Question

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?

Answer 1

a

`0.0028  < p_1 - p_2  < 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 =  2875`

The number of Vioxx users that suffered heart attack is
`k  = 334`

The number of non-Vioxx users that suffered heart attack is
`g  = 272`

Generally the sample proportion for Vioxx users is mathematically represented as

`\r p_1 =  (k)/(n_1)`

=>
`\r p_1 =  (334)/(3025)`

=>
`\r p_1 =  0.11041`

Generally the sample proportion for placebo users is mathematically represented as

`\r p_2 =  (g)/(n_2)`

=>
`\r p_2 =  (272)/(2875)`

=>
`\r p_2 =  0.09461`

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

=>
`\alpha =  0.10`

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

`Z_{(\alpha )/(2) } =  1.645`

Generally the standard error is mathematically represented as

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

=>
`SE =  \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=  Z_{(\alpha )/(2) } *  SE`

=>
`E=  1.645  *  0.0079`

=>
`E=  0.013`

Generally the 90% confidence interval is mathematically represented as

`0.11041 - 0.09461- 0.013 < p_1 - p_2  < 0.11041 - 0.09461+ 0.013`

=>
`0.0028  < p_1 - p_2  < 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