The two diagnostic tests have categorical response (i.e. cancer yes/no).
Is it correct to use the Z test to compare positive and negative predictive values, and likelihood ratios, if I consider them as proportions?
Or do I have to use contingency tables (if so, how might they be computed)?
Hi Leonardo.
Instead of doing a hypothesis contrast, why do you not present the 95 % CI for the likelihood ratios? You know: if the CI do not overlap...
Moreover, when I read a diagnostic accuracy study, I normally pay more attention to an unbiased measure (like the ROC curves for any index test involved in the analysis with their associated AUC, plus 95 % CI), than to the likelihood ratios, predictive values or the sensitivity-specificity values.
Are you an R user? If so, you will find extremely useful the pROC package for some of these calculations.
I hope that I have helped you.
Regards! :)
http://cran.r-project.org/web/packages/pROC/index.html
Thank you Carlos,
your answer was clear and helpful. I use R but I also have access to SPSS and STATA, and I will immediately try the pROC package to build two ROC curves for the two diagnostic tests.
Cheers! :)
For evaluating the difference between two diagnostic tests, I find Newcombe's method is very useful. This is a graphical method, you plot the difference in the probability of correct diagnosis between the two tests, against the prevalence. Where the 95%CI lies above zero, the new test is better than the comparator. The relative importance of false positive and false negative can be specified via a weighting. See: Newcombe RG (2001) Simultaneous comparison of sensitivity and specificity of two tests in the paired design: a straightforward graphical approach. Stat Med. 2001 Mar 30;20(6):907-15.
Likelihood ratio plots described in Biggerstaff Stat Med. 2000 Mar 15;19(5):649-63, are also a useful way to visualise difference between two tests. If both sensitivity and specificity are improved, the test is clearly better. But an improvement in sensitivity may be enough to offset a drop in specificity (or vice versa). You plot the sensitivity on y-axis versus (1-specificity) on x-axis, mark the location of the test, then construct 2 lines, one for which the likelihood ratio of a positive result is constant, and one for which the likelihood ratio of a negative result is constant, these define four regions (inferior to current test, superior, better for confirming absence of disease, and better for confirming presence of disease).
There are examples of the use of these methods here: http://www.malariajournal.com/content/pdf/1475-2875-13-494.pdf
DTComPair package in R has the method of
Leisenring, W., Alonzo, T., and Pepe, M. S. (2000). implemented.
You may also want to look at Computational Statistics and Data Analysis 56 (2012) 1161–1173 José Antonio Roldán Nofuentes ∗, Juan de Dios Luna del Castillo,
Miguel Ángel Montero Alonso
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