Anyone who’s ever watched late-night TV knows how many people want to lose weight the easy way. On the basis of recent medical studies, there may be such a thing. Glaxo Smith Kline bought the drug Orlistat with the hopes of turning it into a modern miracle. Results in prior clinical trials had found that when Orlistat was combined with a diet, subjects taking Orlistat lost more weight. After about a year, a randomized experiment found that obese subjects taking this medication had lost about 11 more pounds, on average, than others who were also dieting, but taking a placebo.14 Further studies showed similar results.
This drug had moderate success, but Glaxo Smith Kline wanted to take it before the Food and Drug Administration (FDA) and ask the agency to approve it for over-the-counter sales. They wanted it to be available without a prescription. To assemble more information, the company needs help in designing a study to test the drug for college students. The company needs to know how many students it must enroll in order to see if the drug works.
Motivation
Worldwide sales were about $500 million in 2004, but projected to soar to more than $1.5 billion annually with the greater access of over-the-counter sales.
(a) Do you think it would be damaging to Glaxo Smith Kline’s case if the proposed study did not fnd the drug to be helpful?
(b) If the study costs $5,000 per subject to run but the potential upside is $1 billion, why should the size of the study matter? Why not recruit thousands?
Method
To get FDA recognition, this study requires a randomized experiment. Let’s assume half of the subjects receive a placebo and half receive Orlistat.
(c) If the subjects are healthy students who take half the dose taken by the obese people in prior studies, would you expect the amount of weight loss to be as large as in previous studies?
(d) Is a two-sample confdence interval of the difference in means appropriate for this analysis?
(e) Will the presence of lurking factors lead to confusion over the interpretation of the difference in means?
(f) What would you recommend if the variation in weight loss is different in the two groups, with those taking Orlistat showing much more variation than those taking the placebo?
Mechanics
For these calculations, let’s assume that Glaxo Smith Kline expects those taking Orlistat to have lost 6 pounds more than the controls after six months. Pilot studies indicate that the SD for the amount of weight lost by an individual is σ ≈ 5.
(g) If the study enrolls 25 students in each group (a total of 50), is it likely that the difference between the two sample means will be far from zero?
(h) Repeat part (g), with 100 students enrolled in each group.
(i) Do you think it’s likely that the confidence interval with 25 or 100 in each group will include zero if in fact μ1 - μ2 = 6?
(j) If the claimed value for s is too small, what will be the likely consequence for the choice of a sample size?
Message
(k) Which sample size would you recommend, 25 in each group or 100?
(l) This drug has some embarrassing side effects (e.g., incontinence). Would this affect your recommendation of how many subjects to enroll? Why?