By including other potential predictors of Donor in the model, along with your BEC predictor, the resulting parameter estimate and odds ratio estimate for BEC tells you the effect of BEC after adjusting for the effects of the other predictors. If some of the other predictors in the model are associated with the Donor response, this gives you a better idea of what the separate effect of BEC is after accounting for those other predictors. As Rick says, the effect of BEC will obviously change if you change the other predictors that are being adjusted for by adding or deleting predictors from the model.
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