Question

2. The FDA approves drugs when the drug has a beneficial effect in a controlled experi- ment, based on a one-sided 5% level test with Ho the drug has no effect. A drug company has developed a new painkiller for chronic pains, although it is doubtful whether the new drug actually has any effect. The company conducts a double-blind ex periment with n = 298 randomly chosen chronic pain patients over a 6 months period. All patients receive the drug for 3 consecutive months and the placebo for 3 consecutive months, but the order of the drug/placebo treatment is unknown to them and to the administering doctor. During the two 3 months periods, patients report their level of pain on a scale from 0 to 10 (higher numbers indicate more pain). For each patient, let d, be the difference in the level of pain between the placebo treatment period and the drug treatment period (such that positive values of di indicate that the patient felt better while taking the drug) a) The outcome of the trial is such that d -n-1^ d, - 0.14 and s^- n-ĩ Σ(di-d)2 ( 2.9. Will the company get the drug approved by the FDA based on this study, using a one- sided hypothesis test at the 5% level? (b) Suppose conducting a study as described above costs $10 million, and getting the drug approved yields profits of $800 million (gross of the costs of the study)

Answer 1

Padst -Revenue - Ce The standans deviation ds the dilesence m-1 The hyforthes one staed a Ho : The dng hos no ebech Ha: The dng hos ebbed The standaeence a.a

The CriticJ Value 妇a Signibi cance level o-oosi 7c 1.6 The P. vale s a.o2 Since , the P-value (o.2o242) >о.os The nesult is not sigribiant hence ue do not reec ebek 50, -heve iso chance thet the diberenes doug appaoed by the FDA based on +fs sludy 1wn re-sided hyperAexd tot at 5% level The P oepece podt & uo million. 30 million

The stes evewe amaätved by FDA is suo illion so, it -lhe Company taies ogain ie el ab could e ut ao milion S01the Crfoy can expect a nef t -le dg 9els approved in anotlen stoe 10 (30-l0 -lo-o) et petit 30 3 million.

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