The data are from Lesson 5 and are based on a 5 year cohort study of men initially diagnosed with CHD who were cigarette smokers.  The exposure variable identifies whether the study subjects continued smoking (+) or quit smoking (-) after the CHD event. The outcome is whether they died  (+) or were still alive (-) after five years of follow-up. The data are shown in the table below.

 

The results of the analyses are below:

 

2 x 2 Table Statistics

 


 

 

Single Table Analysis

 

 

Exposure

 

 

 

 

 

 

(+)

(-)

 

 

 

 

(+)

27

14

41

 

 

Disease

(-)

48

67

115

 

 

 

 

75

81

156

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chi Square and Exact Measures of Association


 

 

Test

Value

p-value(1-tail)

p-value(2-tail)


 

 

Uncorrected chi square

7.041

0.003984

0.007968

 

Yates corrected chi square

6.108

0.006729

0.01346

 

Mantel-Haenszel chi square

6.996

0.004086

0.008171

 

Fisher exact

 

0.006561

0.01312

 

Mid-P exact

 

0.004369

0.008738

 


 

 

 

 

 

 

 

 

 

 

 

All expected values (row total*column total/grand total) are >=5

 

 

OK to use chi square.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Risk-Based* Estimates and 95% Confidence Intervals

(Not valid for Case-Control studies)

 


 

 

 

Point Estimates

 

Confidence Limits

 

 


 

 

 

Type

Value

Lower, Upper

Type

 


 

 

 

Risk in Exposed

36%

26.04, 47.32

Taylor series

 

Risk in Unexposed

17.28%

10.46, 27.07

Taylor series

 

Overall Risk

26.28%

19.98, 33.72

Taylor series

 

Risk Ratio

2.083

1.185, 3.661¹

Taylor series

 

Risk Difference

18.72%

5.086, 32.35°

Taylor series

 

Etiologic fraction in pop.(EFp)

34.24%

9.541, 58.93

 

 

 

Etiologic fraction in exposed(EFe)

51.99%

15.62, 72.68

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Odds-Based Estimates and Confidence Limits


 

 

 

Point Estimates

 

Confidence Limits

 

 


 

 

 

Type

Value

Lower, Upper

Type

 


 

 

 

CMLE Odds Ratio*

2.675

1.277, 5.763¹

Mid-P Exact

 

 

 

 

1.208, 6.142¹

Fisher Exact

 

 

Odds Ratio

2.692

1.279, 5.666¹

Taylor series

 

Etiologic fraction in pop.(EFp|OR)

41.39%

14.88, 67.9

 

 

 

Etiologic fraction in exposed(EFe|OR)

62.85%

21.81, 82.35

 

 

 


 

 

 

*Conditional maximum likelihood estimate of Odds Ratio

 

 

(P)indicates a one-tail P-value for Protective or negative association; otherwise one-tailed exact P-values are for a positive association.
Martin,D; Austin,H (1991) An efficient program for computing conditional maximum likelihood estimates and exact confidence limits for a common odds ratio. Epidemiology 2, 359-362.

 

 

° ¹ 95% confidence limits testing exclusion of 0 or 1, as indicated

 

 

LookFirst items: Editor's choice of items to examine first.