Inputting the Death Penalty data, table 3.1.2, p. 54.
data death; input victim defendant deathp count; cards; 1 1 1 53 1 1 2 414 1 2 1 11 1 2 2 37 2 1 1 0 2 1 2 16 2 2 1 4 2 2 2 139 ; run; proc format; value defendant 1='white' 2='black'; value victim 1='white' 2='black'; value deathp 1='Yes' 2='No'; run; proc freq data = death; format defendant defendant. victim victim. deathp deathp.; weight count; by victim; table defendant*deathp/norow nocol ; exact or; run;
victim=white The FREQ ProcedureTable of defendant by deathp defendant deathp
Frequency| Percent |Yes |No | Total ———+——–+——–+ white | 53 | 414 | 467 | 10.29 | 80.39 | 90.68 ———+——–+——–+ black | 11 | 37 | 48 | 2.14 | 7.18 | 9.32 ———+——–+——–+ Total 64 451 515 12.43 87.57 100.00
Statistics for Table of defendant by deathp Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits —————————————————————– Case-Control (Odds Ratio) 0.4306 0.2072 0.8947 Cohort (Col1 Risk) 0.4952 0.2780 0.8822 Cohort (Col2 Risk) 1.1501 0.9824 1.3464
Odds Ratio (Case-Control Study) ———————————– Odds Ratio 0.4306
Asymptotic Conf Limits 95% Lower Conf Limit 0.2072 95% Upper Conf Limit 0.8947
Exact Conf Limits 95% Lower Conf Limit 0.2003 95% Upper Conf Limit 0.9956
Sample Size = 515 victim=black The FREQ Procedure
Table of defendant by deathp defendant deathp
Frequency| Percent |Yes |No | Total ———+——–+——–+ white | 0 | 16 | 16 | 0.00 | 10.06 | 10.06 ———+——–+——–+ black | 4 | 139 | 143 | 2.52 | 87.42 | 89.94 ———+——–+——–+ Total 4 155 159 2.52 97.48 100.0
Statistics for Table of defendant by deathp Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits —————————————————————– Cohort (Col2 Risk) 1.0288 1.0006 1.0578
One or more risk estimates not computed — zero cell.
Sample Size = 159
Inputting the clinic data and obtaining table 3.2 and odds ratios, p. 58-59.
data temp; input clinic treat response count; cards; 1 1 1 18 1 1 2 12 1 2 1 12 1 2 2 8 2 1 1 2 2 1 2 8 2 2 1 8 2 2 2 32 ; run; proc format; value treat 1='A' 2='B'; value response 1='Success' 2='Failure'; run; proc freq data = temp; format treat treat. response response.; weight count; table clinic*treat*response/norow nocol nopercent; exact or; run;
The FREQ Procedure
Table 1 of treat by response
Controlling for clinic=1
treat response
Frequency|Success |Failure | Total
---------+--------+--------+
A | 18 | 12 | 30
---------+--------+--------+
B | 12 | 8 | 20
---------+--------+--------+
Total 30 20 50
Statistics for Table 1 of treat by response
Controlling for clinic=1
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 1.0000 0.3151 3.1738
Cohort (Col1 Risk) 1.0000 0.6300 1.5872
Cohort (Col2 Risk) 1.0000 0.5001 1.9996
Odds Ratio (Case-Control Study)
-----------------------------------
Odds Ratio 1.0000
Asymptotic Conf Limits
95% Lower Conf Limit 0.3151
95% Upper Conf Limit 3.1738
Exact Conf Limits
95% Lower Conf Limit 0.2669
95% Upper Conf Limit 3.6617
Sample Size = 50
The FREQ Procedure
Table 2 of treat by response
Controlling for clinic=2
treat response
Frequency|Success |Failure | Total
---------+--------+--------+
A | 2 | 8 | 10
---------+--------+--------+
B | 8 | 32 | 40
---------+--------+--------+
Total 10 40 50
Statistics for Table 2 of treat by response
Controlling for clinic=2
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 1.0000 0.1769 5.6541
Cohort (Col1 Risk) 1.0000 0.2501 3.9984
Cohort (Col2 Risk) 1.0000 0.7072 1.4141
Odds Ratio (Case-Control Study)
-----------------------------------
Odds Ratio 1.0000
Asymptotic Conf Limits
95% Lower Conf Limit 0.1769
95% Upper Conf Limit 5.6541
Exact Conf Limits
95% Lower Conf Limit 0.0872
95% Upper Conf Limit 6.5993
Sample Size = 50
Inputting the Chinese Smoking and Lung Cancer data, table 3.3, p. 60.
