Study conclusions this study provided very strong

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Study Conclusions This study provided very strong evidence that children who receive the QIV vaccine are less likely to develop influenza than those who receive a control vaccine (exact one-sided p-value < 0.001, z -score = ± 6.08). An approximate 95% confidence interval for the difference in the probabilities indicates that the probability of influenza (of any severity) is 0.023 to 0.044 (2.3 to 4.4 percentage points) lower when receiving the QIV vaccine. However, focusing on the difference in “success” probabilities has some limitations. In particular, if the probabilities are small it may be difficult for us to interpret the magnitude of the difference between the values. Also, we have to be very careful with our language, focusing on the difference in the influenza probabilities and not the percentage change. An alternative to examining a confidence interval for the difference in the conditional probabilities is to construct a confidence interval for the relative risk (ratio of conditional probabilities). A large sample approximation exists for a z -interval for the ln(relative risk) which can then be back-transformed to an interval for long-run relative risk. Many practitioners prefer focusing on this ratio parameter rather than the difference. From this study, we are 95% confident that ratio of the influenza probabilities is between 1.78 and 3.19. This means that receiving the placebo rather than the real vaccine raises the probability of developing influenza by between 78% and 219%. An alternative would be to calculate the ratio in the other direction, using the relative risk of developing influenza between the vaccinated group compared to the unvaccinated group ( 2 ˆ p 2 / 1 ˆ p = 0.4189). This approach is called examining the “efficacy” of the vaccination. Using the same standard error, a 95% confidence interval for the long-run relative risk is (0.313, 0.561). This means we are 95% confident that the use of the QIV vaccine reduces the probability of developing influenza by between (100 ± 56.1) = 44% and (100 ± 31.3) = 69%. In other words, we are 95% confident that the efficacy of the QIV vaccine in the larger population of children aged 3-8 years is between 44% and 69%.
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Chance/Rossman, 2015 ISCAM III Investigation 3.9 231 Note: It can be risky to interpret the relative risk in isolation without considering the absolute risks (conditional proportions) as well. For example, doubling a very small probability may not be noteworthy, depending on the context. You should also note that the percentage change calculation and interpretation depends on which group (e.g., treatment or control) is used as the reference group. Practice Problem 3.9 A multicenter, randomized, double-blind trial involved patients aged 36-65 years who had knee injuries consistent with a degenerative medial meniscus tear (Shivonen et al., New England Journal of Medicine , 2013). Patients received either the most common orthopedic procedure (arthroscopic partial meniscectomy, n 1 = 70) or sham surgery that simulated the sounds, sensations, and timing of the real surgery ( n 2 = 76). After 12 months, 54 of those in the treatment group, reported satisfaction, compared
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