CMH Test, OR and RR estimates using PROC FREQ 1 The FREQ Procedure Table 1 of treat by response Controlling for center=a treat response Frequency Percent  Row Pct  Col Pct  1 2 Total  1  11  25  36  15.07  34.25  49.32  30.56  69.44   52.38  48.08   2  10  27  37  13.70  36.99  50.68  27.03  72.97   47.62  51.92   Total 21 52 73 28.77 71.23 100.00 Table 2 of treat by response Controlling for center=b treat response Frequency Percent  Row Pct  Col Pct  1 2 Total  1  16  4  20  30.77  7.69  38.46  80.00  20.00   42.11  28.57   2  22  10  32  42.31  19.23  61.54  68.75  31.25   57.89  71.43   Total 38 14 52 73.08 26.92 100.00 CMH Test, OR and RR estimates using PROC FREQ 2 The FREQ Procedure Table 3 of treat by response Controlling for center=c treat response Frequency Percent  Row Pct  Col Pct  1 2 Total  1  14  5  19  36.84  13.16  50.00  73.68  26.32   66.67  29.41   2  7  12  19  18.42  31.58  50.00  36.84  63.16   33.33  70.59   Total 21 17 38 55.26 44.74 100.00 Table 4 of treat by response Controlling for center=d treat response Frequency Percent  Row Pct  Col Pct  1 2 Total  1  2  14  16  6.06  42.42  48.48  12.50  87.50   66.67  46.67   2  1  16  17  3.03  48.48  51.52  5.88  94.12   33.33  53.33   Total 3 30 33 9.09 90.91 100.00 CMH Test, OR and RR estimates using PROC FREQ 3 The FREQ Procedure Table 5 of treat by response Controlling for center=e treat response Frequency Percent  Row Pct  Col Pct  1 2 Total  1  6  11  17  20.69  37.93  58.62  35.29  64.71   100.00  47.83   2  0  12  12  0.00  41.38  41.38  0.00  100.00   0.00  52.17   Total 6 23 29 20.69 79.31 100.00 Table 6 of treat by response Controlling for center=f treat response Frequency Percent  Row Pct  Col Pct  1 2 Total  1  1  10  11  4.76  47.62  52.38  9.09  90.91   100.00  50.00   2  0  10  10  0.00  47.62  47.62  0.00  100.00   0.00  50.00   Total 1 20 21 4.76 95.24 100.00 CMH Test, OR and RR estimates using PROC FREQ 4 The FREQ Procedure Table 7 of treat by response Controlling for center=g treat response Frequency Percent  Row Pct  Col Pct  1 2 Total  1  1  4  5  7.14  28.57  35.71  20.00  80.00   50.00  33.33   2  1  8  9  7.14  57.14  64.29  11.11  88.89   50.00  66.67   Total 2 12 14 14.29 85.71 100.00 Table 8 of treat by response Controlling for center=h treat response Frequency Percent  Row Pct  Col Pct  1 2 Total  1  4  2  6  30.77  15.38  46.15  66.67  33.33   40.00  66.67   2  6  1  7  46.15  7.69  53.85  85.71  14.29   60.00  33.33   Total 10 3 13 76.92 23.08 100.00 CMH Test, OR and RR estimates using PROC FREQ 5 The FREQ Procedure Summary Statistics for treat by response Controlling for center Cochran-Mantel-Haenszel Statistics (Based on Table Scores) Statistic Alternative Hypothesis DF Value Prob  1 Nonzero Correlation 1 6.3841 0.0115 2 Row Mean Scores Differ 1 6.3841 0.0115 3 General Association 1 6.3841 0.0115 Estimates of the Common Relative Risk (Row1/Row2) Type of Study Method Value 95% Confidence Limits  Case-Control Mantel-Haenszel 2.1345 1.1776 3.8692 (Odds Ratio) Logit ** 1.9497 1.0574 3.5949 Cohort Mantel-Haenszel 1.4245 1.0786 1.8812 (Col1 Risk) Logit ** 1.2194 0.9572 1.5536 Cohort Mantel-Haenszel 0.8129 0.6914 0.9557 (Col2 Risk) Logit 0.8730 0.7783 0.9792 ** These logit estimators use a correction of 0.5 in every cell of those tables that contain a zero. Breslow-Day Test for Homogeneity of the Odds Ratios  Chi-Square 7.9955 DF 7 Pr > ChiSq 0.3330 Total Sample Size = 273 Alternatively, can test drug coef in this model 6 GOF tests here are alternatives to B-D test The LOGISTIC Procedure Model Information Data Set WORK.CMH Response Variable response Number of Response Levels 2 Weight Variable count Model binary logit Optimization Technique Fisher's scoring Number of Observations Read 32 Number of Observations Used 30 Sum of Weights Read 273 Sum of Weights Used 273 Response Profile Ordered Total Total Value response Frequency Weight 1 1 14 102.00000 2 2 16 171.00000 Probability modeled is response=1. NOTE: 2 observations having nonpositive frequencies or weights were excluded since they do not contribute to the analysis. Class Level Information