Biostatistics in Practice

Peter D. ChristensonBiostatistician

http://gcrc.humc.edu/Biostat

Session 6: Case Study

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 1991;18(4)S35-38.

Data is available at the class website: http://gcrc.humc.edu/BiostatSelect Courses > Biostatistics in Practice 2004 > Session 6 > Download Data

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.”

Data Collected for Sitting dbp

Visit # Week

Number of Subjects

A B C

Baseline 1 -1 311 total

Acute* 2 0 100 93 95

Post 1 3 2 100 93 94

Post 2 4 4 94 91 94

Post 3 5 6 87 88 93

Post 4 6 12 83 84 91

* 1 hour after 1st dose. We do not have data for this visit.

Sitting dbp from Figure 2 of the Paper

t r eat A B C

dBP

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

Week

- 1 0 1 2 3 4 5 6 7 8 9 10 11 12

A: Carvedilol

B: NifedipineC: Atenolol

A

B

C

Baseline

2 Weeks

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?

Answer #1

N = 255Mean = 102.68SD = 4.63SEM = 0.29Min = 92Max =1170.0

25.0

50.0

75.0

100.0

90.0 97.5 105.0 112.5 120.0

Histogram of dbp1

dbp1

Count

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

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.

Answer #2, Part 1

90.0

100.0

110.0

120.0

A B C

Box Plot

treat

dbp1

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.]

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 (~ >2) than expected by random fluctuation (p=0.29), 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.

Question #3

How much can a patient’s 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?

Answer #3

How much can a patient’s 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 Δ ~95% Prediction Interval A 8.13 8.13 ± 2*9.1 = -10.1 to 26.3 C 11.5 11.5 ± 2*8.7 = - 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 ΔC – ΔA estimated from this study, which incorporates the Ns.

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.

Answer #4

Is there evidence that A and C differ in their dbp lowering ability at 2 weeks post-therapy?

Ans:Test H0: ΔA-ΔC = 0 vs. HA: ΔA-ΔC ≠ 0 with t-test:

Estimate ΔA-ΔC with 3.39, with SE of 1.36.

Since tc = 3.39/1.36 = 2.50 exceeds ~2, choose HA.

95% CI for ΔA-ΔC is 3.39±2*1.36 = 0.67 to 6.11, which does not include 0, so choose HA.

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.

Answer #5

Is there evidence that B and C differ in their dbp lowering ability at 2 weeks post-therapy?

Ans:Test H0: ΔB-ΔA = 0 vs. HA: ΔB-ΔA ≠ 0 with t-test:

Estimate ΔB-ΔA with 0.96, with SE of 1.35.

Since tc = 0.96/1.35 = 0.71 < ~2, choose H0 (p=0.48).

SD for B is 8.29 and SD for A is 9.08.

Question #6

Estimate the true minimal difference in 2 week changes in dbp between B and C that this study was able to detect.

1. Use the conventional risks of making incorrect conclusions that the FDA typically requires.

2. Set both risks of an incorrect conclusion at ≤5%.

Typical Statistical Power Software

Answer #6

1. Use the conventional risks of making incorrect conclusions that the FDA typically requires.

Use α=0.05, power=0.80, NA=83, NB=82, SDA=9.08, SDB=8.29. Find Δ from a power calculation to be 3.8.

1. Set both risks of an incorrect conclusion at ≤5%.

Use α=0.05, power=0.95, NA=83, NB=82, SDA=9.08, SDB=8.29. Find Δ from a power calculation to be 4.9.

Question #7

Suppose that differences in 2 week changes in dbp between B and C of <2 mmHg is clinically irrelevant, but we would like to detect larger differences with 80% certainty. How large should such a study be?

Answer #7

Suppose that differences in 2 week changes in dbp between B and C of <2 mmHg is clinically irrelevant, but we would like to detect larger differences with 80% certainty. How large should such a study be?

Ans:Use α=0.05, power=0.80, SDA=9.08, SDB=8.29, Δ=2.

From a power calculation , NA = NB = 297.