Makers of generic drugs must show that they do not differ significantly from the

Question

Makers of generic drugs must show that they do not differ significantly from the “reference” drugs that they imitate. One aspect in which drugs might differ is their extent of absorption in the blood. We have some data taken from 20 healthy nonsmoking male subjects for one pair of drugs. This is a matched pairs design. Numbers 1 to 20 were assigned at random to the subjects. Subjects 1 to 10 received the generic drug first, followed by the reference drug. Subjects 11 to 20 received the reference drug first, followed by the generic drug. In all cases, a washout period separated the two drugs so that the first had disappeared from the blood before the subject took the second. By randomizing the order, we eliminate the order in which the drugs were administered from being confounded with the difference in the absorption in the blood. We want to know: Do the drugs differ significantly in the amount absorbed in the blood? To answer this, complete the steps below.

DATA:

a. Explain how you know that this is a matched pairs t test. Be specific.   

b. It is appropriate to use a matched pairs t-test here? Answer this questions by reviewing the underlying assumptions for using t procedure

c. Are there any outliers in the differences in absorption? Show your work.

Subj Ref Generic Difference 15 4108 1755 2353 3 2526 1138 1388 9 2779 1613 1166 13 3852 2254 1598 12 1833 1310 523 8 2463 2120 343 18 2059 1851 208 20 1709 1878 -169 17 1829 1682 147 2 2594 2613 -19 4 2344 2738 -394 16 1864 2302 -438 6 1022 1284 -262 10 2256 3052 -796 5 938 1287 -349 7 1339 1930 -591 14 1262 1964 -702 11 1438 2549 -1111 1 1735 3340 -1605 19 1020 3050 -2030

Explanation / Answer

a)

Here, we are trying to test means of 2 related populations and we have

1) Paired or matched samples

2)  Repeated measures (before/after)

3)  We are using difference between paired values.

b)

Assumptions are:-

# Both Populations Are Normally Distributed.

# Or, if not Normal, use large samples.

# Sample is representative of the population.

# We are using difference between paired values.

We can use the t-test matched pairs here.

c)

H0: D = 0

H1: D 0

D-bar=EDi/n

          =-740/20

          =-37

SD=E(Di-D^2)/n-1=1070.62

tSTAT=D-bar-µ/ SD/n=-37-0/1070.62/20=-0.15

Critical value is +-2.093

Hence, cannot reject null hypothesis. There aren’t any outliers in difference in absorption.

Subj Ref Generic Difference Di-D Di-D^2 15 4108 1755 2353 2390 5712100 3 2526 1138 1388 1425 2030625 9 2779 1613 1166 1203 1447209 13 3852 2254 1598 1635 2673225 12 1833 1310 523 560 313600 8 2463 2120 343 380 144400 18 2059 1851 208 245 60025 20 1709 1878 -169 -132 17424 17 1829 1682 147 184 33856 2 2594 2613 -19 18 324 4 2344 2738 -394 -357 127449 16 1864 2302 -438 -401 160801 6 1022 1284 -262 -225 50625 10 2256 3052 -796 -759 576081 5 938 1287 -349 -312 97344 7 1339 1930 -591 -554 306916 14 1262 1964 -702 -665 442225 11 1438 2549 -1111 -1074 1153476 1 1735 3340 -1605 -1568 2458624 19 1020 3050 -2030 -1993 3972049 ED -740 21778378 D-bar -37 1146230 1070.622 SD

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