PSI assignment 1
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PSI assignment 1
3 Question 3 ( 13 marks)
In people with hypertension, medications can be used with the aim of reducing systolic blood pressure (SBP) below the target of 140 mmHg. A commonly used medication is believed to achieve this in approximately 40% of patients but has some unwanted side effects. A new medication has been proposed that may improve the proportion who achieve target SBP and reduce the prevalence and severity of side effects. It is to be tested in a randomised controlled trial, with an equal number of participants allocated to each medication.
Use the methods in chapter 5 of the PSI textbook.
3.1 1 mark
What would be the parameter of interest in such a study?
The manufacturers of the new medication show you data from a pilot study in which 100 participants received each medication. In the 100 on the current medication there were 36 who achieved the target and in the 100 on the new medication there were 42 who achieved the target. The manufacturers request an analysis of these results.
3.2 1 mark
Write down the null and two-sided alternative hypotheses for the study in terms of the parameter of interest.
3.3 2 marks
Using the methods in chapter 5 of the PSI textbook, carry out a hypothesis test … Calculate the parameter estimate and its standard error under the null hypothesis. Calculate the test statistic and the p-value for the test.
3.4 1 mark
What can you conclude from this analysis about the effect of the new medication?
3.5 1 mark
In making this conclusion, are risking making a Type I or Type II statistical error? Explain why.
3.6 1 mark
Calculate a 95% confidence interval for the difference between the two medications in proportions of people achieving target SBP.
3.7 1 mark
The manufacturers wish to design a larger study to definitively compare the two medications. They assume that the percentage achieving target SBP on the current medication is 40% and the new medication will increase this percentage by 10%.
Are these assumptions consistent with the data from the pilot study?
3.8 2 marks
For a study with 80% power and a 5% two-sided significance level, assuming 40% of people on the current medication achieve target SBP, how many participants are required to detect a difference of 10% in this rate for the new medication?
Show the steps in your calculations.
3.9 3 marks
The manufacturers are only willing to recruit a total of 500 study participants.
What is the power of a study of 500 participants to detect a difference of 10% (assuming a control rate of 40% and 5% two-sided significance level)?
Suggest how you might calculate what difference could be detected with a study of 500 participants (assuming 80% power, 40% control rate and 5% two-sided significance level), and what criteria you might use to decide whether that difference is consistent with the results of the pilot study?
2023-04-24