17 Key Odd Some characters may not display properly on non-Windows computers.

Review Questions

  1. Cohort studies follow a group of individuals forward in time. Case-control studies study a portion of individuals, selected based on case status.
  2. Because you do not know sizes of populations at risk.
  3. Parameter:=  or OR. Estimator= : ^ or OR^
  4. natural logarithmic.
  5. H0: = 1
  6. Fisher's test is used when an expected frequency is less than 5.
  7. In the 2-by-2 table used to summarize matched-pair case-control data, table cells t and w contain counts of concordant pairs, while cells u and v contain counts of discordant pairs.
  8. True.
  9. The name of the chi-square statistic used to test matched-pair data is McNemar's test.
  10. Matching can be used to control for confounding factors.
  11. T
  12. F
  13. The odds ratio is significant at alpha = 0.05 if it excludes 1.
  14. (a) and (c) are significant at alpha = 0.05.

Exercises

Part A: Independent Samples

17A.1 Wynder and Grahams study of lung cancer and smoking.

Odds ratios show stronger and stronger associations with higher levels of smoking (clear dose-response relation).

17A.3 Esophageal cancer and tobacco consumption (dichotomized exposure) - BD1 dataset

(A) Estimation: OR^ = 1.961 = 1.96 (96% increase in risk with exposure). To calculate the confidence interval you'll need SE = 0.1768. The 95% confidence is 1.39 to 2.77 

(B) X2stat = 14.838, df = 1,  P = 1.2E-4 or X2stat, c = 14.109, df = 1, P = 1.7E-4. [This is a good opportunity to review the proper interpretation of P-values.] .Calculation are shown below

Expected Frequencies (none are less than 5)
          D+        D- 
E+      43.897   170.103   214
E-     156.103   604.897   761
       200       775       975

X2stat, Pearson's =  (64 - 43.897)2 / 43.897    + (150 - 170.103)2 / 170.103  + (136 - 156.103)2 / 156.103 + (625 - 604.897)2 / 604.897 
                 =  9.206 +  2.376  + 2.589  + 0.668 =  14.838

X2stat, Yates'=  (|64 - 43.897|-0.5)2 / 43.897    + (|150 - 170.103|-0.5)2 / 170.103  + (|136 - 156.103|-0.5)2 / 156.103 + (|625 - 604.897|-0.5)2 / 604.897 =  14.109

(C) Download dataset; print SPSS codebook

File Type: SPSS Data File
Creation Date: 20-JAN-2004 19:30:43
Label: None
N of Cases: 975
Total # of Defined Variable Elements: 6

Name Position

CASE Esophageal cancer         1
Measurement level: Nominal
Format: F8 Column Width: 8 Alignment: Right
Value Label
1 case
2 control

AGEGRP Age Group                2
Measurement level: Ordinal
Format: F8 Column Width: 8 Alignment: Right

Value Label
1 25-34
2 35-44
3 45-55
4 55-64
5 65-74
6 75+

ALC Alcohol consumption         3
Measurement level: Ordinal
Format: F8 Column Width: 8 Alignment: Right

Value Label
1 0 - 39 gm/day
2 40 - 79 gm/day
3 80 - 119 gm/day
4 120+ gm/day

TOB Tobacco consumption          4
Measurement level: Ordinal
Format: F8 Column Width: 8 Alignment: Right

Value Label
1 0-9 gms/day
2 10-19 gms/day
3 20-29 gms/day
4 30+ gms/day

ALC2 Alcohol dichotomized         5
Measurement level: Scale
Format: F8 Column Width: 8 Alignment: Right
Value Label
1 80+ gms/day
2 0-79 gms/day

TOB2 Tobacco dichotomized         6
Measurement level: Scale
Format: F8 Column Width: 8 Alignment: Right
Value Label
1 20+ gms/day
2 1-19 gms/day

(D) SPSS output

17A.5 Doll & Hills 1950 .Cross-tabulation: 

Smoke

Cases

Non-cases

 Total

  +

  647

622  

1269  

 

  2

27  

 29

Total

  649

649  

 1298

  ^ = (647)(27) / (622)(2) = 14.04; ln ^ = 2.6419; SElny ^ = 0.7350; 95% CI for lny  = (1.2013, 4.0825); 95% CI for y  = (3.3, 59.3). This study found a strong association between smoking and lung cancer: smokers had 14 times the risk as non-smokers. The 95% confidence intervals is compatible with an odds ratio parameter between 3.3 and 59.3. 

17A.7 Asbestos, cigarettes, and lung cancer.

(A) OR = 4.8 
(B) OR = 21.3 
(C) ORsmokers = 60.0; ORnon-smokers = 2.0 (95% CI: 0.6, 6.6). Heterogeneous risks (statistical interaction between asbestos and smoking for cancer risk). 

17A.9 Vasectomy and prostate cancer. (PROSTATE)

Interpretation: Data show a small negative association between vasectomy and prostate cancer risk. The p value suggests the observed association cannot be relied upon. The confidence intervals is compatible with odds ratios in the range of 0.64 to 1.42. Thus, data show no support for as vasectomy protective or risky. (We might ask "At what point does a negative study provide support for safety?" This is another question altogether.)

17A.11 Baldness and the risk of heart attack. 

(A) The conditional distribution of exposure is shown below. Cases were more likely to fall into the high baldness categories (e.g., categories 3 � 5), than controls. 

Baldness

Cases

Controls

1 (none)

37.9%

42.9%

2

24.9%

28.6%

3

29.4%

24.0%

4

7.5%

4.4%

5 (extreme)

0.3%

0.1%

Total 

100.0%

100.0%

Odds ratio are as follows: OR^1 = 1.00 (reference group), OR^2 = 0.98, OR^3 = 1.39, OR^4 = 1.94, OR^4 = 2.64, suggesting a possible dose-response relation (after level 2). 

(B) X2stat = 14.570, df = 4, P = 0.0057

(C) Extended Mantel-Haenszel test for trend: chi-sq. = 11.499 [DF = 1] P = 0.00070. 

 

Part B: Matched-pairs

17B.1 Fruits, vegetables, and adenomatous polyps  

(A) Odds ratio = 45 / 24 = 1.875 @ 1.88. Low fruit/veggie consumption is associated with an 88% increase in risk. 
(B) Confidence interval calculation: ln odds ratio= 0.6286; selny^ = sqrt(1/45 + 1/24) = 0.2528; 95% CI for ln = 0.6286 � (1.96)(0.2528) = 0.6286 � 0.4959 = (0.1331, 1.1241); 95% CI for = e(0.1331, 1.1241) = (1.14, 3.07). This allows us to place the odds ratio parameter in this interval. 
(C) H0: y  = 1 versus H1: y  1; X2McN, corrected = (|45 - 24| - 1)2 / (45 + 24) = 5.80 with df = 1; c = 5.80 = 2.41; P = 0.016. The evidence is significant against the null hypothesis.
(D) Data support the theory that low-fruit and vegetable consumption is a risk factor for colon polyps.

17B.3 Thrombotic stoke

(A) Odds ratio = 44 / 5 = 8.8
(B)  Unmatched cross-tabulation shown below. The unmatched odds ratio = (46)(99)/(7)(60) = 10.8. This overestimates the risk. 

Match broken

Case

Control

Total

  Exposed

46

7

53

  Non-exposed 

60

99

159

Total

106

106

212

 

17B.5 Estrogen and cervical cancer.