A city has a population of 10000 with 500 diabetic patients. A new diagnostic test gives true positive result in 350 patients and false positive result in 1900 patients. Which of the following is/are true regarding the test ?a) Prevalence is 5%b) Sensitivity is 70%c) Specificity is 80%d) Sensitivity is 80%e) Specificity is 70%
**Question:** A city has a population of 10000 with 500 diabetic patients. A new diagnostic test gives true positive result in 350 patients and false positive result in 1900 patients. Which of the following is/are true regarding the test?
A) Prevalence is 5%
B) Sensitivity is 70%
C) Specificity is 80%
D) Sensitivity is 80%
E) Specificity is 70%
**Correct Answer:**
**Core Concept:** In this question, we are dealing with the properties of a diagnostic test based on the given information about true positives, false positives, and the total number of individuals in the population.
**Why the Correct Answer is Right:**
1. Prevalence (A) - Prevalence refers to the proportion of people in a population that have a particular disease or condition. Prevalence is calculated as the number of cases (diabetic patients) divided by the total population. Prevalence = (Number of diabetic patients) / (Total population) = 500 / 10000 = 5%.
2. Sensitivity (D) - Sensitivity measures the proportion of true positives among the patients with the condition (diabetic patients). In this case, there are 500 diabetic patients and the test gives true positives for 350 of them. Sensitivity = (True positives) / (Total positives) = 350 / (350 + 1900) = 80%.
3. Specificity (E) - Specificity is the proportion of true negatives among the people without the condition. In this case, there are 9500 non-diabetic individuals, and the test gives false positives for 1900 people. Specificity = (True negatives) / (Total negatives) = (9500 - False positives) / (9500 + True positives) = 70%.
**Why Each Option is/are Incorrect:**
1. False positive rate (B) - False positive rate refers to the proportion of false positives among non-diabetic individuals. In this scenario, false positives are 1900 people who are incorrectly diagnosed as diabetic. False positive rate = (False positives) / (Total non-diabetics) = 1900 / (9500 + False positives) = False positive rate cannot be calculated as there are no known False positives in option B.
2. True positive rate (C) - False positive rate (B) is not applicable here since there are no known False positives. True positive rate refers to the proportion of true positives among diabetic patients. In this scenario, true positives are 350 people correctly diagnosed as diabetic. True positive rate = (True positives) / (Total diabetics) = 350 / (350 + False negatives) = False positive rate cannot be calculated as there are no known False negatives in option C.
3. False negative rate (A) - False negative rate refers