Answer :
a. The sensitivity of palpable splenomegaly for cirrhosis is 40%, and the specificity is 94.7%.
b. The predictive value for cirrhosis in a patient with palpable splenomegaly is 50%.
c. The probability that a different problem exists in those with palpable spleens is 50%.
d. The presence of a palpable spleen is not a strong clue for cirrhosis.
e. The probability that a patient whose spleen is not palpable does not have cirrhosis is 99.4%.
f. 40% of patients with cirrhosis have palpable spleens, while 60% do not have palpable spleens.
a. Sensitivity is a measure of how well a diagnostic test can correctly identify individuals with a particular condition. In this case, the sensitivity of palpable splenomegaly for cirrhosis is 40%. This means that out of all the patients with cirrhosis, the test correctly detects palpable spleens in 40% of them.
Specificity, on the other hand, measures the ability of a test to correctly identify individuals without a specific condition. In this case, the specificity of palpable splenomegaly for cirrhosis is 94.7%. This means that out of all the patients without cirrhosis, the test correctly identifies those without palpable spleens in 94.7% of cases.
b. The predictive value for cirrhosis in a patient with palpable splenomegaly is the probability that a patient who has a positive test result (palpable spleen) actually has the condition (cirrhosis). In this case, the predictive value is 50%, which means that if a patient has a palpable spleen, there is a 50% chance that they have cirrhosis.
c. The probability that a different problem exists in those with palpable spleens can be calculated by subtracting the predictive value of cirrhosis in patients with palpable spleens from 100%. In this case, the predictive value is 50%, so the probability of a different problem existing is 100% - 50% = 50%.
d. The presence of a palpable spleen is not a strong clue for cirrhosis because the sensitivity is only 40%. This means that a significant number of patients with cirrhosis will not have a palpable spleen. Therefore, relying solely on the presence of a palpable spleen may lead to false negatives and missed diagnoses.
e. The probability that a patient whose spleen is not palpable does not have cirrhosis can be calculated using the specificity. In this case, the specificity is 94.7%, which means that if a patient's spleen is not palpable, there is a 94.7% chance that they do not have cirrhosis.
f. To determine the percentage of patients with cirrhosis who have palpable spleens, we divide the number of patients with cirrhosis and palpable spleens (16) by the total number of patients with cirrhosis (40). This gives us a percentage of 40% of patients with cirrhosis who have palpable spleens. The percentage of patients with cirrhosis who do not have palpable spleens would be 100% - 40% = 60%.
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