
| Emergency case | 1.66 | 1.10 -- 2.50 | 0.02 |
The model assumes the OR is constant across all cut points. If open surgery doubles the odds of any complication but quadruples the odds of a life-threatening (Clavien IV/V) one, a single OR cannot describe both -- the assumption is violated.
How to check: The score test (often automatic in software) or the Brant test, both of which compare the per-threshold ORs. A significant result means the assumption fails.
Partial proportional odds: Relax the constraint only for the offending variable, letting its OR vary across thresholds while keeping the others constant.
Multinomial logistic regression: Drop the ordering entirely and estimate a separate OR for each category versus a reference. Flexible, but loses the power gained from the ordering and multiplies the parameters.
Collapsing to binary (e.g., Clavien ≥III vs <III) is sometimes defensible -- a major-complication dichotomy can be clinically meaningful and sidesteps the assumption. But it throws away the information in the ordering, so you lose statistical efficiency. Do it deliberately, not by default.
When the outcome is "how many" -- complications, readmissions, harvested nodes -- you are modeling a count, not a continuous measure.
Poisson regression is the baseline model for counts. It produces incidence rate ratios (IRR): an IRR of 1.4 for a risk factor means the expected count is 40% higher in that group.
Poisson rests on one strong assumption: the mean equals the variance. The model uses that equality to set its standard errors. When it holds, inferences are valid.
Clinical count data are almost always overdispersed -- the variance exceeds the mean -- because patients are heterogeneous and events cluster. Poisson assumes they do not, so it underestimates the standard errors, producing confidence intervals that are too narrow and p-values that are falsely significant.
How to check: Compare residual deviance to degrees of freedom (ratio >> 1 signals overdispersion), or fit a dispersion test. The fix is negative binomial regression, which adds a dispersion parameter and widens the intervals appropriately.
Counts are only comparable when the exposure is comparable. A patient followed 5 years has more opportunity to accrue ED visits than one followed 6 months. To model events per person-time, you add an offset -- the log of the exposure (follow-up time, catheter-days, person-years).
This turns the model into a rate model: instead of "number of catheter infections," you model "infections per 1000 catheter-days." The IRR then compares rates, correctly adjusting for unequal exposure.
Zero-inflation: When far more zeros appear than any count model predicts (e.g., most patients have zero readmissions because most were never at risk), zero-inflated or hurdle models separate the "structural zeros" from the count process.
Red flag: Running ordinary linear regression on a skewed count or on a bounded proportion. Linear regression can predict negative counts, assumes constant variance, and ignores the discrete, bounded nature of the data. Reporting a "mean number of complications" with a symmetric confidence interval is the tell.
Mistakes that pass peer review but corrupt the inference.
"Mean Clavien-Dindo grade was 2.4 in the open group versus 1.9 laparoscopic (p = 0.03 by t-test)."
Clavien-Dindo is ordinal, not continuous. A "mean grade" of 2.4 implies grade II and grade IV are equally spaced and that the gap between I and II equals the gap between IV and V -- clinically false. Treating an ordered scale as a number lets a t-test or linear regression run, but the estimate is meaningless. Use ordinal logistic regression, or collapse to a clinically defined dichotomy (e.g., ≥IIIb).
"We used ordinal logistic regression and reported a single OR of 1.9 across the mRS scale."
Was the proportional odds assumption checked? A single OR is only valid if the effect is constant across every cut point of the mRS. If the treatment helps patients avoid death (the top threshold) but does nothing for mild-to-moderate disability, the common OR averages two different effects into one misleading number. Always report the score/Brant test, and use partial proportional odds or multinomial if it fails.
"Poisson regression showed a strongly significant association (IRR 1.6, p < 0.001) between the device and surgical-site infections."
Was overdispersion ruled out? If the variance of the infection counts exceeds the mean (almost always true), Poisson underestimates the standard errors. The IRR may be fine, but the confidence interval is too narrow and the p-value is falsely small -- that "<0.001" can evaporate under negative binomial. Check the deviance/df ratio and refit if it is well above 1.
"Group A had 18 readmissions, Group B had 11, so Group A has worse outcomes."
What was the follow-up time? If Group A was followed for 900 person-years and Group B for 300, Group A actually has the lower rate (20 vs 37 per 1000 person-years). Comparing raw counts without an offset for differing exposure inverts the conclusion. Any count model with variable follow-up needs an offset for person-time.
Before modeling, name the outcome type out loud: continuous, binary, ordinal, or count. Ordered categories are not numbers. Counts are not continuous. Counts with variable follow-up need an offset. And every "single OR" or "Poisson p-value" carries a hidden assumption you must verify.
Choose the right model and spot the wrong one.
Module 5 - Lesson 4 complete
Next lesson: Assumptions and Diagnostics -- the residual plots, leverage checks, and model diagnostics that tell you whether any regression you fit can actually be trusted.