The SAS System 07:52 Thursday, July 24, 2008 1 Obs clinic trt fav unfav count response 1 1 drug 11 25 11 1 2 1 drug 11 25 25 0 3 1 cntl 10 27 10 1 4 1 cntl 10 27 27 0 5 2 drug 16 4 16 1 6 2 drug 16 4 4 0 7 2 cntl 22 10 22 1 8 2 cntl 22 10 10 0 9 3 drug 14 5 14 1 10 3 drug 14 5 5 0 11 3 cntl 7 12 7 1 12 3 cntl 7 12 12 0 13 4 drug 2 14 2 1 14 4 drug 2 14 14 0 15 4 cntl 1 16 1 1 16 4 cntl 1 16 16 0 17 5 drug 6 11 6 1 18 5 drug 6 11 11 0 19 5 cntl 0 12 0 1 20 5 cntl 0 12 12 0 21 6 drug 1 10 1 1 22 6 drug 1 10 10 0 23 6 cntl 0 10 0 1 24 6 cntl 0 10 10 0 25 7 drug 1 4 1 1 26 7 drug 1 4 4 0 27 7 cntl 1 8 1 1 28 7 cntl 1 8 8 0 29 8 drug 4 2 4 1 30 8 drug 4 2 2 0 31 8 cntl 6 1 6 1 32 8 cntl 6 1 1 0 When cmh option in PROC FREQ is used for data analysis 2 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Table 1 of trt by response Controlling for clinic=1 trt response Frequency| Expected | Percent | Row Pct | Col Pct | 0| 1| Total ---------+--------+--------+ cntl | 27 | 10 | 37 | 26.356 | 10.644 | | 36.99 | 13.70 | 50.68 | 72.97 | 27.03 | | 51.92 | 47.62 | ---------+--------+--------+ drug | 25 | 11 | 36 | 25.644 | 10.356 | | 34.25 | 15.07 | 49.32 | 69.44 | 30.56 | | 48.08 | 52.38 | ---------+--------+--------+ Total 52 21 73 71.23 28.77 100.00 Statistics for Table 1 of trt by response Controlling for clinic=1 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.1109 0.7392 Likelihood Ratio Chi-Square 1 0.1109 0.7391 Continuity Adj. Chi-Square 1 0.0055 0.9407 Mantel-Haenszel Chi-Square 1 0.1093 0.7409 Phi Coefficient 0.0390 Contingency Coefficient 0.0389 Cramer's V 0.0390 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 27 Left-sided Pr <= F 0.7227 Right-sided Pr >= F 0.4702 Table Probability (P) 0.1929 Two-sided Pr <= P 0.7997 Sample Size = 73 When cmh option in PROC FREQ is used for data analysis 3 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Table 2 of trt by response Controlling for clinic=2 trt response Frequency| Expected | Percent | Row Pct | Col Pct | 0| 1| Total ---------+--------+--------+ cntl | 10 | 22 | 32 | 8.6154 | 23.385 | | 19.23 | 42.31 | 61.54 | 31.25 | 68.75 | | 71.43 | 57.89 | ---------+--------+--------+ drug | 4 | 16 | 20 | 5.3846 | 14.615 | | 7.69 | 30.77 | 38.46 | 20.00 | 80.00 | | 28.57 | 42.11 | ---------+--------+--------+ Total 14 38 52 26.92 73.08 100.00 Statistics for Table 2 of trt by response Controlling for clinic=2 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.7917 0.3736 Likelihood Ratio Chi-Square 1 0.8136 0.3671 Continuity Adj. Chi-Square 1 0.3232 0.5697 Mantel-Haenszel Chi-Square 1 0.7765 0.3782 Phi Coefficient 0.1234 Contingency Coefficient 0.1225 Cramer's V 0.1234 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 10 Left-sided Pr <= F 0.8884 Right-sided Pr >= F 0.2883 Table Probability (P) 0.1767 Two-sided Pr <= P 0.5237 Sample Size = 52 When cmh option in PROC FREQ is used for data analysis 4 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Table 3 of trt by response Controlling for clinic=3 trt response Frequency| Expected | Percent | Row Pct | Col Pct | 0| 1| Total ---------+--------+--------+ cntl | 12 | 7 | 19 | 8.5 | 10.5 | | 31.58 | 18.42 | 50.00 | 63.16 | 36.84 | | 70.59 | 33.33 | ---------+--------+--------+ drug | 5 | 14 | 19 | 8.5 | 10.5 | | 13.16 | 36.84 | 50.00 | 26.32 | 73.68 | | 29.41 | 66.67 | ---------+--------+--------+ Total 17 21 38 44.74 55.26 100.00 Statistics for Table 3 of trt by response Controlling for clinic=3 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 5.2157 0.0224 Likelihood Ratio Chi-Square 1 5.3485 0.0207 Continuity