Clinical Trials of OxyContin OxyContin (oxycodone) is a drug u...

Question

Clinical Trials of OxyContin OxyContin (oxycodone) is a drug used to treat pain, but it is well known for its addictiveness and danger. In a clinical trial, among subjects treated with OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjects given placebos, 5 developed nausea and 40 did not develop nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nausea for those treated with OxyContin and those given a placebo.

c. Does nausea appear to be an adverse reaction resulting from OxyContin?

c. Does nausea appear to be an adverse reaction resulting from OxyContin?

Accepted Answer

Hello everyone. Let's take a look at this question together. A new medication is being tested for its side effects. In a clinical study, 38 out of 190 patients treated with the new medication reported headaches, while 7 out of 55 patients in the placebo group reported headaches. At the 0.05 significance level, use a hypothesis test to test if there is evidence of a difference in the rate of headaches between the new medication and placebo groups. Does headache appear to be a side effect of the new medication? So in order to solve this question, we have to use A hypothesis test to test if there is evidence of a difference in the rate of headaches between the new medication and the placebo groups at the 0.05 significance level, as well as if the headaches appear to be a side effect of the new medication. So then we let the first Sample be the patients treated with the new medication, and the second sample be the patients in the placebo group. And so our requirement check includes assuming that the sample proportions are from two simple random samples, that is, every individual has an equal chance of being selected. As well as the two samples are independent, as the study used separate groups with no overlapping patients and no matching or pairing. And lastly, for each of the 2 samples, there are at least 5 successes and at least 5 failures. Which if success is defined as having headaches, there are 38 successes for the first sample, and 190 minus 38, or 152 failures. And for the second sample, there are 7 successes and 55 minus 7, equaling 48. As the failure number. So the next step is to define the hypotheses where our null hypothesis is P1 equals P2, meaning the proportions are equal, and our alternative hypothesis is that P1 does not equal P2 as the proportions are not equal. And we know that P1 refers to the proportion of headaches in the new medication group, and P2 refers to the proportion of headaches in the placebo group. And then we can calculate the sample proportions for P1, which is equal to X1 divided by N1, giving us 0.2, and for P2, which is equal to X2 divided by N2, giving us 0.127. And then we can calculate the pooled sample proportion of Par using the formula for P bar, which is equal to X1 plus X2. divided by N1 plus N2 and plugging in our values into the formula, we get 0.184 as the value for the pooled sample proportion of P bar. So then Q bar is equal to 1 minus P bar, which equals 0.816. And now we can calculate the test statistic of Z using the formula for Z. Which plugging in our values into the formula, we get 1.23 as the value for the test statistic Z. And using the Z value, we can determine the critical value for a two-tail test at alpha divided by 2, which is equal to 0.05 divided by 2 or 0.025, and from the table. We can see that the probability of Z being less than -1.96 is equal to 0.025, so the critical values are positive or negative 1.96. And if the absolute value of Z is greater than 1.96, we reject the null hypothesis, and if the absolute value of Z is greater than 1.96, we reject the null hypothesis, but if it is less than 1.96, we fail to reject the null hypothesis. And since the absolute value of Z is 1.23, which 1.23 is less than 1.96, we fail to reject the null hypothesis. Therefore, Since we failed to reject the null hypothesis, there is insufficient evidence to conclude a significant difference in the rate of headaches between the new medication and the placebo groups, as well as headaches do not appear to be a side effect of the new medication. I hope you found this video to be helpful. Thank you and goodbye.

Key Concepts

Hypothesis Testing

Significance Level

Contingency Table

Watch next