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Let's say I am running Cox proportional regression model for a variable with 4 levels (strongly agree, agree, disagree, strongly disagree). When I code it as an ordinal variable with these 4 categories, it is an insignificant contributor. However, if I make this variable binary (agree vs disagree), it is significant. Is this still appropriate? When is it okay to convert an ordinal to a binary variable? How do I go about interpreting this result? Thank you!

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    $\begingroup$ Please, can you elaborate on how this ordinal variable is coded (e.g., 0,1,2,3) and which software you use. $\endgroup$
    – Alex
    Oct 5, 2022 at 0:30
  • $\begingroup$ I am using SPSS, and it is coded as you describe (0, 1, 2, 3) with each number indicating a specific category. If it were binary it would just be 0 and 1 $\endgroup$
    – Emily Y
    Oct 5, 2022 at 0:58
  • $\begingroup$ I think the issue here is that if the variable is purely numeric, as you confirmed, and the model assumes that the "distances" between 0 and 1, 1 and 2, 2 and 3 are equal, and the coefficient reflects that one step. But in real life the "distances" can be unequal and the model less linear, so the linear model's bad fitting leads to statistical non-significance. If you omit this assumption that the variable is ordinal/ordered and use it just as a non-ordered categorical variable, you may try to get individual hazard ratio coefficients and see how these four categories relate to each other. $\endgroup$
    – Alex
    Oct 5, 2022 at 11:59
  • $\begingroup$ How to code this in R was described in this question. For SPSS, I unfortunately cannot advise :-( $\endgroup$
    – Alex
    Oct 5, 2022 at 11:59
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    $\begingroup$ A plot would go a long way to understand what's going on with your data. $\endgroup$
    – dipetkov
    Oct 5, 2022 at 17:23

2 Answers 2

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Even if you tell software that a predictor is ordinal rather than numeric/scale (which you used isn't completely clear from your question or comment), its handling would generally still be based an an assumption of equal spacing between levels. See, for example, the UCLA web page on how R handles ordinal predictors. A failure of that assumption could lead to the result you found.

As @Alex suggested in comments, the best approach with so few levels might be to treat it as a nominal predictor to get around that assumption, and evaluate the significance of the predictor as a whole rather than relying on tests of individual associated coefficients. For example, do a likelihood-ratio test of two Cox models, one with the predictor and one without.

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This could be a case of the difference between significance and non-significance itself being non-significant. See this paper: http://www.stat.columbia.edu/~gelman/research/published/signif4.pdf

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