The SAS System 20:00 Monday, March 20, 2006 1 The FREQ Procedure Table of treatment by response treatment response Frequency| Expected | Percent | Row Pct | Col Pct |cold |nocold | Total ---------+--------+--------+ absorbic | 17 | 122 | 139 | 23.914 | 115.09 | | 6.09 | 43.73 | 49.82 | 12.23 | 87.77 | | 35.42 | 52.81 | ---------+--------+--------+ placebo | 31 | 109 | 140 | 24.086 | 115.91 | | 11.11 | 39.07 | 50.18 | 22.14 | 77.86 | | 64.58 | 47.19 | ---------+--------+--------+ Total 48 231 279 17.20 82.80 100.00 Statistics for Table of treatment by response Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 4.8114 0.0283 Likelihood Ratio Chi-Square 1 4.8717 0.0273 Continuity Adj. Chi-Square 1 4.1407 0.0419 Mantel-Haenszel Chi-Square 1 4.7942 0.0286 Phi Coefficient -0.1313 Contingency Coefficient 0.1302 Cramer's V -0.1313 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 17 Left-sided Pr <= F 0.0205 Right-sided Pr >= F 0.9910 Table Probability (P) 0.0115 Two-sided Pr <= P 0.0385 The SAS System 20:00 Monday, March 20, 2006 2 The FREQ Procedure Statistics for Table of treatment by response Column 1 Risk Estimates (Asymptotic) 95% (Exact) 95% Risk ASE Confidence Limits Confidence Limits ----------------------------------------------------------------------------- Row 1 0.1223 0.0278 0.0678 0.1768 0.0729 0.1886 Row 2 0.2214 0.0351 0.1527 0.2902 0.1557 0.2993 Total 0.1720 0.0226 0.1278 0.2163 0.1297 0.2215 Difference -0.0991 0.0448 -0.1869 -0.0114 Difference is (Row 1 - Row 2) Column 2 Risk Estimates (Asymptotic) 95% (Exact) 95% Risk ASE Confidence Limits Confidence Limits ----------------------------------------------------------------------------- Row 1 0.8777 0.0278 0.8232 0.9322 0.8114 0.9271 Row 2 0.7786 0.0351 0.7098 0.8473 0.7007 0.8443 Total 0.8280 0.0226 0.7837 0.8722 0.7785 0.8703 Difference 0.0991 0.0448 0.0114 0.1869 Difference is (Row 1 - Row 2) Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits ----------------------------------------------------------------- Case-Control (Odds Ratio) 0.4900 0.2569 0.9343 Cohort (Col1 Risk) 0.5523 0.3209 0.9506 Cohort (Col2 Risk) 1.1273 1.0120 1.2558 Odds Ratio (Case-Control Study) ----------------------------------- Odds Ratio 0.4900 Asymptotic Conf Limits 95% Lower Conf Limit 0.2569 95% Upper Conf Limit 0.9343 Exact Conf Limits 95% Lower Conf Limit 0.2407 95% Upper Conf Limit 0.9740 Sample Size = 279 The SAS System 20:00 Monday, March 20, 2006 3 The GENMOD Procedure Model Information Data Set WORK.SKI Distribution Poisson Link Function Log Dependent Variable count Observations Used 4 Class Level Information Class Levels Values treatment 2 placebo absorbic response 2 cold nocold Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 1 4.8717 4.8717 Scaled Deviance 1 4.8717 4.8717 Pearson Chi-Square 1 4.8114 4.8114 Scaled Pearson X2 1 4.8114 4.8114 Log Likelihood 970.6299 Algorithm converged. Analysis Of Parameter Estimates Standard Likelihood Ratio 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 4.7457 0.0891 4.5663 4.9158 2836.81 <.0001 treatment placebo 1 0.0072 0.1197 -0.2277 0.2422 0.00 0.9523 treatment absorbic 0 0.0000 0.0000 0.0000 0.0000 . . response cold 1 -1.5712 0.1586 -1.8934 -1.2702 98.11 <.0001 response nocold 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. LR Statistics For Type 3 Analysis Chi- Source DF Square Pr > ChiSq treatment 1 0.00 0.9523 response 1 130.59 <.0001 The SAS System 20:00 Monday, March 20, 2006 4 The GENMOD Procedure Observation Statistics Observation count treatment response Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 