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I am looking at time-to-event data by a variable with multiple groups (8). When I plot the stratified KM, some curves cross, some are ok, and some diverge. Also, I'm interested in the 30-day event rate. But by definition, I dont start to count events until after 7 days (only if there is a death I count those, so I may have a tiny drop in the first 7 days). What is the best way to approach this analysis for KM and for Cox?

user213352
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  • What does it mean that a KM curve "diverges"? You mean do not appear proportional with the other groups? – AdamO Jul 10 '23 at 18:10
  • Yes, not proportional over time so earlier times closer together and then later times appear farther away – user213352 Jul 10 '23 at 19:08
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    It's hard to see proportionality on the survival scale - "earlier times closer together and then later times appear farther away" - is actually a perfect description of parallel hazard functions. Try plotting those curves on complementary log log scales to see if the hazard is actually parallel. – AdamO Jul 10 '23 at 19:38
  • I plotted as you suggested. It is definitely not parallel. – user213352 Jul 10 '23 at 21:20
  • Some of my stratas are quite small (11 patients) which may also be a problem – user213352 Jul 10 '23 at 21:26

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A "parametric" check for disproportional hazards is provided by the R-function cox.zph from the survival-package. See here: https://stats.stackexchange.com/a/318319/341520

A common way to fit a model that can deal with disproportionality are aalen additive models, e.g. here: https://rdrr.io/cran/timereg/man/aalen.html

KMs don't depend on proportional hazards, but obviously can't really describe effects of continuous variables and struggle with small sample size.

I dont start to count events until after 7 days (only if there is a death I count those, so I may have a tiny drop in the first 7 days)

Hard to say what the impact would be. You'd assume that a consistent treatment effect would get an unbiased estimator, but the 30 year survival would be overestimated for everyone. If there are large time effects and at the edge of 7 days they might be hidden by not counting. Maybe you should just trust in the "definition" omit those deaths and report 7-30 days survival.

Lukas Lohse
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  • Thank you for your response. Is there a spline-like method that can be used for survival analysis? So I can model the first 7 days differently. – user213352 Jul 10 '23 at 23:38
  • Multiple ways: https://cran.r-project.org/web/packages/survival/vignettes/timedep.pdf – Lukas Lohse Jul 11 '23 at 07:52