Applying the Cox model for censored survival data is common in medical research but usually researchers do not report adequacy of the model unless pressed by reviewers. Residual plots can be useful but hard to interpret especially in the presence of potential outliers. Can someone recommend another approach with a p-value for checking the fit of the model and assumption of proportionality of the hazard functions for covariates?
You can introduce time-dependent variables to check for PH assumption as described here
http://www.ats.ucla.edu/stat/examples/asa/test_proportionality.htm
If you are running R you can find the code for the test on pp 244-245 of J. Lander's book from the link below. Best, David
https://www.amazon.com/Everyone-Advanced-Analytics-Graphics-Addison-Wesley/dp/0321888030/ref=sr_1_1?ie=UTF8&qid=1486075237&sr=8-1&keywords=jared+lander
Thanks you Mehmet and David. I will try time-varying covariates, which most likely will require some data restructuring. Will also take a look at Lander's R textbook.
I'd start with plotting the cumulative hazard function estimates (Nelson Aalen plots) of groups to be compared by logrank test (Cox PH model) in one plot, then judge the slopes by eye-balling (they should fall apart).
P-values and lack of statistical significance will not give reassurance without looking at the data.
Remember also that standard Cox regression will estimate only a constant factor assumed to be valid for the total time of observation - which is a strong assumption with weak justification.
Methods that may give more/additional insight are (i) multi-state modelling, when transitions between clinically identifiable states of chronic disease process are observable, and (ii) Aalen linear regression models which permit time-varying influence of covariates. Meanwhile there are some textbooks (Andersen, Borgan, Gill and Keiding, 2nd ed. Springer; Martinussen and Scheike, Springer, 2006) which will also give hints to R software.
Great! Thanks very much Jochen - appreciate your advice on this topic!
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