Problem 228SE

Consider the treatments in Exercise 2-57. Suppose a patient is selected randomly. Let A denote the event that the patient is treated with ribavirin plus interferon alfa or interferon alfa, and let B denote the event that the response is complete. Determine the following probabilities.

2-57. The article “Term Efficacy of Ribavirin Plus Interferon Alfa in the Treatment of Chronic Hepatitis C,” [Gastroenterology (1996, Vol. 111, no. 5, pp. 1307–1312)], considered the effect of two treatments and a control for treatment of hepatitis C. The following table provides the total patients in each group and the number that showed a complete (positive) response after 24 weeks of treatment.

Let A denote the event that the patient was treated with ribavirin plus interferon alfa, and let B denote the event that the response was complete. Determine the number of patients in each of the following events.

Solution:

Step 1 of 3:

The total patients in each group and the number that showed a complete (positive) response after 24 weeks of treatment is given.

Complete Response Total | ||

Ribavirin plus interferon alfa |
16 |
21 |

Interferon alfa |
6 |
19 |

Untreated controls |
0 |
20 |

We have to find the following probabilities.

- P(A/B)
- P(B/A)
- P(A
- P(AB)