**Core Concept**
The predictive value of a positive test (PV+) is the probability that a person with a positive test result actually has the disease. It is influenced by the prevalence of the disease in the population, the sensitivity of the test, and the specificity of the test.

**Why the Correct Answer is Right**
When the prevalence of a disease increases in the population, the predictive value of a positive test also increases. This is because the proportion of true positive results (i.e., actual disease cases correctly identified by the test) increases relative to the total number of positive test results (true positives + false positives). In other words, as the disease becomes more common, the positive test results are more likely to reflect actual disease cases.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the predictive value of a positive test does not decrease with increasing disease prevalence. In fact, it is the opposite.
* **Option B:** This option is incorrect because the predictive value of a positive test is not directly related to the number of false positives. While false positives can occur at any prevalence, the predictive value is influenced by the overall proportion of true positives.
* **Option C:** This option is incorrect because the predictive value of a positive test is not affected by the test's sensitivity. While a more sensitive test may produce more true positives, the predictive value is influenced by the prevalence and specificity of the test.

**Clinical Pearl / High-Yield Fact**
Remember that the predictive value of a positive test is a function of the disease prevalence, test sensitivity, and test specificity. Always consider the population prevalence when interpreting test results.

**Correct Answer:** A. The predictive value of a positive test increases with increasing disease prevalence.