Question

Steps:

            1) Multiply prevalence (i.e., % in population) by N

            2) Enter value as Total # in the Clinical group

            3) Enter Total for non-clinical by subtracting that result from N

            4) Clinical group column:

                        a) Multiply Clinical total by the sensitivity of the test and enter in top row (Correct +)

                        b) Subtract that value from the Clinical Group total to get the bottom row value (# misses)

            5) Non-clinical group

                        a) Multiply non-clinical total by the specificity of the test and enter in bottom row (correct -)

                        b) Subtract that value from the column total to obtain the top row value (# False +)

            6) Add values in rows to obtain row totals

            7) PPV = (Correct +s / Total +s) = top left cell divided by top row total

            8) NPV = (Correct –s/ Total –s) = bottom right cell divided by bottom row total

1.) COVID Antibody Test: Many antibody tests are being assessed currently. I took the following data for one test from a preliminary report posted by University of California San Francisco researchers three days ago. If you obtain decimal values, round to one decimal place.

            Percentage Cases in Population Tested: 14%                        Sensitivity = .8182      Specificity = .8692

__________________________________________________________________________________________

                                                                           True State (unknown)

                                                Clinical Group                                     Non-Clinical Group                            Total

__________________________________________________________________________________________

            “Clinical”                               

Test Result

            “Non-Clinical”           

__________________________________________________________________________________________

Total                                                                                                                                                                1000

__________________________________________________________________________________________

            PPV = ______________                    NPV = ______________                    % Correct = _____________

Based on these results, do you believe this test is ready for usage? Why or why not? [Consider the 2 types of errors, and which would be the greatest concern for this type of test]

Answer 1

The equations for Sensitivity, specificity, Positive predictive value (PPV) and Negative predictive value (NPV) are given above.

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In the given question;  

N = 1000

Prevalence of case in polulation = 14 %

Sensitivity = 0.8182

Specificity = 0.8692

So, 'Total' in the clinical group = % in population x N = 14 / 100 x 1000 = 140

Total non clinical = 1000 - 140 = 860

In the clinical group - row, True positive = 140 x sensitivity = 140 x 0.8182 = 114.54 114

So, False negative = 140 - 114 = 26

In the Non- clinical group, True negative = 860 x specificity = 860 x 0.8692 = 747.512 747

So, False positive = 860 - 747 = 113

So, the table becomes :

Now, Positive pedictive value (PPV) = True positives / Total positives i.e, a / a + c

PPV = 114 / 227 = 0.50

PPV= 0.50 means that the probability that subjects with a positive test truly have the disease is 50 %

Now, Negative predictive value (NPV) = True negatives / Total negatives i.e, d / b + d

NPV = 747 / 773 = 0.97

NPV= 0.97 means that the probability that subjects with a negative test truly do not have the disease is 97 %

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% correct = True positive + True negative / 1000 = 114 + 747 / 1000 = 0.861

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This test is not ready for usage because, it has a low positive predictive value (PPV) which means that the probability that a subject with a positive test actually have the disease is only 50% .

Type I error is the rejection of a true null hypothesis (false positives) and Type II error is the non-rejection of a false null hypothesis (false negative) Type I errors are generally considered more serious than Type II errors. In this test, false positives are more, which means that Type I error is more.