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Does anybody know how to compare two positive predictive value (PPV) from two different predictive models? I found some papers reporting $\chi^2$-test or Fisher exact test but I can´t figure out how the contingency tables would look like: They cannot be the same as for sensitivity/specifity tests, can they?

To clarify:

Imagine you want to compare one method for detecting cancer with another, newer one. I know how to estimate sensitivity, specificity etc., and to compare the two sensitivities from the two different models (sensitivity_method1 vs. sensitivity_method2; using McNemar) but regarding the comparison between PPV_method1 vs. PPV_method2 you can not use McNemar, because margins differ. There are possibilities to calculate the comparison in SAS catmod but it was too difficult for me to understand. So I thought there may be an easier way.

I would be really thankful for clarifications.

Glen_b
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ru_di
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  • Does this help: [Statistical test for Positive and Negative Predictive Value](http://stats.stackexchange.com/questions/6309/statistical-test-for-positive-and-negative-predictive-value)? – chl Sep 11 '11 at 10:50
  • not enough rep to comment, so I'll post this as an answer. I don't really understand the question. You use the same 2X2 table to estimate sensitivity/specificity and to estimate positive/negative predictive value [(wikipedia helps!)](http://en.wikipedia.org/wiki/Positive_predictive_value), so you should be able to use similar tests. – wolf.rauch Jul 05 '11 at 21:14
  • thanks for your answer. i'll try to formulate it more clearly: imagine you want to compare one method in detecting cancer with another, newer one. i know how to estimate sensitivity, specifity etc. and to compare the 2 sensitivities from the two different models (sensitivity_method1 vs. sensitivity_method2; using McNemar) but regarding the comparison between PPV_method1 vs. PPV_method2 you can not use McNemar, because margins differ. there are possibilities to calculate the comparison in SAS catmod but it was too difficult for me to understand. so i thought there may be an easier way.. – ru_di Jul 12 '11 at 16:40
  • @ru_di Strictly speaking PPV are not random variables, so there’s no test to do, the higher the better... However in practice PPVs are estimated using finite samples and comparison with "the truth" (or with some "gold standard"). In this case, the PPV is the proportion of people truly diseased among those for which the test was positive. I think you can just use usual methods for comparison on proportions, although the number of people with a positive test is not fixed beforehand. If both PPVs are estimated on the same sample, it is slightly different, I need to think it better :) – Elvis Jan 08 '12 at 21:30

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