Can anyone answer this question? The prevalence of undetected diabetes in a population to be screen ed is approximately 1.5% and it is assumed that 10,000 persons will be screened. The screening test will measure blood serum glucose content. A value of 180mg% or higher is considered positive. The sensitivity and specdificity associated with this screening test are 22.9% and 99.8% respectively. (a) What is the predictuve value of a positive test?(b) what is the predictive value of a negative test?
To calculate the predictive value of a positive test and the predictive value of a negative test, we need to understand the terms sensitivity, specificity, prevalence, and the total number of individuals being screened.
(a) The predictive value of a positive test:
To calculate the predictive value of a positive test, we need to use the following formula:
Predictive value of a positive test = (Sensitivity × Prevalence) / [(Sensitivity × Prevalence) + (1 - Specificity) × (1 - Prevalence)]
From the given information, we know:
- Sensitivity = 22.9%
- Prevalence = 1.5%
- Specificity = 99.8%
Plugging in these values into the formula, we can calculate the predictive value of a positive test:
Predictive value of a positive test = (0.229 × 0.015) / [ (0.229 × 0.015) + (1 - 0.998) × (1 - 0.015) ]
(b) The predictive value of a negative test:
To calculate the predictive value of a negative test, we use the formula:
Predictive value of a negative test = (Specificity × (1 - Prevalence)) / [ (1 - Sensitivity) × Prevalence + (Specificity × (1 - Prevalence)) ]
Substituting the given values into the formula, we can calculate the predictive value of a negative test:
Predictive value of a negative test = (0.998 × (1 - 0.015)) / [ (1 - 0.229) × 0.015 + (0.998 × (1 - 0.015)) ]
By calculating the expressions in both formulas, we will find the predictive values of a positive test and a negative test.