Adj. Chi-Square 1 3.8319 0.0503 Mantel-Haenszel Chi-Square 1 5.0784 0.0242 Phi Coefficient 0.3705 Contingency Coefficient 0.3474 Cramer's V 0.3705 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 12 Left-sided Pr <= F 0.9959 Right-sided Pr >= F 0.0244 Table Probability (P) 0.0204 Two-sided Pr <= P 0.0489 Sample Size = 38 When cmh option in PROC FREQ is used for data analysis 5 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Table 4 of trt by response Controlling for clinic=4 trt response Frequency| Expected | Percent | Row Pct | Col Pct | 0| 1| Total ---------+--------+--------+ cntl | 16 | 1 | 17 | 15.455 | 1.5455 | | 48.48 | 3.03 | 51.52 | 94.12 | 5.88 | | 53.33 | 33.33 | ---------+--------+--------+ drug | 14 | 2 | 16 | 14.545 | 1.4545 | | 42.42 | 6.06 | 48.48 | 87.50 | 12.50 | | 46.67 | 66.67 | ---------+--------+--------+ Total 30 3 33 90.91 9.09 100.00 Statistics for Table 4 of trt by response Controlling for clinic=4 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.4368 0.5087 Likelihood Ratio Chi-Square 1 0.4429 0.5057 Continuity Adj. Chi-Square 1 0.0030 0.9561 Mantel-Haenszel Chi-Square 1 0.4235 0.5152 Phi Coefficient 0.1150 Contingency Coefficient 0.1143 Cramer's V 0.1150 WARNING: 50% of the cells have expected counts less than 5. Chi-Square may not be a valid test. When cmh option in PROC FREQ is used for data analysis 6 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Statistics for Table 4 of trt by response Controlling for clinic=4 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 16 Left-sided Pr <= F 0.8974 Right-sided Pr >= F 0.4765 Table Probability (P) 0.3739 Two-sided Pr <= P 0.6012 Sample Size = 33 Table 5 of trt by response Controlling for clinic=5 trt response Frequency| Expected | Percent | Row Pct | Col Pct | 0| 1| Total ---------+--------+--------+ cntl | 12 | 0 | 12 | 9.5172 | 2.4828 | | 41.38 | 0.00 | 41.38 | 100.00 | 0.00 | | 52.17 | 0.00 | ---------+--------+--------+ drug | 11 | 6 | 17 | 13.483 | 3.5172 | | 37.93 | 20.69 | 58.62 | 64.71 | 35.29 | | 47.83 | 100.00 | ---------+--------+--------+ Total 23 6 29 79.31 20.69 100.00 When cmh option in PROC FREQ is used for data analysis 7 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Statistics for Table 5 of trt by response Controlling for clinic=5 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 5.3402 0.0208 Likelihood Ratio Chi-Square 1 7.4949 0.0062 Continuity Adj. Chi-Square 1 3.4058 0.0650 Mantel-Haenszel Chi-Square 1 5.1560 0.0232 Phi Coefficient 0.4291 Contingency Coefficient 0.3943 Cramer's V 0.4291 WARNING: 50% of the cells have expected counts less than 5. Chi-Square may not be a valid test. Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 12 Left-sided Pr <= F 1.0000 Right-sided Pr >= F 0.0261 Table Probability (P) 0.0261 Two-sided Pr <= P 0.0280 Sample Size = 29 When cmh option in PROC FREQ is used for data analysis 8 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Table 6 of trt by response Controlling for clinic=6 trt response Frequency| Expected | Percent | Row Pct | Col Pct | 0| 1| Total ---------+--------+--------+ cntl | 10 | 0 | 10 | 9.5238 | 0.4762 | | 47.62 | 0.00 | 47.62 | 100.00 | 0.00 | | 50.00 | 0.00 | ---------+--------+--------+ drug | 10 | 1 | 11 | 10.476 | 0.5238 | | 47.62 | 4.76 | 52.38 | 90.91 | 9.09 | | 50.00 | 100.00 | ---------+--------+--------+ Total 20 1 21 95.24 4.76 100.00 Statistics for Table 6 of trt by response Controlling for clinic=6 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.9545 0.3286 Likelihood Ratio Chi-Square 1 1.3387 0.2473 Continuity