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 ??