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I'm assessing the effect of an exposure variable on cancer risk. I am not necessarily trying to build the model that best predicts cancer risk, I am instead trying to best isolate the effect on cancer risks due to this specific exposure variable.

I'm doing this with a Cox PH model with the exposure variable as a covariate. All other covariates are those which I believe to be both correlated with both the exposure variable AND associated with cancer risk. If a variable does not meet both these requirements, I don't include it in the Cox PH model. The intention is to adjust for confounders.

I need to check the proportional hazards assumption. Clearly, if the exposure variable violates the PH assumption, then I've got a problem. However, if a different covariate violates the PH assumption, does this actually matter since I don't care about, and won't be reporting, the coefficients associated with these adjustment covariates?

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    $\begingroup$ Limiting predictors to those "both correlated with both the exposure variable AND associated with cancer risk" is risky in Cox models, similar to the situation with binomial regression. Omitting any predictor associated with outcome, whether correlated with other variables or not, can lead to omitted-variable bias and a model that underestimates the magnitude of the exposure effect. See this answer or this answer, for example. $\endgroup$
    – EdM
    Nov 3, 2023 at 15:18
  • $\begingroup$ Thank you - this is useful. I have the same question about whether I need to care if the adjustment variables (even if these consist of all variables associated with outcome, like you say) don't meet the proportional hazards assumption, provided the exposure variable I'm interested in does. $\endgroup$ Nov 3, 2023 at 18:17

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if a different covariate violates the PH assumption, does this actually matter since I don't care about, and won't be reporting, the coefficients associated with these adjustment covariates?

I think it's good practice to report the entire Cox model summary, even if just in supplemental data to a full report. You audience will want to know what you attempted to control for and what associations those "adjustment covariate" themselves had with outcome. If nothing else, that will put the association between your "exposure" and outcome into a more quantitative perspective with respect to other known or suspected risk factors.

Consider simple ways to fix the PH violation. If the adjustment covariate is categorical, a model stratifying on it instead of modeling it should remove the problem. If the adjustment covariate is continuous, you might have mis-specified the functional form of its association with outcome. See this page for an introduction.

If there's still a problem with PH, I'd recommend that you read Sections 6.5 and 6.6 of Therneau and Grambsch, a useful overview of the issues. As they say, "The first two questions to ask are 'does it matter' and 'is it real;' it will often turn out that nothing is required." Cross Validated posts on PH by @AdamO, like this one, are also useful. As those posts point out, when PH is violated you get lower power and a sort of event-averaged hazard ratio, which isn't much of an issue with an adjustment covariate. I would still recommend trying to fix the PH problem, however, as fixing it is less likely to raise problems with reviewers of your report than will arguing that the PH violation doesn't matter.

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  • $\begingroup$ An adjustment variable that strongly violates the PH assumption will be partially ignored by the fitting process, so you can think of this as an under-adjustment situation but not a disaster. $\endgroup$ Nov 4, 2023 at 12:14

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