Key to Exercises: Bin-Coh Exercises
(1) EAR.REC
(A) Eighty-nine (59%) of the 150 cefaclor-treated
ears cleared their infection. In contrast, 56 (44%) of the 128 amoxicillin-treated
ears cleared their infection.
(B) The relative rate of infection-clearance
associated with cefaclor compared with amoxicillin is 1.4 (95% confidence
interval: 1.1, 1.7).
(C) H0: RR
= 1 vs. H1: RR not = 1, let alpha = .05,
Chi-square, Yates (1, N = 278) = 6.11, p = .013, Reject H0
Interpretation: Cefaclor is significantly
better than amoxicillin -- 59% vs. 44% -- at clearing ear infections
in this population.
(2) PRISON.REC
The prevalence of HIV in the IVDU group is
45% (61 of 136). The prevalence in the non-IVDU group is 8% (27 of 339).
The prevalence ratio estimate is 5.6 (95% confidence interval: 3.8, 8.5).
This difference is highly significant (p < .000000005 by the
uncorrected chi-square method).
(3) LABOR.REC
-
(A) p^1 = 1 / 111 = 0.9%; p^2 = 13
/ 117 = 11.1%
-
(B) RR^ = 0.08 (95% confidence interval for RR: 0.01, 0.61)
-
(C) H0: RR = 1 vs. H1: RR
not = 1
Let alpha = .05
Chi-square, Yates (1, N = 228) = 8.61, p = .0033
Reject H0
Interpretation: Significantly lower rates of muconium staining with
induction -- ~1% vs. ~11%.
(4) OSWEGO.REC
Food |
Ate
Food (Exposed) |
Did
Not Eat Food (Unexposed) |
RR |
95%
CI for RR |
p
value |
Ill |
Total |
% |
Ill |
Total |
% |
Baked Ham |
29 |
46 |
63% |
17 |
29 |
59% |
1.1 |
0.7 - 1.6 |
.70 |
Spinach |
26 |
43 |
61% |
20 |
32 |
63% |
1.0 |
0.7 - 1.4 |
.86 |
Mashed Pot. |
23 |
37 |
62% |
23 |
37 |
62% |
1.0 |
0.7 - 1.4 |
1.00 |
Cabbage Sal. |
18 |
28 |
64% |
28 |
47 |
60% |
1.1 |
0.8 - 1.6 |
.69 |
Jell-O |
16 |
23 |
70% |
30 |
52 |
58% |
1.2 |
0.8 - 1.7 |
.33 |
Rolls |
21 |
37 |
57% |
25 |
38 |
66% |
0.9 |
0.6 - 1.2 |
.42 |
Brown bread |
18 |
27 |
67% |
28 |
48 |
58% |
1.1 |
0.8 - 1.6 |
.48 |
Milk |
2 |
4 |
50% |
44 |
71 |
62% |
0.8 |
0.3 - 2.2 |
.64 (F) |
Coffee |
19 |
31 |
61% |
27 |
44 |
61% |
1.0 |
0.7 - 1.4 |
.99 |
Water |
13 |
24 |
54% |
33 |
51 |
65% |
0.8 |
0.6 - 1.3 |
.38 |
Cakes |
27 |
40 |
68% |
19 |
35 |
54% |
1.2 |
0.9 - 1.8 |
.24 |
Van. ice cream |
43 |
54 |
80% |
3 |
21 |
14% |
5.6 |
1.9 - 16.0 |
<.0001 |
Choc. ice cream |
25 |
47 |
53% |
20 |
27 |
74% |
0.7 |
0.5 - 1.0 |
.08 |
Fruit salad |
4 |
6 |
67% |
42 |
69 |
61% |
1.1 |
0.6 - 2.0 |
1.00 (F) |
Comments:
-
(F) indicates p value derived by Fisher's
test. All other p values derived by the uncorrected chi-square test.
-
Percentages are reported to the nearest whole
percentage, as recommended by the APA Publications Guide. Relative risks
are reported to the nearest tenth of a unit.
-
Vanilla ice-cream exposure is the only food
significantly associated with the illness.
Comment: Upon further investigation, and based
on the signs and symptoms of the illness, its incubation period, and the
most plausible explanation of events, it was inferred that the vanilla
ice cream served as the reservoir for be S. aureus, and that contamination
occurred while mixing the ingredients, before the ice cream was frozen.
(5) FOODBRNE
No answer given.
