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: 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.