31 placebo cold 24.086031 3.1816321 0.1561792 24.086031 17.734757 32.711861 6.9139686 1.4087852 1.3483626 2.0994112 2.1934897 2.1551805 2 109 placebo nocold 115.91398 4.7528483 0.0888123 115.91398 97.395437 137.95359 -6.913978 -0.642185 -0.648733 -2.215859 -2.193493 -2.195419 3 17 absorbic cold 23.913989 3.1744636 0.1563437 23.913989 17.602407 32.488674 -6.913989 -1.413848 -1.491801 -2.314435 -2.193496 -2.244533 4 122 absorbic nocold 115.08602 4.7456799 0.0891012 115.08602 96.645029 137.04577 6.913978 0.6444908 0.638194 2.172062 2.1934927 2.1916509 The SAS System 20:00 Monday, March 20, 2006 5 The CATMOD Procedure Data Summary Response treatment*response Response Levels 4 Weight Variable count Populations 1 Data Set SKI Total Frequency 279 Frequency Missing 0 Observations 4 Population Profiles Sample Sample Size --------------------- 1 279 Response Profiles Response treatment response --------------------------------- 1 placebo cold 2 placebo nocold 3 absorbic cold 4 absorbic nocold _Response_ Matrix 1 2 --------------------- 1 1 1 2 1 -1 3 -1 1 4 -1 -1 Maximum Likelihood Analysis Sub -2 Log Convergence Parameter Estimates Iteration Iteration Likelihood Criterion 1 2 ----------------------------------------------------------------------------- 0 0 773.55225 1.0000 0 0 1 0 645.78381 0.1652 0.003584 -0.6559 2 0 642.97126 0.004355 0.003584 -0.7760 3 0 642.95644 0.0000231 0.003584 -0.7855 4 0 642.95644 8.991E-10 0.003584 -0.7856 Maximum likelihood computations converged. The SAS System 20:00 Monday, March 20, 2006 6 The CATMOD Procedure Maximum Likelihood Analysis of Variance Source DF Chi-Square Pr > ChiSq -------------------------------------------------- treatment 1 0.00 0.9523 response 1 98.12 <.0001 Likelihood Ratio 1 4.87 0.0273 Analysis of Maximum Likelihood Estimates Standard Chi- Parameter Estimate Error Square Pr > ChiSq ------------------------------------------------------------------ treatment placebo 0.00358 0.0599 0.00 0.9523 response cold -0.7856 0.0793 98.12 <.0001 The SAS System 20:00 Monday, March 20, 2006 7 The CATMOD Procedure Data Summary Response treatment*response Response Levels 4 Weight Variable count Populations 1 Data Set SKI Total Frequency 279 Frequency Missing 0 Observations 4 Population Profiles Sample Sample Size --------------------- 1 279 Response Profiles Response treatment response --------------------------------- 1 placebo cold 2 placebo nocold 3 absorbic cold 4 absorbic nocold _Response_ Matrix 1 2 3 ------------------------------ 1 1 1 1 2 1 -1 -1 3 -1 1 -1 4 -1 -1 1 Maximum Likelihood Analysis Sub -2 Log Convergence Parameter Estimates Iteration Iteration Likelihood Criterion 1 2 3 ------------------------------------------------------------------------------------------ 0 0 773.55225 1.0000 0 0 0 1 0 643.05576 0.1687 0.003584 -0.6559 0.0968 2 0 638.20563 0.007542 0.1014 -0.7859 0.1558 3 0 638.0849 0.000189 0.1212 -0.8063 0.1776 4 0 638.08474 2.4268E-7 0.1220 -0.8070 0.1784 5 0 638.08474 4.52E-13 0.1220 -0.8070 0.1784 Maximum likelihood computations converged. The SAS System 20:00 Monday, March 20, 2006 8 The CATMOD Procedure Maximum Likelihood Analysis of Variance Source DF Chi-Square Pr > ChiSq ---------------------------------------------------- treatment 1 2.20 0.1383 response 1 96.09 <.0001 treatment*response 1 4.69 0.0303 Likelihood Ratio 0 . . Analysis of Maximum Likelihood Estimates Standard Chi- Parameter Estimate Error Square Pr > ChiSq -------------------------------------------------------------------------------- treatment placebo 0.1220 0.0823 2.20 0.1383 response