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I am a clinical chemist, thus definitely not good in statistics and probability. Could anyone help me to solve following problem. I have situation where I have two different test ran on a patient for a disease. Test 1 has a sensitivity and specificity of 0.7 & 0.6 whereas Test 2 has sensitivity and specificity of 0.3 and 0.9, both test are ran on the patient. How do I calculate a patient having disease if both test are positive, both are negative and one is positive & other is negative. The prevalence of disease is 10% in the population. Is there a simple formula i can use. Thanks

Amin
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  • I want to calculate probability of disease if a patient test positive to both test, negative both test and positive for one and negative for other using bayes law – Amin Dec 04 '22 at 21:52
  • If this is really meant to reflect a real life situation, you haven't provided sufficient information. In real life (as opposed to idealized math problems) you have to understand the possible dependence between the potential errors. If you just want the idealized math problem (so you have no intention of applying this to a real world problem), you can find many similar problems on this site. – lulu Dec 04 '22 at 21:56
  • here is such an idealized problem and it links to others like it. – lulu Dec 04 '22 at 21:57
  • This is not an idealized problem. I am trying to applying this to diagnosis of Sepsis. Test # 1 is WBC and Test # 2 is Procalcitonin (PCT). When used in our ED room, WBC has sensitivity and specificity of 0.7 and 0.6 at WBC cutoff of 11.9 in diagnoses of Sepsis and PCT has sensitivity and specificity of 0.3 and 0.9 at PCT cutoff of 0.05. Actual prevalence of sepsis in my population is 8.7%, Neither of these test are great individually, but used a lot. I am wondering what will happen if we use them together, will it increase post test probability of Sepsis if they both are pos or neg or split – Amin Dec 05 '22 at 22:39
  • Sensitivity is defined as TP/(TP+FN) and specificity as TN/(TN+FP). These were determined by running these two test on 1500 real patient samples, whose diagnosis was determined by physicians. 108 patients were adjudicated as septic and remaining as non-septic. – Amin Dec 05 '22 at 22:42
  • If you have actual data, use that. We can't effectively model the thing without understanding the nature of the tests. – lulu Dec 06 '22 at 00:03

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