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2 x 2 Table Statistics | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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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% |
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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% |
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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% |
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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. | |||||||
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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. | |||||||
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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. | |||||||
LookFirst items: Editor's choice of items to examine first. | |||||||