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Abstract:
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Under a proportional hazards assumption, the time to event outcome and the predictive measures are independent given the hazard function. Provided the model specification is valid, for large samples and consistent estimates of the hazard, the outcome and predictors should appear independent within subsamples with similar values for the estimated hazard. We use this result to develop a graphical diagnostic method. For a given sample point, we can fit a local survival model in the neighborhood of sample points with similar values for the estimated hazard. For a well specified model, the estimated local hazard function at this sample point would be expected to be close to the hazard function estimated from the fitted model. We can splice together the differences between the log estimated hazard for the fitted model and the local survival model in plots against individual predictors. A well specified model should yield a scattering of points centered on the origin. If the plot exhibits curvature then the fitted model would appear to be inadequate or inappropriate. We demonstrate how these plots can identify necessary or useful transformations of the predictors.
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