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I have a problem regarding the comparison of the likelihood ratios in two diagnostic tests. The definition of positive likelihood ratio in screening tests is "the probability of a person who has the disease testing positive divided by the probability of a person who does not have the disease testing positive", which equals to Sensitivity/(1-specificity).

Now I have two different diagnostic tests conducted in two different populations, so I can calculate positive likelihood ratios (LR+) for both tests. I would like to check if there is statistically significant difference for this indicator between the two tests. What kind of statistical tests shall I use? I would appreciate a lot if someone could give me a hint.

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  • $\begingroup$ If these are different tests of different populations, is there reason to believe that they ought to be similar? $\endgroup$
    – gung - Reinstate Monica
    Sep 8, 2015 at 16:54
  • $\begingroup$ Maybe my question is little ambiguous. For instance, I want to test whether the blood sampling method would affect the diagnostic efficacy of a screening test. I have one sample set with the screening test under blood sampling method A, and another sample set with the same screening test under blood sampling method B. The two samples sets are independent, but the population characteristics are comparable of course. LR+ is one diagnosis related indicator that I have interests, I want to know whether the LR+ is statistically different under the two blood sampling methods. $\endgroup$
    – Adam Chen
    Sep 8, 2015 at 18:30

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Putting both samples into a contingency table based on method and outcome will allow you to run Logodds for both A and B. The odds ratio test of independence will not only give you probabilities but the OR as well, which is quite helpful when observations are rare. more info

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