cold -0.8070 0.0823 96.09 <.0001 treatment*response placebo cold 0.1784 0.0823 4.69 0.0303 The SAS System 20:00 Monday, March 20, 2006 9 The GENMOD Procedure Model Information Data Set WORK.SKI Distribution Poisson Link Function Log Dependent Variable count Observations Used 4 Class Level Information Class Levels Values treatment 2 placebo absorbic response 2 cold nocold Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 0 0.0000 . Scaled Deviance 0 0.0000 . Pearson Chi-Square 0 0.0000 . Scaled Pearson X2 0 0.0000 . Log Likelihood 973.0657 Algorithm converged. Analysis Of Parameter Estimates Standard Likelihood Ratio 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 4.8040 0.0905 4.6212 4.9764 2815.59 <.0001 treatment*response placebo cold 1 -1.3700 0.2011 -1.7811 -0.9899 46.40 <.0001 treatment*response placebo nocold 1 -0.1127 0.1318 -0.3720 0.1454 0.73 0.3926 treatment*response absorbic cold 1 -1.9708 0.2589 -2.5141 -1.4928 57.95 <.0001 treatment*response absorbic nocold 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. LR Statistics For Type 3 Analysis Chi- Source DF Square Pr > ChiSq treatment*response 3 135.47 <.0001 The SAS System 20:00 Monday, March 20, 2006 10 The GENMOD Procedure Observation Statistics Observation count treatment response Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 31 placebo cold 31 3.4339872 0.1796053 31 21.801249 44.080042 0 0 0 0 0 0 2 109 placebo nocold 109 4.6913479 0.0957826 109 90.343347 131.50941 2.842E-14 2.722E-15 0 . . . 3 17 absorbic cold 17 2.8332133 0.2425356 17 10.568229 27.346114 0 0 0 . . . 4 122 absorbic nocold 122 4.804021 0.0905357 122 102.16348 145.68807 8.527E-14 7.72E-15 0 . . . The SAS System 20:00 Monday, March 20, 2006 11 The GENMOD Procedure Model Information Data Set WORK.SKI Distribution Poisson Link Function Log Dependent Variable count Observations Used 4 Class Level Information Class Levels Values treatment 2 placebo absorbic response 2 cold nocold Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 0 0.0000 . Scaled Deviance 0 0.0000 . Pearson Chi-Square 0 0.0000 . Scaled Pearson X2 0 0.0000 . Log Likelihood 973.0657 Algorithm converged. Analysis Of Parameter Estimates Standard Likelihood Ratio 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 4.8040 0.0905 4.6212 4.9764 2815.59 <.0001 treatment placebo 1 -0.1127 0.1318 -0.3720 0.1454 0.73 0.3926 treatment absorbic 0 0.0000 0.0000 0.0000 0.0000 . . response cold 1 -1.9708 0.2589 -2.5141 -1.4928 57.95 <.0001 response nocold 0 0.0000 0.0000 0.0000 0.0000 . . treatment*response placebo cold 1 0.7134 0.3293 0.0790 1.3770 4.69 0.0303 treatment*response placebo nocold 0 0.0000 0.0000 0.0000 0.0000 . . treatment*response absorbic cold 0 0.0000 0.0000 0.0000 0.0000 . . treatment*response absorbic nocold 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. The SAS System 20:00 Monday, March 20, 2006 12 The GENMOD Procedure LR Statistics For Type 3 Analysis Chi- Source DF Square Pr > ChiSq treatment 1 2.26 0.1329 response 1 132.85 <.0001 treatment*response 1 4.87 0.0273 Observation Statistics Observation count treatment response Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 31 placebo cold 31 3.4339872 0.1796053 31 21.801249 44.080042 -2.84E-14 -5.1E-15 -1.317E-9 . . . 2 109 placebo nocold 109 4.6913479 0.0957826 109 90.343347 131.50941 -7.11E-14 -6.81E-15 -3.358E-9 . . . 3 17 absorbic cold 17 2.8332133 0.2425356 17 10.568229 27.346114 -3.2E-14 -7.75E-15 0 . . . 4 122 absorbic nocold 122 4.804021 0.0905357 122 102.16348 145.68807 -2.84E-14 -2.57E-15 -4.368E-9 -0.371463 -2.188E-7 -2.188E-7