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I am looking at a survival model based on dosing variables, all of which are continuous. I have noticed when categorized, based on Kaplan Meier Curves, that low, medium, high doses behave differently, but the survival probabilities from least to greatest are high dose, low dose, medium dose. Thus, I created a variable DOSECAT with 3 levels (low, medium, high), and I expected an interaction with DOSECAT to be significant with DOSE. When DOSE, DOSECAT, and their interaction are all in a model together, DOSE and the interaction are both nonsignificant. However, if I remove one of them, the other is significant. What model do I use and/or how should this be interpreted?

proc phreg data=data;
CLASS DOSECAT/ PARAM=GLM;
model SURVIVALTIME*EVENT(1)= DOSE DOSECAT DOSE*DOSECAT; 
    HAZARDRATIO DOSECAT / DIFF=distinct;
    HAZARDRATIO DOSE / AT (DOSECAT=ALL);
run;

Kaplan Meier Curves

Cox Results

enter image description here

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    $\begingroup$ This occurs all the time in many regression models. See stats.stackexchange.com/search?q=significant+regression+not. $\endgroup$
    – whuber
    Commented Oct 8, 2021 at 15:00
  • $\begingroup$ Are your doses on some continuous scale, or are there just 3 doses? It's not clear to me just what you were trying to accomplish with the dose:dosecat interaction term. There might be a better way to accomplish your goal, for example flexible modeling ofdose levels to deal with the apparently non-monotonic association with outcome. Please edit your question to provide those details about your study, as comments are easy to overlook and can get deleted. $\endgroup$
    – EdM
    Commented Oct 8, 2021 at 15:06
  • $\begingroup$ RE: EdM, I edited the question, but here is the relevant change: "I am looking at a survival model based on dosing variables, all of which are continuous. I have noticed when categorized, based on Kaplan Meier Curves, that low, medium, high doses behave differently, but the survival probabilities from least to greatest are high dose, low dose, medium dose. " $\endgroup$ Commented Oct 8, 2021 at 15:10
  • $\begingroup$ RE: whuber, it's not the change in significance that gets me. It is specifically the fact that it is an interaction term that doesn't really make sense if the main effect isn't in the model. $\endgroup$ Commented Oct 8, 2021 at 15:11
  • $\begingroup$ We have plenty of posts about that, too: search the collection of keywords that appear in your comment. $\endgroup$
    – whuber
    Commented Oct 8, 2021 at 20:00

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To address your scientific analysis question:

Although binning continuous data at an early stage of data exploration can make sense, binning generally shouldn't be used for statistical analysis. There are well-established ways to model a continuous predictor flexibly without binning in regression, including Cox regressions. My favorite is restricted cubic splines as implemented by rcs() in the R rms package, but a vignette shows how to use tools in the standard survival package to do that: with an example of a non-monotonic association with survival as you seem to have. I'm pretty sure SAS also provides that functionality, although I don't use it myself.

You can thus show continuous plots of association of dose with outcome. Depending on your audience you might want to display some categorical breakdown, but don't do that for analysis. As the categorical breakdown for Kaplan-Meier plots won't accommodate other predictors you might be modeling, I prefer to show example model predictions based on realistic combinations of predictors, with confidence limits.

To address your question about interactions:

As @whuber commented, loss of "statistical significance" when you add an interaction term is common. With small data sets, this could be something so simple as losing a degree of freedom to fitting the interaction term.

In your analysis of the full interaction model (leftmost table), there's probably an additional issue from the collinearity you have introduced. First, you introduced some collinearity by including both the dose and the dose-category even in the model without interaction (rightmost): dose-category is specified exactly by dose, so there's an inherent interdependence of those predictors. Then you compound that problem by multiplying the dose-determined dose-category by dose itself in the interaction term in the leftmost model.*

I suspect that the process has led to substantial collinearity in the model predictors, leading to high negative correlations among the coefficient estimates. Examine the coefficient covariance matrix. In that case neither dose nor the interaction might appear significant, but a combined Wald test on dose that includes both terms and thus takes the coefficient covariances into account might show that dose is "significant" overall.

Finally, your middle model has an interaction term without a term for dose itself. That's seldom a good idea. I'd recommend reading the extensive discussion on that page carefully, to understand why and how that might show up in apparent "significance." My guess is that your omitting a term for dose in that model minimized the collinearity and thus the high negative correlations among the coefficient estimates that otherwise made dose appear to lose "significance."


*I'm still not clear just what you were trying to model with this particular interaction term, but the principles I describe are generally applicable.

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  • $\begingroup$ Thank you, this is very helpful. I will look at the restricted cubic splines, and it's no problem going from SAS to R. $\endgroup$ Commented Oct 8, 2021 at 17:34
  • $\begingroup$ Here is my rationale for the interaction. The survival time seems to depend on if the dose is high, medium, or low, so I am trying to model that dependence. I also wasn't suggesting that the model including the interaction but not the fixed effect was a good model. I was simply showing there is evidence to suggest the interaction is significant. $\endgroup$ Commented Oct 8, 2021 at 17:36
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    $\begingroup$ @jrheintz91 the interaction would model a different slope of the outcome-dose relationship depending on whether the dose was in the low, medium, or high group. I guess that could be a start toward modeling the shape of the relationship, but at best it would depend a lot on where you drew those cutoff boundaries. Look at the coefficient covariance matrices; I'm pretty sure that the reason for the change in "significance" is within them. If so, maybe edit your question to include them. See if a Wald test combiningdose and its interaction with dose-category is "significant." $\endgroup$
    – EdM
    Commented Oct 8, 2021 at 18:07
  • $\begingroup$ Really appreciate all of your help. All tests of significance of the entire model are highly significant, which makes sense especially since DOSECAT is significant. You are right that multicollinearity is a significant issue; I posted the covariance and correlation matrices. And the cutoffs for the categories were arbitrarily made at Q1 and Q3, but yes that change in slope is exactly what I am trying to model. I am now looking for ways to do so without the categorization. $\endgroup$ Commented Oct 8, 2021 at 18:23
  • $\begingroup$ @jrheintz91 continuous modeling of dose will be your best bet in general. Be careful that the dose levels aren't serving as a proxy for something else associated with survival if this isn't a randomized trial. For example, if someone came in sicker, might a higher dose have been prescribed? $\endgroup$
    – EdM
    Commented Oct 9, 2021 at 14:14

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