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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?

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  • $\begingroup$ What does it mean that a KM curve "diverges"? You mean do not appear proportional with the other groups? $\endgroup$
    – AdamO
    Commented Jul 10, 2023 at 18:10
  • $\begingroup$ Yes, not proportional over time so earlier times closer together and then later times appear farther away $\endgroup$
    – user213352
    Commented Jul 10, 2023 at 19:08
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    $\begingroup$ 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. $\endgroup$
    – AdamO
    Commented Jul 10, 2023 at 19:38
  • $\begingroup$ I plotted as you suggested. It is definitely not parallel. $\endgroup$
    – user213352
    Commented Jul 10, 2023 at 21:20
  • $\begingroup$ Some of my stratas are quite small (11 patients) which may also be a problem $\endgroup$
    – user213352
    Commented Jul 10, 2023 at 21:26

1 Answer 1

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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.

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