Many parts of the developing world have limited access to clean and safe drinkin

Question

Many parts of the developing world have limited access to clean and safe drinking water. There is a gold standard test that can be performed in a laboratory to tell for certain whether there are harmful pathogens in drinking water. However, this test requires trained researchers, expensive equipment, and takes several days. Public health researchers have developed a new screening test that anyone can perform, using inexpensive filter paper that, when dipped in a water sample for 5 seconds, will indicate by color the presence of harmful pathogens. If, after proper dipping the filter paper remains white, the water is safe to drink. If the filter paper turns any shade of orange or red, pathogens are present and water should be boiled prior to consumption.

Public health researchers get permission to evaluate this new screening test in a community in Bangladesh, where water contamination is a frequent problem. Researchers collect water samples from the main community well three times a day for two weeks, a total of 42 samples. A portion of each of these samples is sent to the lab to undergo the gold standard test, while the remainder of each sample is tested using the new filter paper method. The gold standard laboratory test reveals that 21 of the 42 water samples are truly contaminated. The filter paper screening method results in 24 positive test results. Of these filter paper results, 19 are confirmed to be true positives.

my answer to the sensitivity was :

Sensitivity= 19/19+2*100= 90%

I'm having a hard time interpreting these results. I need help understanding sesitivity.

Based on your calculations for sensitivity above, select the correct interpretations for this calculation from the options below. There may be more than one correct interpretation listed.

Question 28 options:

Out of 42 samples, 91% of them were contaminated.

The filter paper test will be correct 91% of the time.

91% of the samples that were truly contaminated were correctly identified by the filter paper screening test.

Of the water samples tested, 91% of them will test positive for contamination.

The proportion of water samples with pathogens present that was correctly identified as such by the filter paper screening method was 91%.

A)

Out of 42 samples, 91% of them were contaminated.

B)

The filter paper test will be correct 91% of the time.

C)

91% of the samples that were truly contaminated were correctly identified by the filter paper screening test.

D)

Of the water samples tested, 91% of them will test positive for contamination.

E)

The proportion of water samples with pathogens present that was correctly identified as such by the filter paper screening method was 91%.

Explanation / Answer

Sensitivity (of a test) means the proportion of positives that are correctly identified.

Here, number of positive cases (ie., contaminated samples) = 21 (assuming laboratory tests are pretty much accurate)

Number of positives that were correctly identified (true positives) = 19

Sensitivity = 19/21 = 91% (approximately)

Hence, sensitivity of 91% means that out of all the contaminated samples (positives), 91% were truly identified by the filter paper screening method.

Hence, C and E are correct interpretations.  

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