Consider the following causal research question: In children undergoing tonsillectomy, to what extent does a new anti-nausea medication reduce the risk of vomiting in the immediate post-operative recovery period compared to standard care?
A randomized controlled trial (RCT) was implemented to address this question and produced the following data:
Postoperative vomiting Treatment arm No Yes Standard care 55 35 New anti-nausea medication 65 25 Total 120 60 Total 90 90 180
a [3 marks] Given the information above, define a suitable target population parameter, the natural estimator for this parameter, and the (approximate) sampling distribution of the estimator, noting your assumptions and using clear notation throughout.
b [2 marks] For the given sample above, calculate an estimate of the target population parameter and a 95% confidence interval based on the normal approximation.
c [1 mark] Consider now a larger RCT where the sample sizes within each treatment arm are 5 times those in the table above, i.e., n = 450 patients in each arm. If the observed proportion of patients reporting postoperative vomiting in each treatment arm is the same as those given in the table above, repeat part b above.
d [1 mark] Compare your answers to parts b and c above.
e [1 mark] Which of the following is a valid interpretation of the 95% CI calculated in part b above?
i. The true value of the risk difference lies within this CI with 95% probability.
ii. If this study were repeated many times using the same design, then 95% of such studies would obtain a risk difference lying within this CI.
iii. This CI was calculated in such a way that if this study and CI calculation were repeated many times using the same design, then the resulting CI would capture the true value of the risk difference on 95% of occasions.
Is it valid to say, "Treatment with a new anti-nausea medication reduces the absolute risk of children reporting postoperative vomiting following tonsillectomy by 11%," based on the CI?