Class Value Design Variables center a 1 0 0 0 0 0 0 b 0 1 0 0 0 0 0 c 0 0 1 0 0 0 0 d 0 0 0 1 0 0 0 e 0 0 0 0 1 0 0 f 0 0 0 0 0 1 0 g 0 0 0 0 0 0 1 h -1 -1 -1 -1 -1 -1 -1 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Alternatively, can test drug coef in this model 7 GOF tests here are alternatives to B-D test The LOGISTIC Procedure Deviance and Pearson Goodness-of-Fit Statistics Criterion Value DF Value/DF Pr > ChiSq Deviance 9.7463 7 1.3923 0.2034 Pearson 8.0256 7 1.1465 0.3303 Number of unique profiles: 16 Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 362.828 295.020 SC 364.229 307.631 -2 Log L 360.828 277.020 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 83.8082 8 <.0001 Score 76.8096 8 <.0001 Wald 58.9946 8 <.0001 Type 3 Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq center 7 58.4897 <.0001 drug 1 6.4174 0.0113 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.2554 0.2692 21.7413 <.0001 center a 1 -0.0667 0.3133 0.0453 0.8315 center b 1 1.9888 0.3556 31.2789 <.0001 center c 1 1.0862 0.3596 9.1236 0.0025 center d 1 -1.4851 0.5707 6.7711 0.0093 center e 1 -0.5866 0.4582 1.6390 0.2005 Alternatively, can test drug coef in this model 8 GOF tests here are alternatives to B-D test The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq center f 1 -2.2136 0.9171 5.8260 0.0158 center g 1 -0.8644 0.7016 1.5178 0.2180 drug 1 0.7769 0.3067 6.4174 0.0113 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits center a vs h 0.110 0.027 0.450 center b vs h 0.859 0.202 3.648 center c vs h 0.348 0.081 1.502 center d vs h 0.027 0.004 0.157 center e vs h 0.065 0.013 0.325 center f vs h 0.013 0.001 0.143 center g vs h 0.050 0.007 0.365 drug 2.175 1.192 3.967 Association of Predicted Probabilities and Observed Responses Percent Concordant 51.3 Somers' D 0.089 Percent Discordant 42.4 Gamma 0.095 Percent Tied 6.3 Tau-a 0.046 Pairs 224 c 0.545 To get loglikelihood value for LRT of dose effect 9 The LOGISTIC Procedure Model Information Data Set WORK.CMH Response Variable response Number of Response Levels 2 Weight Variable count Model binary logit Optimization Technique Fisher's scoring Number of Observations Read 32 Number of Observations Used 30 Sum of Weights Read 273 Sum of Weights Used 273 Response Profile Ordered Total Total Value response Frequency Weight 1 1 14 102.00000 2 2 16 171.00000 Probability modeled is response=1. NOTE: 2 observations having nonpositive frequencies or weights were excluded since they do not contribute to the analysis. Class Level Information Class Value Design Variables center a 1 0 0 0 0 0 0 b 0 1 0 0 0 0 0 c 0 0 1 0 0 0 0 d 0 0 0 1 0 0 0 e 0 0 0 0 1 0 0 f 0 0 0 0 0 1 0 g 0 0 0 0 0 0 1 h -1 -1 -1 -1 -1 -1 -1 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. To get loglikelihood value for LRT of dose effect 10 The LOGISTIC Procedure Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 362.828 299.689 SC 364.229 310.898 -2 Log L 360.828 283.689 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 77.1394 7 <.0001 Score 71.9800 7 <.0001 Wald 57.0913 7 <.0001 Type 3 Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq center 7 57.0913 <.0001 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -0.8657 0.2134 16.4630 <.0001 center a 1 -0.0410 0.3093 0.0176 0.8945 center b 1 1.8642 0.3447 29.2461 <.0001 center c 1 1.0770 0.3541 9.2532 0.0024 center d 1 -1.4369 0.5661 6.4416 0.0111 center e 1 -0.4780 0.4507 1.1250 0.2888 center f 1 -2.1288 0.9122 5.4460 0.0196 center g 1 -0.9261 0.6950 1.7755 0.1827 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits center a vs h 0.121 0.030 0.485 center b vs h 0.814 0.195 3.397 center c vs h 0.371 0.088 1.564 To get loglikelihood value for LRT of dose effect 11 The LOGISTIC Procedure Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits center d vs h 0.030 0.005 0.173 center e vs h 0.078 0.016 0.377 center f vs h 0.015 0.001 0.163 center g vs h 0.050 0.007 0.361 Association of Predicted Probabilities and Observed Responses Percent Concordant 47.3 Somers' D 0.071 Percent Discordant 40.2 Gamma 0.082 Percent Tied 12.5 Tau-a 0.037 Pairs 224 c 0.536