Question

1. In a large clinic located in an inner city hospital, 56 patients with nonsymptomatic HIV infection have been treated with an experimental drug believed to have the capability of restoring certain immune system functions associated with HIV infection. Of these patients, 12 had CD4 cell counts below 250 at the initial visit, 20 had counts between 250 and 400, and 24 had counts above 400. (The lower the count, the worse the prognosis.) It is desired to take a stratified random sample of 30 patients, 10 from each of the three groups described above, for purposes of estimating the 12-month incidence of AIDS-defining events among these patients. (Incidence is defined as the number of events divided by the total number of persons).

a. How many samples of 30 patients taken as described above are possible?

b. Assuming that a patient can have more than one AIDS-defining event during this period, show algebraically how you would estimate the 12-month incidence of AIDS-defining events from the sample.

Answer 1

a.

Formula: number of ways of selecting 'r' items from 'n' items =C(n, r)

So, the number of possible samples that can be obtained are:

No. of samples =C(12, 10)*C(20, 10)*C(24, 10) =66*184,756*1,961,256 =23,915,351,693,376

b.

Sample size, n =30 patients

Total number of events from all 30 patients =

Estimate of 12-month AIDS defining events is =

It gives the average number of AIDS defining events per patient.

Let total number of events be =90

= =90/30 =3. It means on an average, a patient has 3 AIDS defining events.