Semester Two Final Examinations, 2017 STAT1201 Analysis of Scientific Data Question 1 A study aimed to determine if grapefruit juice has beneficial effects on the pharmacokinetics of oral digoxin, a drug often prescribed for heart ailments. Seven healthy non-smoking volunteers participated in the study. Subjects took digoxin with water for 2 weeks, no digoxin for 2 weeks, and then digoxin with grapefruit juice for 2 weeks. The peak plasma digoxin concentrations (Cmax; ng/mL) when subjects took digoxin under the two conditions are given in the following table: Subject Water Grapefruit Juice 3.03 Decrease -0.69 1 2.34 2 2.46 3.46 -1.00 3 1.87 1.97 -0.10 4 5 3.09 5.59 4.05 3.81 3.07 -0.72 2.52 6 7 6.21 2.62 3.44 1.43 2.77 While small, note that the sample size was chosen carefully by the authors. In their paper they state that "assuming an a level of 0.05, a sample size of seven subjects has a power of 85% to detect a 25% change in digoxin Cmax". Lower values of Cmax are better since they imply that digoxin is available in the body for longer. Is there any evidence that grapefruit juice increases the effectiveness of oral digoxin, by decreasing Cmax? (a) Identify one issue in the design of this experiment that undermines being able to use the data to answer this question. How could the design be improved? [2 marks] Initial digoxin exposure might carry over, even after 2 weeks without. Randomly allocate order of water /grapefruit treatments to subjects. (b) Suppose u is the true mean decrease in digoxin Cmax with grapefruit compared to water. Define the null and alternative hypotheses for this study in symbols. [1 mark] H?: M=0 H1: M > 0 Page 2 of 20
STAT1201 Analysis of Scientific Data Semester Two Final Examinations, 2017 (c) We have two sets of Cmax measurements, one for water and one for grapefruit. Briefly explain why we work with the differences rather than carrying out a two- sample t-test to compare the treatments. [1 mark] Observations are not independent since they came from same subjects (d) The seven differences in Cmax have mean 0.601 ng/mL with standard deviation 1.609 ng/mL. Use these values to test the hypotheses in (b). What do you conclude? [2 marks] 0.601- 0 t6= 1.609/57] = 0.988 P-value is P(To ?, 0.988) > 0.1 no evidence to suggest a decrease in Cmax with grapefruit juice. (e) How many of the seven subjects had a lower Cmax value with grapefruit juice? Use this to find the P-value for a sign test of whether grapefruit juice tends to lower Cmax. What do you conclude? [2 marks] x=3. P-value is P(X> 3) =. 273+.273+164+.055+,008 = 0.773 1 again no evidence that (max tends to be lower with grapefruit juice. (f) For a sign test from seven subjects, what is the minimum number of reductions in Cmax needed to give evidence of an effect at the 5% level? [1 mark] P(x7,7)= . 008 but P(X>,6) =. 055+.008 = . 063, So