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In a multiple Cox regression model, one dependent continuous variable is categorized into a categorical variable, and conduct the analysis. And then, due to some small sample size in some subgroup, I combine two subgroups as one subgroup, and conduct analysis the same as before. My question is whether the coefficients of other covariates will be changed in the model in these two scenarios.

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Yes, unless the estimated effects of those two small groups were equal.

If they weren't equal in the original fit, one of them will have to change in the new fit. If one effect changes, the others will change as well, to maximize the likelihood.

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