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Accuracy of a diagnostic test can be assessed by sensitivity, specificity, positive and negative predictive values. How are these affected if test is repeated one more time (total 2 times). Is there any formulae for this?

Also how to assess accuracy of repeated testing if Bayes theorem is also to be taken into account. That is, post-test probability is to be calculated considering pre-test probability (prevalence) also.

Thanks for your insight.

Edit: For a specific example, there is a diagnostic test with sensitivity of 70% and specificity of 95%. I want to apply this test to 2 populations with prevalences of 10% and 90%. How do I calculate accuracy scores if I repeat the test 2 times in this situation?

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  • $\begingroup$ I agree that the question was changed such that the answer became obsolete. $\endgroup$
    – Diana Petitti
    Sep 9, 2020 at 20:32

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Diagnostic test results are often analysed with a generalised linear mixed effects model, incorporating random intercepts for any repeated measures and/or clustering.

A Bayesian approach, which incorporates priors on relevant parameters, can easily be adopted by using a suitable package, such as brms in R.

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  • $\begingroup$ I have edited my question to add a specific situation. It will be great if you could elaborate your answer with that situation. $\endgroup$
    – rnso
    Jul 26, 2020 at 8:04
  • $\begingroup$ Now you've changed the question, rendering my answer obsolete. This is not the way to use this site. If you are asked for more focus then fine, but if just want to change the question substantially after getting an answer then you should post a new question. $\endgroup$
    – Robert Long
    Jul 26, 2020 at 8:09
  • $\begingroup$ I have not changed the question. I have just added an example one can use to explain the steps. $\endgroup$
    – rnso
    Jul 26, 2020 at 11:23
  • $\begingroup$ You are now asking about a specific situation. You were previously asking about a general situation,. That is completely different and requires answering completely differently !!!!! :( $\endgroup$
    – Robert Long
    Jul 26, 2020 at 11:25
  • $\begingroup$ I was hoping you will expand your two line answer using my example. $\endgroup$
    – rnso
    Jul 26, 2020 at 11:36
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If one just wants to combine probability from single test to get final accuracy values, one can use false negative and false positive rates. Hence, one can use usual formulae derived from Bayes theorem to get post-test probabilities (positive and negative predictive values) using sensitivity, specificity and prevalence:

PPV = SENS*PREV / [SENS*PREV + (1-SPEC)*(1-PREV)]
NPV = SPEC*(1-PREV) / [SPEC*(1-PREV) + (1-SENS)*PREV]

False positive rate will be 1-PPV and false negative rate will be 1-NPV.

Results for example in the question are:

enter image description here

For repeated testing, false rates can be multiplied to get final false rates. Hence, if the test is repeated twice, False negative rates for prevalence of 10% will be 0.03*0.03 = 0.0009. Similarly, FNR for prevalence of 90% will be 0.74*0.74=0.548

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