Comparing 2 Person-Time Rates


Values for Stratum 1
Exposure
ExposedNot Exposed
Cases17320
DiseasePerson-Time100025122268222293
100042122271222313

Values for Stratum 2
Exposure
ExposedNot Exposed
Cases819
DiseasePerson-Time7853177932156463
7853977933156472

Unstratified (Crude) Values
Exposure
ExposedNot Exposed
Cases25429
DiseasePerson-Time178556200200378756
178581200204378785


z-Score and Exact Measures of Association

StratumTestValuep-value(1-tail)p-value(2-tail)

1z-score3.5960.00016160.0003231
Fisher exactlower=1.00
upper=0.0002769
0.0005538
Mid-P exactlower=0.9998
upper=0.0001564
0.0003127

2z-score2.3220.010120.02024
Fisher exactlower=0.9980
upper=0.02008
0.04015
Mid-P exactlower=0.9890
upper=0.01105
0.02210

Crudez-score4.2140.000012530.00002506
Fisher exactlower=1.00
upper=0.00001462
0.00002923
Mid-P exactlower=1.00
upper=0.000008270
0.00001654
Adjustedz-score statistic4.280.0000093600.00001872
Fisher exactlower=1.00
upper=0.00001118
0.00002235
Mid-P exactlower=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 EstimatesConfidence Limits

StratumTypeValueLower, UpperType

1Rate in the exposed179.895, 27.21
Rate in the unexposed2.4540.4932, 7.169
Overall Rate8.9975.494, 13.9
1RateRatio6.9272.03, 23.63
1RateDifference14.546, 23.08
1CMLE Rate Ratio*6.9272.21, 29.63Mid-P Exact
2.004, 36.89Fisher Exact

2Rate in the exposed10.194.387, 20.07
Rate in the unexposed1.283'?', 7.139
Overall Rate5.7522.625, 10.92
2RateRatio7.9390.9931, 63.47
2RateDifference8.9041.411, 16.4
2CMLE Rate Ratio*7.9391.27, 177.6Mid-P Exact
1.064, 352.3Fisher Exact

CrudeCMLE Rate Ratio*7.0082.616, 23.57Mid-P Exact
2.42, 27.71Fisher Exact
CrudeRate in the exposed149.059, 20.67
Rate in the unexposed1.9980.5376, 5.115
Overall Rate7.6575.127, 11
CrudeRateRatio7.0082.439, 20.13
CrudeRateDifference126.176, 17.83
CrudeEtiologic fraction in pop.(EFp)73.9%40.42%, 90.02%
Etiologic fraction in exposed(EFe)85.73%59%, 95.03%

AdjustedCMLE Rate Ratio*7.1852.681, 24.18Mid-P Exact
2.479, 28.42Fisher Exact
AdjustedDirectly Adjusted RR7.1752.494, 20.65Taylor series
MH Adjusted RR7.2012.499, 20.75Taylor series
Directly Adjusted RD11.365.723, 16.99Taylor series

Breslow-Day test for interaction of Risk Ratio over strata: chi square=0.01226p=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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