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I am using Cox Proportional Hazards for a set of data. I continue to find variables with hazard ratios equal to one. I understand that these variables are not hazardous/protective to the life of the response. However I see that the increase the Goodness of Fit and they have a larger -log(p) when added to the model.

  1. How should I practically interpret variables that increase the Goodness of Fit, but are not hazardous/protective to the response?
  2. Should I continue to add variables that have a hazard ratio of one, but increase GoF? When should I stop adding variables in this manner?

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First off, it doesn't make sense to test the individual levels of a covariate in a goodness of fit test. "Component" for instance is a categorical contrast, and it seems like "Component D" is taken as referent.

Adding any ol' variable to a model will increase the predictiveness of that model. So you can't look simply at a "higher" value of $-\log_2(p)$. In fact it doesn't make much sense to add or subtract a model from the output based on statistical significance alone. If you're interested in the predictiveness of the model covariates, one option to consider splitting the sample into a test and validation set, then use the test set to fit a nomogram to assess predictiveness in the validation set. The approach you have here is fairly weak and prone to error, I have no additional belief this model "fits" well based on the output.

Not having said which goodness of fit test is being used, I gather this is just a kitchen sink model and all covariates have their standard wald statistics reported. What's unusual is that the individual tests have HR=1 but the result is statistically significant. This can only be the result of rounding error. Coef does not equal 0, but rounded to two decimal places it practically is, hence why se(coef) = 0 (note standard errors can't be exactly 0 for model coefficients).

So, no your hazard ratios do not actually equal 1. And including all significant model factors do not give you a good fitting model, especially if you have a large sample size.

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  • $\begingroup$ Thanks for the input, this is a kitchen sink model.. Theres a lot of information not being discussed here.. Im using a standard stepwise approach, Tucky's HSD for variable selection, k-fold validation, etc. I simply want to understand the hazard ratio of one and its impact on artificial inflation in accuracy / GoF. So far, test subset groups are scoring well. Perhaps my question is too broad. Thanks. $\endgroup$
    – Starbucks
    Commented Apr 7, 2021 at 20:27

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