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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.

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  • $\begingroup$ 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. $\endgroup$
    – Glen_b
    Commented Sep 9, 2014 at 22:33
  • $\begingroup$ @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? $\endgroup$
    – Fijoy Vadakkumpadan
    Commented Sep 10, 2014 at 15:59
  • $\begingroup$ Perhaps; it depends on what 'strength' means, exactly. But odds ratio and predictive accuracy sound like reasonable possibilities. $\endgroup$
    – Glen_b
    Commented Sep 10, 2014 at 16:03

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I read the previous thread and I think the contingency table is redundant here. Instead of 1), run the logistic regression using just the binary predictor.

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You said "...I have developed a new predictor (binary) for a disease...." I am not quite sure what you mean by that. We do not develop predictors like vaccines. May be you identified a hitherto-unrecognized predictor. In any case, you have stated that there are already established predictors for the disease of interest. And you want to determine the unique predictive influence of the 'new predictor' given the already established predictors for the disease. I feel here block entry logistic regression would be very appropriate. Enter the already known predictors in the first block and enter the 'new predictor' in the second block.

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