Your table set-up uses a template that is well-documented. TRUTH IS AT THE TOP.
The calculation of the negative predictive value (NPV) (0.95 or 95%) and the false negative rate (FNR) (0.60 or 60%) are correct.
The table provided in the question permits an assessment of how “good” this (hypothetical) test might be considering not just the specificity of the test but also the sensitivity and the prevalence of disease in this (hypothetical) population. NOTE: Assume that there is no sample size issue.
The sensitivity of the test that is examined—the number of positive tests among the people who were screened divided by the number of people who truly have the disease—is low.
Sensitivity=TP/(TP + FN)=True Positives/(True Positive + False Negative)=11/28=0.40 or 40%
This means that the test identifies only 40% of the people truly have the disease. The remaining 60% of people who truly have the disease have a negative test—the test is a false negative.
The positive predictive value—the number of people with a positive test who truly have the disease--is also low in the population with a prevalence of disease that is 0.07 (7%).
PPV=TP/(TP + FP)=True Positive/(True Positive + False Positive)=11/38=0.29 or 29%
This means the only 29% of the people with a positive test truly have the disease. The remaining 71% of people who have a positive test do not truly have the disease—the test is a false positive.
The classic description of the principles of screening for diseases is by Wilson and Jungner.
Wilson JMG, Jungner G. Principles and practices of screening for disease. Geneva, Switzerland: World Health Organization; 1968. Report No.: Public Health Papers No. 34. Available from: http://whqlibdoc.who.int/php/WHO_PHP_34.pdf.
In it, the authors state:
Ideally ……a test should be highly sensitive and should miss very few
persons with the disease, though a relatively high proportion of false
positives can be accepted…page 22
Writing in 2011, several current and former members of the United States Preventive Services Task Force state this another way:
Test must be easy and quick, may be less sensitive and specific than a
diagnostic test. In a screening test, one may accept a higher
false-positive rate, but a high false-negative rate would not be
acceptable. Table 1.
Harris R, Sawaya GF, Moyer VA, Calonge N. Reconsidering the criteria for evaluating proposed screening programs: reflections from 4 current and former members of the US Preventive Services Task Force. Epidemiologic Reviews. 2011;33:20-35.
Your instinct is correct. This is NOT a good screening test in a population with this disease prevalence. It has both a high false negative rate (60%) and a high false positive rate (71%).