Question

BEYOND THE NUMBERS 3.10 | LEARNING OUTCOMES 1 TO 3

BEYOND THE NUMBERS 3.10 LEARNING OUTCOMES 1 TO 3 Bayes' Rule EXTEND Name Section Number To be graded, all assignments must be completed and submitted on the original book page Background The notation P(A|B) is read as "the probability of A, given B, has occurred." So the "I" symbol is read as "given." Formally, A and B are called events and P(AIB) is a conditional probability Bayes rule is a very useful way of relating conditional and unconditional probabilities. According to this rule, for any two events A and B, we have P(B) Let's use "T+" to denote the event "the screening test concludes that the condition (disease, pregnancy, etc.) is present." Likewise "T-" is notation for the event "the screening test concludes that the condition is not present." "CP" denotes that a condition is actually present, while "CA" denotes that a condition is actually absent. You already know some of the following definitions, though the notation is probably new to you. Others are likely all new: 1. P(T+ICP) is the sensitivity of the test 2, PT-ICA) is the specificity of the test. P(CPIT+) is the positive predictive value of the test. 4. P(CAIT- is the negative predictive value of the test. 5. P(CP) is the prevalence of the condition in the population. 3. EXHIBIT 1 Ottawa Ankle Rules Sensitivity of the Ottawa Rules G. Lucchesi, R., Jackson RE, W. Peacock WF, C. Cerasani, and R. Swor Title: Authors: Sor: Ann Emerg Med. 1995 Jul;26(1):1-5 The Ottawa ankle rules, commonly used in medicine, are designed to exclude fractures of the ankle (or midfoot). The rules first require a careful examination of two particular places on the ankle. If there is tenderness in either of those two places, or an inability to bear weight on the foot, then the Ottawa rules conclude that there is a fracture. Else, the rules conclude that there is not a fracture. In this publication, the authors conducted one of the first sensitivity and specificity studies on the Ottawa ankle rules. The following table did not appear in the referenced article, but was reconstructed from summary values that were recorded therein. A total of 421 patients with ankle injuries were studied. The truth regarding their fractures was confirmed with x-rays after the Ottawa ankle rules were applied 249 BEYOND THE NUMBERS 3.10

Answer 1

1) PPV = P(CP | T+) = P(CP and T+)/P(T+) = 88/365=   0.24109589          
              
NPV=P(CA|T-)=51/56=   0.910714286  

2)a patient would be more interested in P(T+|CP) i.e sensitivity of test

sensitivity represent the true positives.

  
3) PPV = P(CP | T+) = P(CP and T+)/P(T+)              
              
if T+ does not change with prevalence then PPV value does not change as prevalnce increases              
              
this does not seem reasonable because this will result in increase in false negatives              
              
4)sensitivity of test=88/93=94.62%

SPECIFICITY=51/328=15.55%

No, this is not useful,because specificity  is very less
              
true negatives are only 15.55%