9B Key Odd
9B.1.
Smoking cessation trial (confidence interval)
(A)
Calculate
the success proportions in each of the groups. Treatment group 
1
= 87 / 245 = 0.3551 or about 35.5%; Control group 2
= 40 / 244 = 0.1639 or about 16.4%
(B) Calculate
the difference in proportions (risk difference) in the sample. Interpret this
results. What
does this mean in plain terms? 1
- 2
= 0.1912. There was 19% greater success with the treatment.
(C) Use the plus-four method to calculate the 95% confidence interval
for risk difference parameter p1 - p2. Interpret
this interval. p~1
= 0.3563, q~1 = 0.6437, n~1
= 247, p~2 = 0.1667, q~2
= 0.8333, n~2 = 246, SEp~1-
p~2 = 0.03864;
95% CI for p1
- p2 = (0.3563 - 0.1167) ±
(1.96)(0.03864) = 0.1896 ± 0.0758 = (0.1138, 0.2654). This interval
allows us to say with 95% confidence that the true benefit will be between 11.4% to
26.5%.
9B.3.
Smoking Cessation (significance test)
-
H0:
p1 = p2
= p vs. Ha:
p1 
p2
-
Test statistics: 1
- 2
= 0.1912, pooled
= 0.2597, SE = 0.03966, zstat = 0.1912 / 0.03996
= 4.78
-
P-value 
0 (P = 1.8E-0006 two-tailed) There is good evidence the difference is not random.
-
Eighty-seven
of 245 (36%) of the subjects in the treatment group (bupropion + nicotine
patch) were successful in ceasing smoking, while 40 of 244 (16%) of the
subjects in the control group (nicotine patch alone) were successful (P =
0.0000018).
9B.5.
Cytomegalovirus and coronary restenosis. Risk in the infected group 1
= 21 / 49 = 0.4286, Risk in the non-infected group 2
= 2 / 26 = 0.0769,
Risk difference 1
- 2
= 0.4286 - 0.0769 = 0.3517 (35% higher risk in the infected group),
95% CI by the plus-four method: p~1
= 22 / 51 = 0.4314, p~2
= 3 / 28 = 0.1071, SEp~1-p~2
= 0.0907, 95%CI for p1
- p2
= (0.4314 - 0.1071) ± (1.96)(0.0907) = 0.3243 ± 0.1778 = (0.1465,
0.5021) or from 15% to 50%. [Comment: Wilson's method via WinPepi computed
0.143 to 0.501, which is very close--nearly identical--to the interval
calculated with the plus-four method.]
9B.7
Women’s Health Initiative.
(A) Risks
Risk in treatment group: 1
= 751 / 8506 = 0.08829 (about 8.8%).
Risk in control group: 2 =
623 / 8102 = 0.07690 (about 7.7%)
Risk difference: 1
- 2 =
0.011396.
Interpretation: The treatment group experience 1.1%
greater risk than the control group.
(B) Hypothesis test
(Hypotheses)
H0: p1 = p2 (no
difference in risk) vs. H1:
p1
p2
(Test statistic) p-hat pooled = 1374 / 16604 = 0.082751; q-hat pooled =
0.91725; zstat = (.08829 - .0769) / sqrt(.0828 ×
.09172[8506-1 + 8102-1]) = 2.66
(P-value) P = 0.00781
(Conclusion) The evidence against H0 is highly
significant.
9B.9 Framingham Heart
Study. Risk difference = 0.12028 - 0.03524 = 0.08504 (about 8.5%); 95%
confidence interval for p1
- p2
(by Wilson's method, which should be close to the plus-four
method) = 0.0502 to 0.1220 (about 5.0% to 12.2%)
9B.11
Scandinavian Simvastatin Survival Study (4S). 1 =
111 / 2221 = 0.049977 2 =
189 / 2223 = 0.085020 (5.0% vs. 8.5%). In testing H0:
p1 = p2
= p, zstat = 4.66 and P = 0.0000032 (two-tailed).
Taking the medication significantly reduced the risk from 5.0% to 8.5% over the
5.4-year period.
9B.13 Joseph Lister and anti-septic surgery.
1 =
0.457143 (about 46%); 2 =
0.1500 (15%); In testing H0:
p1 = p2
= p, zstat = 2.91, P = 0.004 (two-tailed).
9B.15.Treatment of acute otitis media in children. zstat
= 2.054, P = 0.040 The evidence against the null hypothesis is significant. [Note for advanced students: with continuity correction zstat =
1.913, P = 0.056].
9B.17 Hypothetical situation. (A) mean = 0, SE =
sqrt[(.25)(.75)/(3,750) + (.25)(.75)/(3,750)] = 0.01 (B) About 95%
9B.19 Safety of echinacea. Risks and P-values
are reported below. P-value based on z test not corrected for continuity.
All measured outcomes were more common with echinacea. Only rash and
"other" reaction reached statistical significance at alpha =
0.05.
|
Adverse
event
|
Treatment
Group
(n = 337)
|
Control
Group
(n = 370)
|
P-value from zstat |
|
Itchiness
|
3.9%
|
1.9%
|
0.115
|
|
Rash
|
7.1%
|
2.7%
|
0.006
|
|
“Hyper”
behavior
|
8.9%
|
6.2%
|
0.176
|
|
Diarrhea
|
11.3%
|
9.2%
|
0.359
|
|
Vomiting
|
6.5%
|
5.7%
|
0.636
|
|
Headache
|
9.8%
|
6.5%
|
0.107
|
|
Stomachache
|
15.1%
|
11.1%
|
0.110
|
|
Drowsiness
|
11.3%
|
9.7%
|
0.502
|
|
Other
|
18.7%
|
13.0%
|
0.037
|
|
Any
adverse event
|
45.1%
|
39.5%
|
0.129
|
Notes for advanced users: Below are the P-values derived by
different methods The different methods do not materially affect the
interpretation of results.
|
Adverse
event
|
P-value from zstat |
P-value from zstat,cc |
P-value from
published source* |
|
Itchiness
|
0.115
|
0.178
|
0.14
|
|
Rash
|
0.006
|
0.010
|
0.008
|
|
“Hyper” behavior
|
0.176
|
0.226
|
0.31
|
|
Diarrhea
|
0.359
|
0.428
|
0.35
|
|
Vomiting
|
0.636
|
0.752
|
0.56
|
|
Headache
|
0.107
|
0.140
|
0.11
|
|
Stomachache
|
0.110
|
0.137
|
0.16
|
|
Drowsiness
|
0.502
|
0.584
|
0.52
|
|
Other
|
0.037
|
0.047
|
0.06
|
|
Any
adverse event
|
0.129
|
0.129
|
0.14
|
* Published P-values are adjusted for multiple URIs in
the same child.