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  • Unadjusted Cox regression - the association between two groups depends on inclusion of a third group

    Hi,

    This may be more related to basic statistical understanding than to Stata. However, maybe Stata handles data in a way that this can be explained.

    In an doing two unadjusted Cox regression analyses.
    In the first analysis, I have four exposure groups (1, 2, 3, and 4). In the second analysis I have three exposure groups (1, 2, and 3). The individuals in the exposure groups are exactly the same in the two analyses ( e.g. individuals in group 1 in the first analysis are the same individual as group 1 in the second analysis).

    However, compared with the association observed in analysis 1, the associations between group 1, 2, and 3 changes when I exclude group 4 in the second analysis. Why is that?

    I cannot provide my real data, but I get the same problem in the following example including three exposure groups (based on a Stata tutorial where I recode the exposure groups):

    Code:
    clear all
    webuse drugtr
    
    recode drug (0=2) if inrange(_n, 1, 5)
    recode drug (1=2) if inrange(_n, 30, 35)
    
    stset studytime, failure(died)
    
    stcox i.drug, base
    stcox i.drug if drug!=2, base
    As you can see, the HR goes from 0.176 in the first analysis to 0.137 in the second analysis.
    My initial thought was, that the HR for group 1 (compared to group 0) would not depend on the presence of group 2 - but clearly it does.

    What is the explanation for this?
    I am not a statistician, so please keep it simple (if that is possible).
    Thank you.

    Best

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