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Correlation, regression and survival analysis
A correlation coefficient describes the strength and direction of a linear relationship between two variables, regression predicts an outcome and allows adjustment for several variables at once, and survival analysis handles time to an event when some subjects are censored.
Why it matters in the exam
Items on this topic present model output – a correlation coefficient, a coefficient of determination (r squared), an OR from logistic regression or an HR from a Cox model – and ask you to interpret it correctly. Other items show a Kaplan–Meier curve and ask for the median survival, the assumption without which the method cannot be used (censoring independent of the chance of the event), or what an HR of 0.7 expresses. Also tested are the difference between correlation and causation, and between Pearson correlation (linear, normal data) and Spearman correlation (ranks). A typical example: in a Cox model in which a new treatment has an HR of 0.7 with a confidence interval that excludes 1, the instantaneous risk of the event is about 30% lower at every time point, assuming the hazards are proportional throughout follow-up. Remember also that a variable entered into the model is "adjusted for" – the exposure estimate describes its effect with the other variables held constant. In Kaplan–Meier items the median survival is read where the curve falls to 50%, each "step" in the curve is an event, and small tick marks on the curve are censored subjects. If fewer than half of the subjects had an event by the end of follow-up, the median survival cannot be calculated.
Key points
- The correlation coefficient ranges from minus 1 to 1 and describes a linear link only.
- r squared is the share of variance in the outcome explained by the variable.
- Logistic regression produces an OR, and Cox regression produces an HR.
- Kaplan–Meier requires censoring independent of the chance of the event.
- The log-rank test compares survival curves.
Summary table
| Method | Outcome | What it produces | Exam point |
|---|---|---|---|
| Pearson correlation | Two quantitative variables | r between minus 1 and 1 | Linear only; r squared is the share of variance explained |
| Spearman correlation | Ordinal or non-normal variables | Rank correlation | Robust to outliers |
| Linear regression | Quantitative | Slope – change in outcome per unit change in exposure | Prediction and adjustment for several variables |
| Logistic regression | Binary (yes/no) | Adjusted OR | Suits case-control and cross-sectional studies |
| Kaplan–Meier and log-rank | Time to event | A survival curve and a comparison between groups | Requires censoring independent of the chance of the event |
| Cox regression | Time to event | Adjusted HR | Assumption of proportional hazards over time |
A free exam question
מה השלב הראשון בתהליך הערכת הסיכון בחשיפה סביבתית? (the question as examined, in Hebrew)
- א. ניתוח חשיפה על סמך מדידות סביבתיות
- ב. אפיון סיכון בקרב קבוצות רגישות
- ג. זיהוי הסכנ/?ה ות ( Hazard Identification )
- ד. תקשורת סיכונים עם בעלי עניין
In the full version for subscribers
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Sources
- Kirkwood & Sterne, Essential Medical Statistics, 2nd ed., 2003 — Linear regression and correlation; Logistic regression; Survival analysis
- Bland, An Introduction to Medical Statistics, 4th ed., 2015 — Regression and correlation; Time to event data
Sources are given for further reading; the text is written afresh and not copied from them.
Reviewed by the Examqo AI Professor · 2026-11-06. The text may contain errors; when in doubt, check the source.