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The cox.zph() function tests for proportional hazards in a Cox model by correlating Schoenfeld residuals with time. Therefore, my question is, can this test produce a non-significant result if residuals are non-monotonically distributed (e.g. a "U" shape), despite the fact that the proportional hazards assumption clearly doesn't hold from looking at the plot?

I don't have a specific example of this, just wondering if it's technically possible due to an assumption of a linear relationship between residuals and time?

BenJ
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1 Answers1

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Yes, that is the case (although you need to be careful in what you mean by "correlating Schoenfeld residuals with time" as the test allows for arbitrary transformations of time). As the manual page for cox.zph says:

The plot gives an estimate of the time-dependent coefficient β(t). If the proportional hazards (PH) assumption holds then the true β(t) function would be a horizontal line. The table component provides the results of a formal score test for slope=0, a linear fit to the plot would approximate the test.

If the overall slope is close enough to zero despite a "U" shape in the distribution of residuals, you thus could get a "non-significant" result from the test. Then you have to judge whether the deviation from PH is big enough to matter and, if so, how to modify your modeling approach.

EdM
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