The Cox proportional hazards model estimates how a treatment or risk factor changes the rate of an event over time, adjusting for other variables. Its result is the hazard ratio (HR): below 1, a lower event rate; above 1, a higher one. Medical journals expect each HR with its confidence interval, the adjustment set, and a word on whether the model's main assumption held.
What you need before you write a single word
- The number of patients and events in the model.
- For each variable: the hazard ratio, its 95% CI and P value.
- Unadjusted and adjusted HRs, and which covariates the adjusted model includes, chosen in advance.
- The proportional hazards check (Schoenfeld residuals or log-minus-log plots).
The template
In a Cox proportional hazards model adjusted for [covariates], [exposure] was associated with a [lower] risk of [event] (HR, X.XX; 95% CI, X.XX-X.XX; P = .XX). The proportional hazards assumption was checked with [Schoenfeld residuals] and was not violated.
A worked example
In the 120-patient cohort (66 deaths), a Cox model with treatment group and age gives:
| Variable | HR (95% CI) | P value |
|---|---|---|
| New treatment (vs standard care) | 0.58 (0.35-0.95) | .03 |
| Age, per year | 1.01 (0.99-1.03) | .49 |
Written up:
In a Cox proportional hazards model including 120 patients and 66 deaths, the new treatment was associated with a 42% lower hazard of death than standard care after adjustment for age (HR, 0.58; 95% CI, 0.35-0.95; P = .03). Age was not significantly associated with survival (HR per year, 1.01; 95% CI, 0.99-1.03; P = .49).
"42% lower hazard" is 1 − 0.58. Say "hazard" or "rate", not "risk of dying 42% less", since an HR compares instantaneous event rates rather than cumulative risks.
Mistakes reviewers catch
- No events count. The model's precision depends on events, not patients; a common rule is at least 10 events per variable.
- Unclear adjustment set. List the covariates and why they were chosen.
- No proportional hazards check. If hazards are not proportional, the single HR is an average that may mislead.
- HR read as relative risk. They are related but not the same.
- Leading zeros dropped: in AMA style, HR, 0.58 keeps its zero.
Let KyroStat do the write-up for you
KyroStat fits the Cox model, checks proportional hazards, builds the hazard-ratio table, and writes the paragraph with the adjustment set from your data.
Frequently asked questions
Should I report unadjusted and adjusted HRs? Usually both: the unadjusted HR in the text or table, and the adjusted one as the main result.
How do I describe the survival curves? See how to report Kaplan-Meier survival and the log-rank test.
What if my outcome is not time to an event? For a yes/no outcome without time, use logistic regression and odds ratios; see relative risk vs odds ratio.