I am investigating the predictors for adverse events (AEs) from a sample of 400 patients recieving an injection therapy. The outcome AEs is binary and I will use a multiple logistic regression model:
AEs = diagnosis + region + structure
(R code: model=glm(AEs~Dia+Reg+Struc,family="binomial"))
The levels of each of the variables are:
AEs: 1 or 0
Diagnosis: RA, OA, or other
Region: Shoulder, elbow, foot, hand, hip, knee
Structure: Joint, tendon, bursa
Then I came to think about:
1) Is it a problem, that some combinations are impossible/will not be present in the dataset? E.g. ’other’ will never be combined with ’hip’, ’elbow’ will never be combined with ’joint’ etc.
2) If not; I have considered adding interactions between all the predictors, because it clinically makes sense. However, will 1) be a problem for the model in that case (I am aware of that I will not get any estimate for e.g. ’elbox:joint’ etc., but does it harm the model?).
(R code: model=glm(AEs~Dia+Reg+Struc+Dia*Reg*Struc,family="binomial"))
Thanks in advance
Best regards
Sabrina
Sabrina,
The values of the nominal variables need to be coded as binary dummy variables, with the number of variables one less than the number of values. In other words, diagnosis should be coded with two binary variables: RA and OA whereas ‘other’ will be implied when both RA and OA equal zero. In the same manner, Region will be coded with five binary dummies. With this setup, you can add meaningful interactions to the model, when two binary variables co-occur. Just note that you should add all possible second-degree interactions before you attempt to add the third-degree interactions. Note that in this setup, you will be able to account for the AEs that affect more than one region or structure at the same time, if this is the case in your data.
Hope this helps,
Alex
You should only use interactions that occur with sufficient numbers to be able to reliably estimate parameters ; if you go looking for everything it is very likely that you model will fit the data well but not be generalisable to other new patients.
You might want to use classification trees in R (a variant used to be called Automatic Interaction Detection) and use cross validation (predicting aginst randomly dropped observations which is done automatically) to guard against over-fitting
see
http://www.di.fc.ul.pt/~jpn/r/tree/tree.html
http://www.statmethods.net/advstats/cart.html
https://cran.r-project.org/web/packages/rpart/vignettes/longintro.pdf
.Even with 400 patients you can see what problems you can get into here
https://www.researchgate.net/post/Is_it_weird_to_get_a_very_big_odds_ratio_in_logistic_regression
An alternative approach might be to use a method such as latent class analysis to determine classes of patient based on adverse events. You can then use these adverse event classes to predict outcomes from the intervention in a logistic regression model.
In theory I think you could do this in a single model - but that gets complicated. Also there is value to extracting classes that are plausible.
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