Adj. Chi-Square 1 0.0000 1.0000 Mantel-Haenszel Chi-Square 1 0.9091 0.3404 Phi Coefficient 0.2132 Contingency Coefficient 0.2085 Cramer's V 0.2132 WARNING: 50% of the cells have expected counts less than 5. Chi-Square may not be a valid test. When cmh option in PROC FREQ is used for data analysis 9 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Statistics for Table 6 of trt by response Controlling for clinic=6 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 10 Left-sided Pr <= F 1.0000 Right-sided Pr >= F 0.5238 Table Probability (P) 0.5238 Two-sided Pr <= P 1.0000 Sample Size = 21 Table 7 of trt by response Controlling for clinic=7 trt response Frequency| Expected | Percent | Row Pct | Col Pct | 0| 1| Total ---------+--------+--------+ cntl | 8 | 1 | 9 | 7.7143 | 1.2857 | | 57.14 | 7.14 | 64.29 | 88.89 | 11.11 | | 66.67 | 50.00 | ---------+--------+--------+ drug | 4 | 1 | 5 | 4.2857 | 0.7143 | | 28.57 | 7.14 | 35.71 | 80.00 | 20.00 | | 33.33 | 50.00 | ---------+--------+--------+ Total 12 2 14 85.71 14.29 100.00 When cmh option in PROC FREQ is used for data analysis 10 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Statistics for Table 7 of trt by response Controlling for clinic=7 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.2074 0.6488 Likelihood Ratio Chi-Square 1 0.2003 0.6545 Continuity Adj. Chi-Square 1 0.0000 1.0000 Mantel-Haenszel Chi-Square 1 0.1926 0.6608 Phi Coefficient 0.1217 Contingency Coefficient 0.1208 Cramer's V 0.1217 WARNING: 75% of the cells have expected counts less than 5. Chi-Square may not be a valid test. Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 8 Left-sided Pr <= F 0.8901 Right-sided Pr >= F 0.6044 Table Probability (P) 0.4945 Two-sided Pr <= P 1.0000 Sample Size = 14 When cmh option in PROC FREQ is used for data analysis 11 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Table 8 of trt by response Controlling for clinic=8 trt response Frequency| Expected | Percent | Row Pct | Col Pct | 0| 1| Total ---------+--------+--------+ cntl | 1 | 6 | 7 | 1.6154 | 5.3846 | | 7.69 | 46.15 | 53.85 | 14.29 | 85.71 | | 33.33 | 60.00 | ---------+--------+--------+ drug | 2 | 4 | 6 | 1.3846 | 4.6154 | | 15.38 | 30.77 | 46.15 | 33.33 | 66.67 | | 66.67 | 40.00 | ---------+--------+--------+ Total 3 10 13 23.08 76.92 100.00 Statistics for Table 8 of trt by response Controlling for clinic=8 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.6603 0.4164 Likelihood Ratio Chi-Square 1 0.6655 0.4146 Continuity Adj. Chi-Square 1 0.0232 0.8789 Mantel-Haenszel Chi-Square 1 0.6095 0.4350 Phi Coefficient -0.2254 Contingency Coefficient 0.2199 Cramer's V -0.2254 WARNING: 75% of the cells have expected counts less than 5. Chi-Square may not be a valid test. When cmh option in PROC FREQ is used for data analysis 12 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Statistics for Table 8 of trt by response Controlling for clinic=8 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 1 Left-sided Pr <= F 0.4371 Right-sided Pr >= F 0.9301 Table Probability (P) 0.3671 Two-sided Pr <= P 0.5594 Sample Size = 13 When cmh option in PROC FREQ is used for data analysis 13 Method suggested by Agresti, Categorical Data book, p. 640 07:52 Thursday, July 24, 2008 The FREQ Procedure Summary Statistics for trt by response Controlling for clinic 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 1.2302 1.0464 1.4463 (Col1 Risk) Logit 1.1455 1.0213 1.2849 Cohort Mantel-Haenszel 0.7020 0.5316 0.9271 (Col2 Risk) Logit ** 0.8200 0.6437 1.0447 ** 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