Please answer both questions and show all step-by-step methods and formulae used Document Preview: PAPER 1 JUNE 2007 Question 1 Three separate epidemiological studies were carried out to estimate the...

PAPER 1 JUNE 2007 Question 1 Three separate epidemiological studies were carried out to estimate the prevalence of a particular eye disorder in different populations. In each study a randomly selected sample of adults were examined. Results of the studies were as follows: Study Country Gender N Patients with eye disorder 1 Pakistan Females 10 0 2 Bangladesh Females 100 5 3 Bangladesh Males 100 25 (a) Calculate the probability of the result in study 1 occurring if the true prevalence of the eye disorder is 10% in females in Pakistan. [10%] (b) Using an approximate method, calculate the probability of obtaining an observed prevalence of 5% or lower in study 2 if the true prevalence of the eye disorder is 10% in females in Bangladesh. [15%] (c) Calculate an approximate 95% confidence interval for the true prevalence of the eye disorder in study 2. [20%] (d) Without carrying out further calculations discuss the extent to which the results from the two studies carried out in females are consistent. [15%] (e) Write down the estimate of the odds ratio relating the eye disorder to gender (males versus females) in Bangladesh. [10%] (f) Calculate a confidence interval for the odds ratio in (e) Write down the assumptions necessary for the confidence interval to be valid. [30%]PAPER 1 JUNE 2007 Question 3 A randomised clinical trial is being planned to compare angioplasty with stent insertion in patients with leg artery disease. The primary outcome is treatment failure within one year. A standard power calculation shows that in order to detect a difference between one year failure rates of 45% and 25% with a two-sided type I error of 0.05 and 80% statistical power, a total of 172 are patients are required. (a) Explain what is meant by the terms i) ‘type I error’ and ii) ‘type II error’. [10%] (b) Explain what is meant by the term ‘statistical power’. [10%] (c) In order to have 90% power, instead of 80% power, by...