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I'm investigating survival in a cancer patients cohort. The Cox model I'm using is stratified by stage and adjusted for several variables. I would like to add one variable RT (Radiotherapy) which is of particular importance in higher stages.

How should I modify my Cox model so that it include this variable only for certain stage strata? I am using SAS, but I would like to learn the concept rather than the application code.

Thanks in forward.

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  • $\begingroup$ Is RT a yes/no variable, or are you also including information about dose per day, number of days, etc? $\endgroup$ – EdM Aug 18 '18 at 14:37
  • $\begingroup$ @EdM Yes it's a categorical variable and not continuous. In another words, one of the strata can be split into two using the variable RT, in others however it's always 0. My exposure variable isn't the variable RT, but I need to adjust for it to get precise my estimation. $\endgroup$ – ebay Aug 18 '18 at 15:29
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If the proportional hazards (PH) assumption won't hold between your (+) RT and (-) RT groups for high-stage cases (e.g., RT was withheld because of prior cancer with radiation, or because of poor patient performance status, so a different shape of survival curve might be expected) then you can simply break your high-stage stratum in two: high-stage(+)RT, high-stage(-)RT. That just requires minimal recoding of the data.

If PH is expected to hold, then you could just add the +/- RT variable to all cases. Make sure that (-) RT is the reference level for that factor (whether the first or last level for a factor is the default for reference depends on software).

Then the RT value will be (-) for all low stages and the hazard ratios (HR) reported for the other predictors will be for (-) RT. The (+) RT HR will represent the (presumably lower) hazard for those at high stage receiving RT. You should avoid the temptation to use the (+) RT HR to estimate what might happen if RT were used in lower-stage cases.

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  • $\begingroup$ I see. So you are saying that splitting the strata into low-stage, high-stage RT+, and high-stage RT- is the solution if the PH assumption doesn't hold. If PH hold I can add RT just as a adjustment variable in the model and I should used RT- as a reference value. Is that correct? $\endgroup$ – ebay Aug 18 '18 at 18:22
  • $\begingroup$ @ebay that is my suggestion. The stratification might be a safer bet, and you probably want to evaluate the interaction of your 'exposure variable' with the strata (and RT, if you go that way) in terms of relation to outcome. $\endgroup$ – EdM Aug 18 '18 at 18:34

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