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Part 1 Smoking is an important risk factor in cardiovascular disease. Serum cotinine is a metabolic product of nicotine, which is often used to measuring smoking status. The data below on serum cotinine were obtained from 1539 cases and 3445 controls (Modified from [1]). Hint: Assume Smokers are ‘cases’ and Non-smokers are ‘controls’. Serum cotinine level (ng/ml) Smokers (N = 1539) Non-Smokers (N = 3445) 0-13 78 3300 14-49 133 72 50-99 142 23 100-149 206 15 150-199 197 7 200-249 220 8 250-299 151 9 300+ 412 11 Suppose a serum cotinine level of 150+ ng/mL is proposed as a screening criterion for cardiovascular disease cases. a. What is the sensitivity of the test? b. How do you interpret this result? c. What is the specificity of the test? d. How do you interpret this result? e. What are the LR+ and the LR-? f. Is this test better for ruling in or ruling out a diagnosis? Explain.Your patient is a 51-year-old female. The prevalence of smoking is about 18.5% in women 45-64 years of age [2]. What is the positive predictive value for the test? How do you interpret this result? g. What is the negative predictive value for the test? How do you interpret this result? h. What are the prior odds for smoking? How do you interpret this result? i. What are the posterior odds for smoking? (both positive and negative) How do you interpret this result? Use the data above to construct a ROC curve for the serum cotinine test. (Hint: plot using cutoffs of 0+, 14+, 50+, 100+, 150+, 200+, 250+, 300+, and .) You can graph this by hand, or using any software. Be sure to include your graph as well.

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Sensitivity measures how often do we positively identify what we are looking for, when we see it. That is, since we're interested in using serum cotinine level to identify smokers – it quantifies how well is our criterion doing at identifying a smoker when we encounter one.
That being said, the sensitivity is not high, that is, it's not particularly close to 1.
We can interpret the result as follows: though the criterion (150+ ng/mL of serum cotinine) serves as a somewhat good indicator for identifying smokers – it's far from doing so perfectly, thus failing to identify many smokers as such.
If failing to identify a smoker is a very bad thing, then our test is doing badly. However, if strictly identifying all smokers is not an issue, or all we care about is, say, to sample a group of smokers for the purposes of our study (which seems to be the case) – then the test may still be good enough....
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