If you have two independent samples, then you can use Pearson's chi-square* to compare the two sensitivities. But if you have one sample of individuals who were given both diagnostic tests, then you have paired observations, and need to use the McNemar chi-square. Here are examples using SAS:

https://onlinecourses.science.psu.edu/stat509/node/152

* If the expected counts are too low to justify using Pearson's chi-square, use the N-1 chi-square instead. See http://www.iancampbell.co.uk/twobytwo/twobytwo.htm for details and an online calculator.

Dear Waqas,

سلام علیکم

the sensitivity is an effect size itself and when a test has higher sensitivity than the other one it works better and there is no need for a statistical test.

However if you insist on running a statistical test, you can use chi square test to compare them statistically.

Ramin

You should apply ROC curves, and calculate the confidence intervals of the AUCs or test directly the significance of the difference of the AUCs (or with a gold standard) with chi2 test. STATA is one of the softwares providing the appropriate tools.

If you have two independent samples, then you can use Pearson's chi-square* to compare the two sensitivities. But if you have one sample of individuals who were given both diagnostic tests, then you have paired observations, and need to use the McNemar chi-square. Here are examples using SAS:

https://onlinecourses.science.psu.edu/stat509/node/152

* If the expected counts are too low to justify using Pearson's chi-square, use the N-1 chi-square instead. See http://www.iancampbell.co.uk/twobytwo/twobytwo.htm for details and an online calculator.

I agree with Thanos Chantzaras: the way is the calculation of ROC curves and subsequent comparison of AUC. Is the way to compare different cut-off points because Sensitivity/Specificity varies with the cut-off. Serveral stat.soft are ready for the analysis.

Waqas has asked how to compare two sensitivities. AUC does not equal sensitivity. So I would definitely not compare AUCs here.

EDITED 28-APR-2014

I forgot to mention that Wald & Bestwick (2014) published an interesting article pointing out some limitations of AUC. Those with institutional access can download it here:

http://msc.sagepub.com/content/21/1/51

Waqas, I just noticed that the "additional material" for Robert Newcombe's book has Excel worksheets for comparing sensitivities for both the paired and unpaired cases. You can download a zip file here:

http://www.crcpress.com/product/isbn/9781439812785

Cheers!

How could we compare AUC manually or via SPSS?

The appropriate statistical test depends on the setting. If diagnostic tests were studied on two independent groups of patients, then two-sample tests for binomial proportions are appropriate (chi-square, Fisher's exact test). If both diagnostic tests were performed on each patient, then paired data result and methods that account for the correlated binary outcomes are necessary (McNemar's test).

I think that the question is misleading. Comparing the sensitivity of two tests is not appropriate to identify which test is the better. In some situations, two tests have an equal area under curves but they differed in sensitivity and specificity. Suppose test A has higher sensitivity and lower specificity than test B but both tests are equal in the area under the curve. Which of them is better?

The test A performed better than test B where high sensitivity is required, and test B performed better than B when high specificity is needed. When we comparing the sensitivity of the two tests the results may be not always correct.

Dear Sir, herewith, the answers of your questions including the codes of SAS with examples. I hope it will be useful fro you.

my question is when to compare one sample for detecting lesion with two method and one is 100% the other one is 85 %. what can i do because neither chi2 nr mc menar accept that one is 100% proportion 

Hello Mohamed.  Please provide the observed cell counts for your 2x2 table in this format:

• a = both tests positive
• b = Test 1 positive, Test 2 negative
• c = Test 1 negative, Test 2 positive
• d = both tests negative

Thanks.

the first test fir all lesion = a =87 b =2. c =5 d= 0 

second test for lesion unfer 1 cm a = 17 . b = 3 . c =0 d=0

test 1 : lesion seen =92 not seen 94 ; test 2 : lesion seen 89 not seen 5

when choosing lesion under 1cm : test1:20/20 test2 17/20

If I follow, your 2x2 table for the 100% vs 85% example looks like this:

• a = (T1+, T2+) = 17
• b = (T1+, T2-) = 3
• c = (T1-, T2+) = 0
• d = (T1-, T2-) = 0

McNemar's Chi-square test is equivalent to a Chi-square goodness of fit test on the discordant cells (b and c).  But with such a small number of observations, you should use a binomial test instead.  If your software doesn't have an easy way to carry out the binomial test, you can use the Graphpad calculator linked below:  Enter N = 3 and number of successes = either 0 or 3.  In both cases, you'll get a two-tailed p-value = .2500. 

HTH.

https://graphpad.com/quickcalcs/binomial1.cfm

The best way to compare sensitivity/specificity of two diagnostic test is:

1- To construct a ROC curve for each test (different cut-off points).

2- To calculate and compare Area Under the Curve of both ROC curves.

Many statistical packages can do it, 

And what if I have 4 sensitivity results? All dependent?

I have the same 42 subjects that ware evaluated by 2 professionals (P1 and P2), each using 2 different methods (M1 and M2). The 4 diagnostics where then compared (separately) to a gold standard. Resulting in 4 different sensitivity outcomes (P1M1; P1M2; P2M1; P2M2). 

Is there a way to verify if the result among them are significant different? 

Dear Researcher. i am working on brain signal processing, right now EEG source localization undergoing, i have compared EEG brain source localization by sLOERTA and eLORETS and writing research paper on this.. kindly inform me how can i extend my research as i have done statistics test but i could not understand i how to deal with it... your little guide make me good researcher..... so please advise me step by step as i can work under your cooperation and coordination, thanks

Very nice information anc links

Good question

Spatial Efficiency metric (SPAEF) is proven to be robust when comparing two raster maps. Python and Matlab codes are available at: http://space.geus.dk/tools_products/index.html

Two papers on the metric:

1) https://www.hydrol-earth-syst-sci.net/22/1299/2018/hess-22-1299-2018-assets.html

2) https://www.geosci-model-dev-discuss.net/gmd-2017-238/

http://statistics4everyone.blogspot.kr/2017/04/comparison-of-two-tests-in-sensitivity.html

this may be helpful to you, I hope.