Biostatistics in Practice

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Biostatistics in Practice
Session 6 Case Study
Peter D. Christenson Biostatistician http//gcrc
.humc.edu/Biostat
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Case Study
Hall S et al A comparative study of Carvedilol,
slow release Nifedipine, and Atenolol in the
management of essential hypertension. J of
Cardiovascular Pharmacology 199118(4)S35-38. Dat
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Case Study Outline
Subjects randomized to one of 3 drugs for
controlling hypertension A Carvedilol (new)
B Nifedipine (standard) C Atenolol
(standard) Blood pressure and HR measured at
baseline and 5 post-treatment periods. Primary
analysis ? The present study compares A, B,
and C for the management of hypertension.
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Data Collected for Sitting dbp
1 hour after 1st dose. We do not have data for
this visit.
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Sitting dbp from Figure 2 of the Paper
Baseline
A Carvedilol B Nifedipine C Atenolol
A
B
2 Weeks
C
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Question 1
Describe dbp at baseline for the study
population. Give an appropriate graphical
display, and summarize dbp with just a few
numbers. Is the mean appropriate? Would the
median be better? Is a transformation necessary?
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Answer 1
N 255 Mean 102.68 SD 4.63 SEM
0.29 Min 92 Max 117
Median 102. Log-transformation gives geometric
mean 102.58. No transformation is necessary.
Mean is best. 95 of subjects between 102.68
2(4.63) 93.42 to 111.94
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Question 2
It appears that group B may have had lower dbp at
baseline than group A, on the average. Is there
evidence for this? Is the lower group B mean dbp
lower (relative to A) than expected by
chance? Write out a formal test for this
question, and use software to perform the test.
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Answer 2, Part 1
Drug Mean SD A 102.9 4.8
B 102.2 4.3 C 103.0 4.8
So, the mean for B is low, as in the earlier
figure, but the overall distribution is similar
to that for A and C, so this is entirely due to
chance, but we will formally test B vs. A on the
next slide. Would use ANOVA to include C.
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Answer 2, Part 2
We are formally testing, where µx represents the
mean baseline dbp among those who eventually
receive treatment x H0 µA µB vs. HA µA ?
µB Since µA µB is estimated by 0.75 with a SE
of 0.71 , tc 0.75/0.71 1.05 is not larger (
gt2) than expected by random fluctuation (p0.29),
so there is not sufficient evidence that the A
and B groups differed in their baseline dbp. Note
that we do not expect A and B to differ at
baseline due to the randomization in the study
design.
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Question 3
How much can a patients dbp be expected to be
lowered after 2 weeks of therapy with A? We are
95 sure that this lowering will be between what
two values? Repeat for drug C. Do the intervals
for A and for C overlap considerably? Can this
overlapping be used to compare A and C in their
dbp lowering ability?
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Answer 3
How much can a patients dbp be expected to be
lowered after 2 weeks of therapy with A? with
C? We are 95 sure that this lowering will be
between what two values? Ans Drug Estimated
? 95 Prediction Interval A 8.13 8.13
29.1 -10.1 to 26.3 C 11.5 11.5 28.7
- 5.9 to 28.9 The intervals for A and for C
do overlap considerably. However, to compare A
and C, we need to examine not these expected
intervals for individuals, but rather the
precision of ?C ?A estimated from this study,
which incorporates the Ns.
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Question 4
Is there evidence that A and C differ in their
dbp lowering ability at 2 weeks
post-therapy? Formally test for this. Give a 95
confidence interval for the C-A difference in
change in dbp after 2 weeks.
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Answer 4
Is there evidence that A and C differ in their
dbp lowering ability at 2 weeks
post-therapy? Ans Test H0 ?A-?C 0 vs.
HA ?A-?C ? 0 with t-test Estimate ?A-?C with
3.39, with SE of 1.36. Since tc 3.39/1.36
2.50 exceeds 2, choose HA. 95 CI for ?A-?C is
3.3921.36 0.67 to 6.11, which does not
include 0, so choose HA.
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Question 5
Is there evidence that B and A differ in their
dbp lowering ability at 2 weeks post-therapy? We
want to examine whether the study was large
enough to detect a difference in 2 week changes
in dbp between B and A. To do so, we need the SD
of these changes among subjects receiving B and
among subjects receiving A. Find these SDs.
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Answer 5
Is there evidence that B and C differ in their
dbp lowering ability at 2 weeks
post-therapy? Ans Test H0 ?B-?A 0 vs.
HA ?B-?A ? 0 with t-test Estimate ?B-?A with
0.96, with SE of 1.35. Since tc 0.96/1.35
0.71 lt 2, choose H0 (p0.48). SD for B is 8.29
and SD for A is 9.08.
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Question 6

• Estimate the true minimal difference in 2 week
  changes in dbp between B and C that this study
  was able to detect.
• Use the conventional risks of making incorrect
  conclusions that the FDA typically requires.
• Set both risks of an incorrect conclusion at 5.

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Typical Statistical Power Software
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Answer 6

• Use the conventional risks of making incorrect
  conclusions that the FDA typically requires.
• Use a0.05, power0.80, NA83, NB82, SDA9.08,
  SDB8.29. Find ? from a power calculation to be
  3.8.
• Set both risks of an incorrect conclusion at 5.
• Use a0.05, power0.95, NA83, NB82, SDA9.08,
  SDB8.29. Find ? from a power calculation to be
  4.9.

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Question 7
Suppose that differences in 2 week changes in dbp
between B and C of lt2 mmHg is clinically
irrelevant, but we would like to detect larger
differences with 80 certainty. How large should
such a study be?
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Answer 7
Suppose that differences in 2 week changes in dbp
between B and C of lt2 mmHg is clinically
irrelevant, but we would like to detect larger
differences with 80 certainty. How large should
such a study be? Ans Use a0.05, power0.80,
SDA9.08, SDB8.29, ?2. From a power calculation
, NA NB 297.