Treatment with statins can reduce the risk of a major cardiovascular event in people with specified risk factors. During about 2 years of follow-up in the JUPITER trial, 142 of 8901 subjects treated with a statin had a major cardiovascular event.
1)First, estimate the 2-year risk, and give a 95% confidence interval for this estimate. Assuming that risk remains constant over time, give an estimate of the 10-year risk of a major cardiovascular event on statin therapy.
2)Suppose the expected 2-year risk of a major cardiovascular event in similar but untreated people is 0.028. Test whether the 2-year risk in those treated with a statin is significantly different from this expected risk at the 5% level. Make sure to state your null and alternative hypotheses and specify your conclusion.
1. The 95% confidence interval for this estimate is between 0.013 and 0.019.
2. The hypothesis being tested is:
H0: p = 0.028
Ha: p ≠ 0.028
The test statistic is -6.89.
The p-value is 0.0000.
Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.
Therefore, we can conclude that the 2-year risk in those treated with a statin is significantly different from this expected risk.
Observed | Hypothesized | |
0.016 | 0.028 | p (as decimal) |
142/8901 | 249/8901 | p (as fraction) |
142. | 249.228 | X |
8901 | 8901 | n |
0.002 | std. error | |
-6.89 | z | |
5.61E-12 | p-value (two-tailed) | |
0.013 | confidence interval 95.% lower | |
0.019 | confidence interval 95.% upper | |
0.003 | margin of error |
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