However, what I meant to refer to was a class of non-steroidal anti-inflamatory drugs known as COX-2 inhibitors, most famously Vioxx. COX-2 inhibitors interfere with the action of the COX-2 enzyme, an enzyme involved in the body's inflammatory response (COX is an abbreviation for cyclooxygenase). Vioxx was in some ways like aspirin (in reducing inflammation and being non-steroidal) but was not as hard on the stomach as aspirin is.

Based on a study involving a sample of 5,000 patients, the FDA found Vioxx to be safe and effective and approved its use in 1999. However, a later study of 8000 patients, known as the VIGOR study (for Vioxx GI Outcomes Research), was carried out to determine the extent of adverse effects of Vioxx compared to that of another drug, naproxen. Patients at high risk for heart attacks had a higher risk (at 0.4%) when taking Vioxx than when taking naproxen (at 0.1%). Merck initially interpreted the difference as being due to a "protective effect" of naproxen rather than a negative effect of Vioxx. However, additional studies showing increased rates of sudden death for patients on Vioxx eventually led Merck to voluntarily withdraw Vioxx from the market.

Write a news article about this case. Be sure to address the following issues.
[1] Assuming a 0.4% risk of heart attack among users of Vioxx who are already at high risk of a heart attack (so p = 0.004) and a confidence level of 95%, how large a sample of patients at high risk for heart attacks must be taken for the margin of error not to include the 0.1% risk of naproxen? (If the 0.1% risk level for naproxen is within the Vioxx margin of error, it would be reasonable to conclude that the difference between the Vioxx rate of 0.4% and the naproxen rate of 0.1% is not statistically significant.) If you do this correctly, you will find that the sample size needed is substantially smaller than 5000.
[2] Mention possible reasons why the original safety and efficacy study of 5000 patients did not see any heightened risk among Vioxx users.

Here is more explanation: In order to be confident that the observed difference between Vioxx and naproxen wasn't just due to chance we would want the margin of error to be smaller than 0.4% - 0.1% = 0.3% = 0.003. So first find what n gives this margin of error, assuming p^ = 0.4%. To get s^ we take half the margin of error, so s^ = 0.003/2 = 0.0015. Now plug into s^ = (p^(1 - p^)/n)^(1/2) and solve for n. This gives
n = 0.004(1 - 0.004)/(0.0015*0.0015).
So you need n bigger than what this calculation gives in order for 0.1% to be outside the margin of error. It is also worth checking how big n must be for us to be confident that the sampling distribution is normal. The formula for this is that both of the following inequalities must hold:
n > 9p^/(1 - p^) and
n > 9(1 - p^)/p^.
So you should mention how big n must be in order both for 0.1% to be outside the margin of error, assuming p^ = 0.4%, and for the sampling distribution to be approximately normal. The sample size used in the initial study was 5000. Was this big enough? If not, maybe that explains why the testing did not initially indicate problems. If so, why do you suppose that the study with 5000 subjects did not see any problems? (Keep in mind that the 0.4% risk for Vioxx users is not across the board; it is for people already at high risk for heart attacks. Probably most of the initial 5000 test subjects were not in this high risk group. Could this partly explain why no problems were seen initially? How?)