## 2 x 2 Table Statistics

Values for Stratum 1
|  | 'Disease'
|  | (+) | (-)
| (+) | 66 | 28 | 94
|  | 70.2% | 29.8% | 100%
|  | 64.7% | 46.7% |
'Exposure' | (-) | 36 | 32 | 68
|  | 52.9% | 47.1% | 100%
|  | 35.3% | 53.3% |
|  | 102 | 60 | 162
|  | 63% | 37% | 100%
|  | 100% | 100%

Values for Stratum 2

|  | 'Disease'
|  | (+) | (-)
| (+) | 139 | 61 | 200
|  | 69.5% | 30.5% | 100%
|  | 59.9% | 53% |
'Exposure' | (-) | 93 | 54 | 147
|  | 63.3% | 36.7% | 100%
|  | 40.1% | 47% |
|  | 232 | 115 | 347
|  | 66.9% | 33.1% | 100%
|  | 100% | 100%

Unstratified (Crude) Values

'Disease'
(+)(-)
(+)205 89 294
69.7%30.3%100%
61.4%50.9%
'Exposure'(-)129 86 215
60%40%100%
38.6%49.1%
334 175 509
65.6%34.4%100%
100%100%

Chi Square and Exact Measures of Association

Stratum Test Value p-value(1-tail)p-value(2-tail)

1 Uncorrected chi square 5.047 0.01233 0.02466
Yates corrected chi square 4.334 0.01868 0.03736
Mantel-Haenszel chi square 5.016 0.01256 0.02511
Fisher exact 0.9920(lower)
0.01881(upper)0.03762
Mid-P exact lower=0.9866
upper=0.01341 0.02682

2 Uncorrected chi square 1.486 0.1116 0.2233
Yates corrected chi square 1.218 0.1354 0.2708
Mantel-Haenszel chi square 1.482 0.1120 0.2239
Fisher exact 0.9088(lower)
0.1349(upper)0.2698
Mid-P exact lower=0.8869
upper=0.1131 0.2261

Crude Uncorrected chi square 5.209 0.01124 0.02247
Yates corrected chi square 4.787 0.01434 0.02868
Mantel-Haenszel chi square 5.199 0.01130 0.02260
Fisher exact 0.9912(lower)
0.01448(upper)0.02895
Mid-P exact lower=0.9883
upper=0.01166 0.02331

Adjusted Mantel-Haenszel Summary Chi Sqr 5.211 0.02245
Fisher exact 0.9912(lower)
0.01438(upper)0.02876
Mid-P exact lower=0.9884
upper=0.01158 0.02316

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
Stratum | Type | Value | Lower, Upper | Type
1 | Risk in Exposed | 70.21 | 60.29, 78.55 | Taylor series
| Risk in Unexposed | 52.94 | 41.24, 64.33 | Taylor series
| Overall Risk | 62.96 | 55.3, 70.02 | Taylor series
| Risk Ratio | 1.326 | 1.023, 1.72¹ | Taylor series
| Risk Difference | 17.27 | 2.232, 32.31° | Taylor series
2 | Risk in Exposed | 69.5 | 62.79, 75.47 | Taylor series
| Risk in Unexposed | 63.27 | 55.22, 70.63 | Taylor series
| Overall Risk | 66.86 | 61.74, 71.61 | Taylor series
| Risk Ratio | 1.099 | 0.9421, 1.281¹ | Taylor series
| Risk Difference | 6.235 | -3.837, 16.31° | Taylor series
Crude | Risk in Exposed | 69.73 | 64.24, 74.7 | Taylor series
| Risk in Unexposed | 60 | 53.33, 66.32 | Taylor series
| Overall Risk | 65.62 | 61.39, 69.62 | Taylor series
| Risk Ratio | 1.162 | 1.018, 1.327¹ | Taylor series
| Risk Difference | 9.728 | 1.334, 18.12° | Taylor series
| Etiologic fraction in pop.(EFp) | 8.563 | 1.099, 16.03
| Etiologic fraction in exposed(EFe) | 13.95 | 1.75, 24.64
Adjusted | Directly Adjusted RR | 1.153 | 1.011, 1.317¹ | Taylor series
| MH Adjusted RR | 1.162 | 1.018, 1.327¹ | Taylor series
| Directly Adjusted RD | 9.652 | 1.283, 18.02° | Taylor series
Breslow-Day test for interaction of Risk Ratio over strata: chi square=1.495 | p=0.2219
p greater than 0.05 does not suggest interaction. Adjusted RR can be used.
Breslow-Day test for interaction of Risk Difference over strata: chi square=1.428 | p=0.2326
p greater than 0.05 does not suggest interaction. Adjusted RD can be used.

Odds-Based Estimates and Confidence Limits
| Point Estimates |  | Confidence Limits
Stratum | Type | Value | Lower, Upper | Type
1 | CMLE Odds Ratio* | 2.085 | 1.088, 4.028¹ | Mid-P Exact
|  |  | 1.04, 4.223¹ | Fisher Exact
| Odds Ratio | 2.095 | 1.094, 4.012¹ | Taylor series
2 | CMLE Odds Ratio* | 1.322 | 0.8409, 2.078¹ | Mid-P Exact
|  |  | 0.8213, 2.127¹ | Fisher Exact
| Odds Ratio | 1.323 | 0.8432, 2.076¹ | Taylor series
Crude | CMLE Odds Ratio* | 1.534 | 1.06, 2.222¹ | Mid-P Exact
|  |  | 1.043, 2.259¹ | Fisher Exact
| Odds Ratio | 1.536 | 1.061, 2.221¹ | Taylor series
| Etiologic fraction in pop.(EFp|OR) | 21.41 | 5.495, 37.32
| Etiologic fraction in exposed(EFe|OR) | 34.88 | 5.793, 54.98
Adjusted | CMLE Odds Ratio* | 1.535 | 1.06, 2.223¹ | Mid-P Exact
|  |  | 1.044, 2.259¹ | Fisher Exact
| Directly Adjusted OR | 1.536 | 1.061, 2.225¹ | Taylor series
| Mantel-Haenszel OR | 1.536 | 1.062, 2.222¹ | Robins,Greenland,Breslow
Breslow-Day test for interaction of Odds Ratio over strata: chi square=1.298 | p=0.2554
p greater than 0.05 does not suggest interaction. Adjusted OR can be used.
*Conditional maximum likelihood estimate of Odds Ratio
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
P-values < 0.05 and confidence limits excluding null values (0,1, or [n]) are highlighted.
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