Q 1.91. - Elementary Statistics

Question

Treating Heart Failure. In the journal article "Cardiac-Resynchronization Therapy with or without an Implantable Defibrillator in Advanced Chronic Heart Failure" (New England Journal of Medicine, Vol. 350, pp. 2140-2150), M. Bristow et al. reported the results of a study of methods for treating patients who had advanced heart failure due to ischemic or nonischemic cardiomyopathies. A total of 1520 patients were randomly assigned in a 1:2:2 ratio to receive optimal pharmacologic therapy alone or in combination with either a pacemaker or a pacemaker-defibrillator combination. The patients were then observed until they died or were hospitalized for any cause. 

(a) How many treatments were there? 

(b) Which group would be considered the control group? 

(c) How many treatment groups were there? Which treatments did they receive? 

(d) How many patients were in each of the three groups studied? 

(e) Explain how a table of random numbers or a random-number generator could be used to divide the patients into the three groups.

Step-by-Step Solution

Answer

Part (a) Pharmacologic therapy alone, pharmacologic therapy with a pacemaker, and pharmacologic therapy with a pacemaker-defibrillator.

Part (b) group getting only pharmacologic therapy 

Part (c) 2, Pharmacologic Therapy with Pacemaker, and Pharmacologic Therapy with Pacemaker-Defibrillator Combination 

Part (d) 304 and 608

Part (e) Use the procedure of selecting a random number using a table of random numbers.

Part (a) Step 1. Given information.

The given statement is:

 A total of 1520 patients were randomly assigned in a 1:2:2 ratio to receive optimal pharmacologic therapy alone or in combination with either a pacemaker or a pacemaker-defibrillator combination. The patients were then observed until they died or were hospitalized for any cause.

Part (a) Step 2. Name the treatments used in the study.

The experimental design included three different treatments.

Pharmacologic therapy alone, pharmacologic therapy with a pacemaker, and pharmacologic therapy with a pacemaker-defibrillator.

Part (b) Step 1. Name the control group.

Because the investigation is about "Cardiac Resynchronization Therapy with or without an implanted Defibrillator in Advanced Chronic Heart Failure," the group getting only pharmacologic therapy would be deemed the control group.

Part (c) Step 1. The number of treatment groups and the treatments they were receiving.

There are two types of treatment groups.

(1) Pharmacologic Therapy with Pacemaker, and 

(2) Pharmacologic Therapy with Pacemaker-Defibrillator Combination was the treatment they were receiving.

Part (d) Step 1. Find the Number of patients studied in each group.

We know that the 1520 patients were randomly divided in a 1:2:2 ratio.

The group receiving just pharmacologic therapy includes:

$\frac{1520}{\left(1+2+2\right)}\times 1=304$

therefore there are 304 patients receiving just pharmacologic therapy.

Patients in the group getting Pharmacologic Therapy with Pacemaker:

$\frac{1520}{(1+2+2) }\times 2 = 608$

608 patients in the group getting Pharmacologic Therapy with Pacemaker.

Part (e) Step 1. Divide the patient into three groups using a table of random numbers.

A random number generator or a table of random numbers could be used to split the patients into three groups by selecting patients at random. 

Assign the patients numbers 1 through 1520 then, using the number from the table or generator, choose the first person and place them in group 1. 

Then, in group 2, pick two random numbers and the patients who correspond to those numbers.

Repeat the procedure, this time selecting two patients and assigning them to Group 3.

Repeat the process until all of the patients have been sorted into three groups.