a.What would the predictive value of a pooled ear-notch PCR test be for the region?
b.What is the probability that a herd testing negative in your region is actually uninfected?
1.Sensitivity defines the ability of classify correctly of a test on a disease of an individual.
Mathematically expressed as
where a is true positive, and
a+c is true positive + true negative. The result gives the probability of an individual or animal being tested positive in case of the presence of a disease.
Using the provided statistics; the sensitivity = 68/68+11
=0.883 which is equivalent to 88.3%. This means the probability of the BVD disease of the herds of 97 cattle was 88.3% attack level.
Specificity tests if an individual or an animal is free from a disease. It helps in the identification and correct testing to ascertain that an individual is not suffering from a disease
Specificity is mathematically expressed as d/b+d where d=true negative, b+d= true negative+ false positive. From specificity calculations, the probability of being tested negative for a disease in an individual or animal is determined. From the given data, the specificity is calculated as;
20/20+11=0.645 which is equivalent to 64.5%. This means 64.5% of the beef cattle tested disease free of BVD on AC-ELISA test.
2.A hypothetically ideal gold standard definition test would always give a return of 100% on the sensitivity with regard to the prevailing disease that is under test (Howlett, 2013). This it does by identifying all the animals using a proper defined disease processes and does not give any false-negative results. Such a gold standard test also offers 100% of specificity. Such specificity does not identify an individual to be suffering from a condition that he does not suffer from in the real sense. In other words such specificity does not offer any false-positive results. This is not the normally observable gold standard tests available in practice but instead imperfect standards.
By changing the gold standard test from classifying a herd as infected if one cow is infected to two cows to be classified as infected, the accuracy of the gold standard test on the evaluation of the ear-notch PCR would be compromised (Howlett, 2013). By increasing the number of animals that would determine positive classification for infection, the test would not be analyzing individual animals. This would translate to wholesome interpretation and conclusion thereby lowering the accuracy of the gold standard test. An ideal gold standard test returns 100% on both specificity and sensitivity.
These returns are only achievable if the tests are done on each and every animal from the herd in which the evaluation was being conducted. An increase in the number of animals that is used in the classification of a positive result of either of the test does not allow for proper identification and study of an animal in the possible aspects and disease processes (Jekel, 2015). The chances of falsely identifying an animal with a disease or condition it does not have is increased if the number of animals is increased that is as the number of animals are increased, the level of accuracy of the gold standard test decreases.
3.The predictive values are either positive or negative. Positive predictive values indicate the number of animals from the herd that actually have the BVD disease while negative predictive values determines the number of animals from the region that have tested negative and do not have the disease in their bodies.
Positive predictive value, PPV=a/a+b where a is true positive
a+b is true positive+ false positive
using the provided statistics once again for the calculations;
the true positive is 15% of 500 animals=75 animals
75/75+425=0.15 which is an equivalent of 15%. This means a probability of 0.15 of a positive test if any one of the 500 animals in the region would be tested for BVD disease.
b.The probability of a herd from the 500 animals testing negative is actually uninfected is determined by calculating the negative predictive value of the population which is estimated from the expression;
NPV= d/c+d where d is true negative, c+d is false negative + true negative
=0.85 which in an equivalent of 85% of the animals. It means 85% of the 500 animals would test negative and would actually be uninfected in case a test is done.
Howlett, B. (2013). Evidence Based Practice for Health Professionals. New York: Jones & Bartlett Publishers.
Jekel, J. F. (2015). Epidemiology, Biostatistics, and Preventive Medicine. New York: Elsevier Health Sciences.