data cmh; input center smoke cancer count @@; cards; 1 1 1 126 1 1 2 100 1 2 1 35 1 2 2 61 2 1 1 908 2 1 2 688 2 2 1 497 2 2 2 807 3 1 1 913 3 1 2 747 3 2 1 336 3 2 2 598 4 1 1 235 4 1 2 172 4 2 1 58 4 2 2 121 5 1 1 402 5 1 2 308 5 2 1 121 5 2 2 215 6 1 1 182 6 1 2 156 6 2 1 72 6 2 2 98 7 1 1 60 7 1 2 99 7 2 1 11 7 2 2 43 8 1 1 104 8 1 2 89 8 2 1 21 8 2 2 36 ; run;
The Mantel-Haenszel odds ratio and the Breslow-Day statistic, p. 62-63.
proc freq data=cmh; weight count; table center*smoke*cancer/ relrisk cmh norow nocol nopercent ; ods output RelativeRisks=temp; run;
Table 1 of smoke by cancer
Controlling for center=1
smoke cancer
Frequency| 1| 2| Total
---------+--------+--------+
1 | 126 | 100 | 226
---------+--------+--------+
2 | 35 | 61 | 96
---------+--------+--------+
Total 161 161 322
Statistics for Table 1 of smoke by cancer
Controlling for center=1
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 2.1960 1.3432 3.5902
Cohort (Col1 Risk) 1.5292 1.1460 2.0406
Cohort (Col2 Risk) 0.6964 0.5641 0.8596
Sample Size = 322
Table 2 of smoke by cancer
Controlling for center=2
smoke cancer
Frequency| 1| 2| Total
---------+--------+--------+
1 | 908 | 688 | 1596
---------+--------+--------+
2 | 497 | 807 | 1304
---------+--------+--------+
Total 1405 1495 2900
Statistics for Table 2 of smoke by cancer
Controlling for center=2
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 2.1430 1.8457 2.4881
Cohort (Col1 Risk) 1.4927 1.3762 1.6191
Cohort (Col2 Risk) 0.6966 0.6491 0.7476
Sample Size = 2900
Table 3 of smoke by cancer
Controlling for center=3
smoke cancer
Frequency| 1| 2| Total
---------+--------+--------+
1 | 913 | 747 | 1660
---------+--------+--------+
2 | 336 | 598 | 934
---------+--------+--------+
Total 1249 1345 2594
Statistics for Table 3 of smoke by cancer
Controlling for center=3
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 2.1753 1.8445 2.5654
Cohort (Col1 Risk) 1.5289 1.3889 1.6829
Cohort (Col2 Risk) 0.7028 0.6542 0.7551
Sample Size = 2594
Table 4 of smoke by cancer
Controlling for center=4
smoke cancer
Frequency| 1| 2| Total
---------+--------+--------+
1 | 235 | 172 | 407
---------+--------+--------+
2 | 58 | 121 | 179
---------+--------+--------+
Total 293 293 586
Statistics for Table 4 of smoke by cancer
Controlling for center=4
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 2.8503 1.9695 4.1252
Cohort (Col1 Risk) 1.7820 1.4196 2.2368
Cohort (Col2 Risk) 0.6252 0.5369 0.7280
Sample Size = 586
Table 5 of smoke by cancer
Controlling for center=5
smoke cancer
Frequency| 1| 2| Total
---------+--------+--------+
1 | 402 | 308 | 710
---------+--------+--------+
2 | 121 | 215 | 336
---------+--------+--------+
Total 523 523 1046
Statistics for Table 5 of smoke by cancer
Controlling for center=5
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 2.3191 1.7745 3.0309
Cohort (Col1 Risk) 1.5723 1.3446 1.8384
Cohort (Col2 Risk) 0.6779 0.6036 0.7615
