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I have been asked an interesting modelling question by a clinician. The outcome he is trying to predict whether a particular type of cancer will occur. One of the covariates is an indicator variable if the patient previously had another kind of cancer. Other covariates are cancer diameter and margin size of this prior cancer. The margin size is how many millimetres the surgeon cut around the cancer when it was removed. For patients that have not had the prior cancer, these values are obviously missing.

I believe that making diameter be 0 millimetres makes sense, but there can be no sensible value for margin size. What model formula should I use? What theory should I learn?

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  • $\begingroup$ See this answer by whuber. Basically you can estimate a model that nests the boy model and the girl model in the same equation, improving efficiency in the estimates compared to estimating seperate equations. $\endgroup$ – Andy W Apr 14 '14 at 15:22
  • $\begingroup$ Wonderful. This is what I was searching for, but had trouble describing it. $\endgroup$ – Dario Apr 15 '14 at 2:00
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I think the simplest thing to do is to make two models: One for people who had no previous cancer and one for those who did. If you try to make a model for all the people, you will run into both nonsensical things like the margin size of a cancer that isn't there and collinearity issues.

Another option within logistic regression is to include "missing" as a value for the variables, but 1) There could still be collinearity and 2) That removes the possibility of using those variables numerically.

Yet another would be to use a classification tree.

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