# Logistic regression, Chi-square, and study design

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?

Thank you.

• You say you're interested in finding out if your predictor is strongly associated with the outcome. But a significant chi-square will indicate only that it's not zero, not that it's strong; when the sample is large a statistically significant effect may be extremely weak. ["Statistical significance is not practical significance," as some people put it.] ... the same issue occurs with testing a logistic regression - you can't judge effect size from significance. Commented Sep 9, 2014 at 22:33
• @Glen_b I agree that significance does not measure strength of association, but only that there is an association. I plan to report odds ratio in part 1, and predictive accuracy (perhaps via cross-validation) in part 2, to indicate strength. Are there better means to report strength? Commented Sep 10, 2014 at 15:59
• Perhaps; it depends on what 'strength' means, exactly. But odds ratio and predictive accuracy sound like reasonable possibilities. Commented Sep 10, 2014 at 16:03