Sample Size = 1046
Table 6 of smoke by cancer
Controlling for center=6
smoke cancer
Frequency| 1| 2| Total
---------+--------+--------+
1 | 182 | 156 | 338
---------+--------+--------+
2 | 72 | 98 | 170
---------+--------+--------+
Total 254 254 508
Statistics for Table 6 of smoke by cancer
Controlling for center=6
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 1.5880 1.0948 2.3032
Cohort (Col1 Risk) 1.2714 1.0396 1.5548
Cohort (Col2 Risk) 0.8006 0.6736 0.9517
Sample Size = 508
Table 7 of smoke by cancer
Controlling for center=7
smoke cancer
Frequency| 1| 2| Total
---------+--------+--------+
1 | 60 | 99 | 159
---------+--------+--------+
2 | 11 | 43 | 54
---------+--------+--------+
Total 71 142 213
Statistics for Table 7 of smoke by cancer
Controlling for center=7
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 2.3691 1.1351 4.9447
Cohort (Col1 Risk) 1.8525 1.0541 3.2557
Cohort (Col2 Risk) 0.7819 0.6523 0.9373
Sample Size = 213
Table 8 of smoke by cancer
Controlling for center=8
smoke cancer
Frequency| 1| 2| Total
---------+--------+--------+
1 | 104 | 89 | 193
---------+--------+--------+
2 | 21 | 36 | 57
---------+--------+--------+
Total 125 125 250
Statistics for Table 8 of smoke by cancer
Controlling for center=8
Estimates of the Relative Risk (Row1/Row2)
Type of Study Value 95% Confidence Limits
-----------------------------------------------------------------
Case-Control (Odds Ratio) 2.0032 1.0906 3.6796
Cohort (Col1 Risk) 1.4626 1.0163 2.1050
Cohort (Col2 Risk) 0.7301 0.5686 0.9377
Sample Size = 250
Summary Statistics for smoke by cancer
Controlling for center
Cochran-Mantel-Haenszel Statistics (Based on Table Scores)
Statistic Alternative Hypothesis DF Value Prob
---------------------------------------------------------------
1 Nonzero Correlation 1 280.1375 <.0001
2 Row Mean Scores Differ 1 280.1375 <.0001
3 General Association 1 280.1375 <.0001
Estimates of the Common Relative Risk (Row1/Row2)
Type of Study Method Value 95% Confidence Limits
-------------------------------------------------------------------------
Case-Control Mantel-Haenszel 2.1745 1.9840 2.3832
(Odds Ratio) Logit 2.1734 1.9829 2.3823
Cohort Mantel-Haenszel 1.5192 1.4417 1.6008
(Col1 Risk) Logit 1.5132 1.4362 1.5942
Cohort Mantel-Haenszel 0.6999 0.6721 0.7290
(Col2 Risk) Logit 0.7011 0.6734 0.7300
Breslow-Day Test for
Homogeneity of the Odds Ratios
------------------------------
Chi-Square 5.1997
DF 7
Pr > ChiSq 0.6356
Total Sample Size = 8419
proc print data=temp noobs; where studytype="Case-Control (Odds Ratio)"; var table value; title 'Odds Ratio by Center'; run;
Odds Ratio by Center
Table Value
Table 1 of smoke * cancer 2.1960
Table 2 of smoke * cancer 2.1430
Table 3 of smoke * cancer 2.1753
Table 4 of smoke * cancer 2.8503
Table 5 of smoke * cancer 2.3191
Table 6 of smoke * cancer 1.5880
Table 7 of smoke * cancer 2.3691
Table 8 of smoke * cancer 2.0032