a logarithm transform of a predictor fixed proportional hazards in Cox model - how can that be ??

statlimp

New Member
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I have survival data to which I am fitting a Cox model with a continuous predictor. The cumulative martingale residual method (supremum test) of Lin, Wei and Ying https://cdr.lib.unc.edu/indexablecontent/uuid:f93e67cf-e968-4903-9b63-9c38a8f138b9suggested that both proportional hazards (PH) and functional form assumptions of the predictor were significantly in error. I log transformed the predictor and the functional form p-value improved (now non significant) but the p-value for the PH assumption is now also non-significant indicating no significant deviation from PH. How can this be ? How can transforming a predictor make the hazard ratio between different levels of the predictor constant over time ??

hlsmith

Not a robit
Did you plot the IV for each outcome group to see the distributions.

statlimp

New Member
ah no -I'll trythat next week thanks hlsmith - probaby the IV is skewed
I don't usually just log transform a predictor when its skewed though ( I can see that might remove over influential outliers) but rely on residuals etc to see if the corret transform is used - I'm not sure what the consensus is on this though and I've tried to find out - stil cant see how a log transform would ever fix PH though

statlimp

New Member
I think the Schoenfeld residuals on which the plot to test PH is based do actually depend on the parameter estimates and the values of the variables so they will change so therefore the test p-value will change - I wouldn't expect a transformation to systematically affect PH but it might change the p-value in some random way and in this case maybe thats why its now non-significant having been significan before

hlsmith

Not a robit
The term significant is fairly arbitrary - are you talking 0.04 to 0.06, which may not be a change of magnitude beyond just being trivial.

statlimp

New Member
sorry hlsmith not to get back sooner - not its from 0.01 to 0.28 !! I take your point re just going over 0.05 but its a bigger swing than that