I have a study in which I have developed a new predictor (binary) for a disease (also a binary variable). The study has two parts. In the first part, I want to test if my predictor is strongly associated with disease. I am planning to use a chi-square test on the predictor vs. disease contingency table (2x2) for this first part.
In the second part, I want to test if my predictor is complementary to existing predictors (which are binary or continuous). To do this, I am planning to compare 2 nested logistic regression models to predict disease: model 1 with my predictor & existing predictors, and model 2 with only existing predictors. I will use likelihood ratio test or Akaike information criterion for the comparison.
My main question is: should I be using logistic regression for the first part also, instead of a chi-square test? Or, is chi-square test more powerful than logistic regression to test association in 2x2 contingency tables? These questions are related to a previous thread, but my questions were not fully answered there.
Also, is logistic regression the best way to test my hypothesis in the second part of the study?
Finally, if the answer to the test in the second part of my study is yes, will the first part become too redundant to be included in the study?