# Is this a valid use of “positive predictive value”?

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!