[SPLIT] effectiveness study of clopidogrel

Williams

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The below text is from a practice exam, which has the answer of interest. I am having a lot of difficulty understanding how to arrive at that result, if anyone can provide the process by which z=-460.83, I would greatly appreciate it.



A large study was conducted to test the effectiveness of an experimental blood thinner, clopidogrel, in warding off heart attacks and strokes. The study involved 19,185 patients who had suffered heart attacks, strokes, or pain from clogged arteries. They were each randomly assigned to take either aspirin or clopidogrel for a period of 1 to 3 years. Of the patients taking aspirin, 5.3% suffered heart attacks, strokes, or death from cardiovascular disease; the corresponding percentage in the clopidogrel patients was 5.8%.


  1. The article states that each patient was randomly assigned to one of the two medications. Explain how you could use the random number table to make these assignments.
  2. Although the article does not give the sample sizes, assume that the randomization in part (a) results in 9925 aspirin and 9260 clopidogrel assignments. Are the results of the study statistically significant? Use the appropriate test of hypothesis.
  3. What do the results of the study mean in terms of their practical importance?

Answer: b. yes, z=-460.83
 
The below text is from a practice exam, which has the answer of interest. I am having a lot of difficulty understanding how to arrive at that result, if anyone can provide the process by which z=-460.83, I would greatly appreciate it.



A large study was conducted to test the effectiveness of an experimental blood thinner, clopidogrel, in warding off heart attacks and strokes. The study involved 19,185 patients who had suffered heart attacks, strokes, or pain from clogged arteries. They were each randomly assigned to take either aspirin or clopidogrel for a period of 1 to 3 years. Of the patients taking aspirin, 5.3% suffered heart attacks, strokes, or death from cardiovascular disease; the corresponding percentage in the clopidogrel patients was 5.8%.


  1. The article states that each patient was randomly assigned to one of the two medications. Explain how you could use the random number table to make these assignments.
  2. Although the article does not give the sample sizes, assume that the randomization in part (a) results in 9925 aspirin and 9260 clopidogrel assignments. Are the results of the study statistically significant? Use the appropriate test of hypothesis.
  3. What do the results of the study mean in terms of their practical importance?

Answer: b. yes, z=-460.83
The null hypothesis would be that the two treatments are equal and aspirin is the base case, or the null hypothesis could be that the two are equal to the mean, which is 5.58%. The alternate hypothesis might be that the clopidrogel is "different", or the alternate hypothesis might be that the rate for clopidrogel is greater than the rate for aspirin (or the mean). Which H0 and which HA did you use?

Under the null hypothesis, the mean heart attack rate of the population would be specified. When you take a sample of size N=9260, using a binary distribution, what is the mean and standard deviation of the percentage of heart attacks? Where does the observation fall in that distribution? I find it to be a huge number of standard deviations - utterly impossible to consider a random fluctuation. [No, I haven't found a combination of H0 and HA that gives precisely z=-460.83.]

There is also a more sophisticated test for the equality of two means. Are you supposed to use that?
 
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