## Comparing 2 Person-Time Rates

Values for Stratum 1
|  | Exposure
|  | Exposed | Not Exposed
| Cases | 17 | 3 | 20
Disease | Person-Time | 100025 | 122268 | 222293
|  | 100042 | 122271 | 222313

Values for Stratum 2

|  | Exposure
|  | Exposed | Not Exposed
| Cases | 8 | 1 | 9
Disease | Person-Time | 78531 | 77932 | 156463
|  | 78539 | 77933 | 156472

Unstratified (Crude) Values

Exposure
Exposed Not Exposed
Cases 25 4 29
Disease Person-Time 178556 200200 378756
178581 200204 378785

z-Score and Exact Measures of Association

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

1 z-score 3.596 0.0001616 0.0003231
Fisher exact lower=1.00
upper=0.0002769 0.0005538
Mid-P exact lower=0.9998
upper=0.0001564 0.0003127

2 z-score 2.322 0.01012 0.02024
Fisher exact lower=0.9980
upper=0.02008 0.04015
Mid-P exact lower=0.9890
upper=0.01105 0.02210

Crude z-score 4.214 0.00001253 0.00002506
Fisher exact lower=1.00
upper=0.00001462 0.00002923
Mid-P exact lower=1.00
upper=0.000008270 0.00001654
Adjusted z-score statistic 4.28 0.000009360 0.00001872
Fisher exact lower=1.00
upper=0.00001118 0.00002235
Mid-P exact lower=1.00
upper=0.000006306 0.00001261

Exact Rate Ratio Estimates and Confidence Limits
Per 100000 Person-Time Units
Rate-Based* Estimates and 95% Confidence Intervals
| Point Estimates |  | Confidence Limits
Stratum | Type | Value | Lower, Upper | Type
1 | Rate in the exposed | 17 | 9.895, 27.21
| Rate in the unexposed | 2.454 | 0.4932, 7.169
| Overall Rate | 8.997 | 5.494, 13.9
1 | RateRatio | 6.927 | 2.03, 23.63
1 | RateDifference | 14.54 | 6, 23.08
1 | CMLE Rate Ratio* | 6.927 | 2.21, 29.63 | Mid-P Exact
|  |  | 2.004, 36.89 | Fisher Exact
2 | Rate in the exposed | 10.19 | 4.387, 20.07
| Rate in the unexposed | 1.283 | '?', 7.139
| Overall Rate | 5.752 | 2.625, 10.92
2 | RateRatio | 7.939 | 0.9931, 63.47
2 | RateDifference | 8.904 | 1.411, 16.4
2 | CMLE Rate Ratio* | 7.939 | 1.27, 177.6 | Mid-P Exact
|  |  | 1.064, 352.3 | Fisher Exact
Crude | CMLE Rate Ratio* | 7.008 | 2.616, 23.57 | Mid-P Exact
|  |  | 2.42, 27.71 | Fisher Exact
Crude | Rate in the exposed | 14 | 9.059, 20.67
| Rate in the unexposed | 1.998 | 0.5376, 5.115
| Overall Rate | 7.657 | 5.127, 11
Crude | RateRatio | 7.008 | 2.439, 20.13
Crude | RateDifference | 12 | 6.176, 17.83
Crude | Etiologic fraction in pop.(EFp) | 73.9% | 40.42%, 90.02%
| Etiologic fraction in exposed(EFe) | 85.73% | 59%, 95.03%
Adjusted | CMLE Rate Ratio* | 7.185 | 2.681, 24.18 | Mid-P Exact
|  |  | 2.479, 28.42 | Fisher Exact
Adjusted | Directly Adjusted RR | 7.175 | 2.494, 20.65 | Taylor series
| MH Adjusted RR | 7.201 | 2.499, 20.75 | Taylor series
| Directly Adjusted RD | 11.36 | 5.723, 16.99 | Taylor series
Breslow-Day test for interaction of Risk Ratio over strata: chi square=0.01226 | p=0.9118
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=0.9456 | p=0.3308
p greater than 0.05 does not suggest interaction. Adjusted RD can be used.
*Conditional maximum likelihood estimate of Rate 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.
Martin,DO; Austin,H (1996) Exact estimates for a rate ratio.Epidemiology 7, 29-33.
1=Byar method; 2=Taylor series; 3=as described in Abramson and Gahlinger, PEPI software

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