Is this a valid use of "positive predictive value"?

Question

So here's your typical table for evaluating the performance of a diagnostic test:

                                Gold standard result      
                       +------------------------------------+
                       |      Positive    |     Negative    |
           +-----------+==================+=================+
           |  Positive |        (A)       |      (B)        |
    Test   |-----------+------------------+-----------------+
   result  |  Negative |        (C)       |      (D)        |
           +-----------+==================+=================+

Where:

(A) True positive
(B) False positive
(C) False negative
(D) True negative

And where: $$ \text{Positive Predictive Value (PPV)} = \frac{(A)}{(A)+(B)} $$

I'm wondering if I can determine the PPV of a physician's ordering of a test, not the PPV of the test itself.

Consider the following table, which mirrors the first table but is an attempt to measure the PPV of ordering a test. The following table functions under the assumption that "true infection status" is determined by a test with perfect sensitivity and specificity:

                       
                                 True infection status     
                       +------------------------------------+
                       |      Infected    |    Uninfected   |
           +-----------+==================+=================+
           |    Yes    |        (A)       |      (B)        |
     Test  |-----------+------------------+-----------------+
   ordered |    No     |        (C)       |      (D)        |
           +-----------+==================+=================+

Where:

(A) Tested Appropriately
(B) Tested Inappropriately
(C) Untested Inappropriately
(D) Untested Appropriately

I have the data for (A) and (B), but not (C) and (D). Would I be breaking any rules by determining the PPV of test ordering? Or, is there a better measurement for this?

Thanks!

Answer 1

There's nothing inherently wrong with this idea. If you think about it a slightly different way, the physician is performing a 'test' based on his observations of the patient, the outcomes of which are "decide to order blood work" and "decide not to order blood work". This is exactly the same as the scenario you have in the second table, just re-phrased.

If you have some way of measuring the 'true' value that the physician's decision should have taken, such as the blood work test result, or some gold standard of infection status, you can get PPV, sensitivity, specificity, or NPV measures to assess how well the physician makes his decision.