I have (matched) case-control data. The data is collected in batches in such a way that the batch determines some quality of the data (there is a 'batch' effect).

Also, the cases and controls were not randomly distributed among these batches. So batch 1 contains only cases, batch 2 contains only controls, batch 3 is mostly cases (a couple controls) and batch 4 is mostly controls (a couple cases).

I'm trying to do logistic regression to determine if some covariates are associated with disease. I need to control for the batch effect. Will the fact that the cases/controls are not randomly distributed among the batches have a negative impact on my model if I include the batch as a covariate?


From my reading it appears that can be somewhat of a common problem called Quasi or Complete separation.


Let's say that the predictor variable involved in complete quasi-complete separation is called X.

In the case of complete separation, make sure that the outcome variable is not a dichotomous version of a variable in the model. If it is quasi-complete separation, the easiest strategy is the "Do nothing" strategy. This is because that the maximum likelihood for other predictor variables are still valid. The drawback is that we don't get any reasonable estimate for the variable X that actually predicts the outcome variable effectively. This strategy does not work well for the situation of complete separation.

Another simple strategy is to not include X in the model. The problem is that this leads to biased estimates for the other predictor variables in the model. Thus, this is not a recommended strategy.

Possibly we might be able to collapse some categories of X if X is a categorical variable and if it makes substantive sense to do so. Exact method is a good strategy when the data set is small and the model is not very large.

Firth logistic regression is another good strategy. It uses a penalized likelihood estimation method. Firth bias-correction is considered as an ideal solution to separation issue for logistic regression. For more information on logistic regression using Firth bias-correction, we refer our readers to the article by Georg Heinze and Michael Schemper.

Bayesian method can be used when we have some additional information on the parameter estimates of the predictor variable.

source: http://www.ats.ucla.edu/stat/mult_pkg/faq/general/complete_separation_logit_models.htm


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