(6) RESTENOS
-
(A) 2-by-2 table w/ restenosis rates
|
Resten + |
Resten - |
Total |
Cytomeg. + |
21 |
28 |
49 |
Cytomeg. - |
2 |
24 |
26 |
p^1 = 21 of 49 (42.9%)
p^2 = 2 of 26 (7.7%)
-
(B) RR^ = 5.6 (95% confidence interval
for RR: 1.4, 21.9; p = .0017 Yates' chi-square method).
-
(C) Yes. A significant association between
cytomegalovirus infection and arterial restenosis is suggested.
(7) PHENFORM
Cardiovascular death rates by group: Phenformin group: 13% (26 of 204);
Placebo group: 3% (2 of 64).
Data, in two-by-two table format (This
was not requested explicity, but is needed in order to calculate the required
inferential statistics with STATCALC.)
|
Died |
Survived |
Total |
Phenformin |
26 |
178 |
204 |
Control |
2 |
62 |
64 |
RR^ = 4.1 (95% confidence interval
for RR: 1.0, 16.7)
Hypothesis test: H0:
RR = 1 vs. H1: RR is not equal to 1. Let
alpha = .05. Chi-square, uncorrected (1, N = 268) = 4.82, p =
.028. Reject H0.
Interpretation: The phenformin group had
a significantly higher risk of death due to cardiovascular disease (13%
vs. 3%). (Comment: The trial was discontinued and phenformin was removed
from use as a result.)
(8) SIZE-COH
-
(A) Sample size requirements for assumptions:
alpha = .05; power = .8; allocation ratio = 1:1; p2 =
25%.
-
For RR = 2.0, N = 132
-
For RR = 3.0, N = 38
-
For RR = 4.0, N = 16
-
(B) Power calculations for assumptions: n1
= 50, n2 = 100, (allocation ratio = n2
/ n1 = 2), p2 = 5%, alpha = .05
-
For RR = 2.0, power = 15.6%
-
For RR = 3.0, power = 43.2%
-
For RR = 4.0, power = 69.2%
(9) BI-HELM1
-
(A) Group 1 = Santa Clara County; Group 2 = Contra Costa County
-
p^1 = 312 / 844 = 37.0%; p^2 = 335 / 807 = 41.5%
(B) RR^ = 0.89 (95% confidence interval for RR: 0.79,
1.00)
-
(C) H0: RR = 1 vs. H1: RR
not = 1
Let alpha = .05
Chi-square, Yates' (1, N = 1651) = 3.39, p = .066
Retain H0
Interpretation: No significant difference in helmet use rates (although
data are suggestive -- some statisticians might call this marginally significant,
but that's another story).
(10) Directed Paraphrasing Question
No answer provided.
(11) OC / MI
Follow-up time is 3 years.
(A) 2-by-2 Table
|
MI+
|
MI-
|
|
OC+
|
13
|
4987
|
5000
|
OC-
|
7
|
9993
|
10,000
|
|
20
|
14,980
|
15,000
|
-
(B) Estimates
-
p^1 = 13 / 5000 = .0026; p^2
= 7 / 10,000 = .0007
-
RR^ = .0026 / .0007 = 3.71
-
95% confidence interval for RR = (1.48,
9.30)
-
(C) Test of statistical significance
-
-
The expected table is:
|
MI+
|
MI-
|
|
OC+
|
6.7
|
4993.3
|
5000
|
OC-
|
13.3
|
9986.7
|
10,000
|
|
20
|
14,980
|
15,000
|
-
-
Because none of the expected values are less
than 5, a chi-square test may be used.
-
H0: RR = 1 H1:
RR not = 1
-
Let alpha = .01
-
Chi-square, Yate's (1, N = 15,000)
= 7.67, p = .0056
-
Reject H0
(D) Summary [2]: The summary should make clear that OC users appear to
have a 3.7-fold increase in the risk of myocardial infarction and that
this finding is statistically significant.
(12) Hypothetical sample size calculation
Before one could estimate the sample size requirements of a cohort study
of breast cancer and oral contraceptive use, one would need to have a reliable
estimate of brease cancer in non-exposed women (p2).
One would also need to state a RR worth detecting, and allocation
ratio of nonexposed to exposed study subjects, alpha (usually .05, by convention),
and power (usually 0.80). For example, a we might assume p2
= 2 / 100, a RR worth detecting = 2, n2 / n1
= 4, alpha = .05, and power = .8. ased on these assumptions, EpiTable
calculates:
Number of Exposed
: 824
Number of Non exposed
: 3296
Total #
: 4120
This example is only illustrative.