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In the early part of this century, the drug company, Merck, produced a powerful non- steroidal anti-inflammatory drug (NSAID) known as Vioxx. Vioxx was very effective in reducing pain due to arthritis and, unlike some NSAIDs, did not cause digestive system or liver problems. However, a couple of years after Vioxx was introduced to the market, some independent studies showed a possible connection between NSAIDs and increased risk of heart attack in the elderly. Since many arthritis sufferers (and many Vioxx users) are elderly, these studies were a cause of concern.

To test whether this was the case for Vioxx, Merck conducted a large-scale study in which 3025 randomly selected elderly Vioxx users were put on the drug while 2875 were given a placebo. The volunteers were monitored for 18 months. During this time, 334 of the Vioxx group members and 272 members of the placebo group suffered heart attacks.

Required:
a. Compute by hand a 90% confidence interval for the difference in heart attack risk between Vioxx users and non-Vioxx users (the placebo group.)
b. Interpret the interval. What action does it suggest should be taken regarding Vioxx?

1 Answer

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Answer:

a


0.0028 &nbsp;< p_1 - p_2 &nbsp;< 0.0288

b

The interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack and the non-Vioxx users (the placebo group ) who suffered from heart attack lie within the interval

The use of Vioxx drug should be stopped

Explanation:

From the question we are told that

The sample size for Vioxx users is
n_1 = 3025

The second sample size for placebo is
n_2 = &nbsp;2875

The number of Vioxx users that suffered heart attack is
k &nbsp;= 334

The number of non-Vioxx users that suffered heart attack is
g &nbsp;= 272

Generally the sample proportion for Vioxx users is mathematically represented as


\r p_1 = &nbsp;(k)/(n_1)

=>
\r p_1 = &nbsp;(334)/(3025)

=>
\r p_1 = &nbsp;0.11041

Generally the sample proportion for placebo users is mathematically represented as


\r p_2 = &nbsp;(g)/(n_2)

=>
\r p_2 = &nbsp;(272)/(2875)

=>
\r p_2 = &nbsp;0.09461

Generally the confidence level is 90% , then the level of significance is
\alpha = &nbsp;(100-90)\%

=>
\alpha = &nbsp;0.10

Generally the critical value of
(\alpha )/(2) from the normal distribution table is


Z_{(\alpha )/(2) } = &nbsp;1.645

Generally the standard error is mathematically represented as


SE = &nbsp;\sqrt{(\r p_1 (1- \r p_1))/(n_1) + (\r p_2 (1- \r p_2))/(n_2) }

=>
SE = &nbsp;\sqrt{(0.11041 (1- 0.11041))/(3025) + (0.09461 (1-0.09461))/(2875) }

=>
SE = 0.0079

Generally the margin of error is mathematically represented as


E= &nbsp;Z_{(\alpha )/(2) } * &nbsp;SE

=>
E= &nbsp;1.645 &nbsp;* &nbsp;0.0079

=>
E= &nbsp;0.013

Generally the 90% confidence interval is mathematically represented as


0.11041 - 0.09461- 0.013 < p_1 - p_2 &nbsp;< 0.11041 - 0.09461+ 0.013

=>
0.0028 &nbsp;< p_1 - p_2 &nbsp;< 0.0288

The interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack and the non-Vioxx users (the placebo group ) lie within the interval

Looking at the interval we see that proportion of Vioxx users who suffered is more compared to non-Vioxx users (the placebo group )[i.e the both limit of the interval is positive ] hence the use of Vioxx drug should be stopped

User Olle Kullberg
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