************************************************************************* * This is a program that illustrates the use of PROC GLM in SAS to * * perform ANCOVA. * * * * The data set is taken from the following article: * * Carithers RL, et al (1989). Methylprednisolone therapy in * * with severe alcoholic hepatitis. Annals of Internal Medicine 110, * * 685-690. * *************************************************************************; proc format; value trtfmt 0='Placebo' 1='Methylprednisolone'; run; data alc_hep; input subject center treatment albumin0-albumin4 prothrombin0-prothrombin4 bilirubin0-bilirubin4 hematocrit0-hematocrit4 sgot0-sgot4; format treatment trtfmt.; cards; 1 1 0 2.4 2.4 1.7 . . 20 18 23 . . 14.3 17.4 17.9 . . 24 23 20 . . 74 99 75 . . 2 1 0 3.8 3.4 3.2 3.1 3.0 16 16 19 19 18 16.1 11.9 12.6 10.4 9.8 34 32 32 31 34 95 68 58 55 65 3 1 0 2.9 2.6 3.3 3.5 3.4 15 13 14 14 14 19.2 11.6 7.5 5.0 3.2 34 30 34 33 33 94 87 142 82 54 4 1 0 2.0 2.1 2.2 2.4 . 22 20 23 17 18 19.4 13.7 8.1 6.1 4.9 30 33 34 36 30 131 115 76 60 59 5 1 0 2.6 2.8 2.7 2.6 2.6 20 20 19 18 18 8.5 8.3 4.9 4.0 4.0 35 30 28 33 35 52 . 49 40 33 6 1 0 1.9 1.9 2.6 2.3 2.4 19 19 17 17 15 9.3 6.4 6.9 6.8 3.0 27 26 33 30 29 49 69 88 101 86 7 1 0 1.9 1.9 2.0 2.1 . 23 22 23 18 . 4.4 3.3 3.7 3.0 . 29 31 31 31 . 39 43 48 45 . 8 1 0 2.4 2.1 . . . 16 16 . . . 24.0 19.1 . . . 24 23 . . . 159 400 . . . 9 1 0 2.2 2.1 2.0 1.9 1.9 18 19 20 22 21 12.3 11.7 10.8 9.8 6.4 27 26 27 27 26 179 156 130 111 94 10 1 0 2.1 . . . . 18 . . . . 28.3 . . . . 30 . . . . 89 . . . . 11 1 0 2.6 2.1 2.4 2.5 2.2 18 16 15 15 15 16.0 10.1 7.8 6.9 5.6 30 24 34 31 28 67 47 . 67 58 12 1 0 2.2 1.9 2.1 2.1 2.4 16 16 16 15 15 25.4 16.9 9.3 5.6 4.2 21 28 32 26 29 55 75 73 59 43 13 1 0 2.6 2.5 1.3 1.8 2.3 18 17 16 16 18 20.2 19.3 14.4 14.3 10.5 22 28 29 26 24 43 53 50 46 34 14 1 0 1.8 3.0 . . . 25 24 31 . . 14.0 15.1 11.4 . . 22 29 15 . . 88 47 . . . 15 1 1 1.9 2.4 2.9 3.0 . 19 15 14 14 . 8.7 2.6 2.3 1.9 . 33 36 41 42 . 135 74 66 48 . 16 1 1 2.0 2.6 3.0 3.6 3.1 18 15 15 15 11 15.6 9.0 5.1 4.4 2.9 30 28 29 33 30 115 68 59 70 63 17 1 1 2.1 2.3 2.8 2.8 2.9 17 16 15 16 16 11.0 8.2 8.4 9.4 8.1 27 21 22 21 25 31 62 56 57 45 18 1 1 2.2 2.0 1.7 1.5 1.4 21 36 34 24 24 16.0 17.8 13.4 10.4 14.2 30 31 29 26 23 170 206 108 76 47 19 1 1 2.1 2.4 2.8 2.6 2.9 16 14 14 14 12 21.7 12.9 7.0 4.1 2.8 23 27 30 34 35 346 414 345 144 104 20 1 1 3.3 . 3.4 3.2 3.0 18 16 15 13 14 35.0 25.6 16.7 10.2 5.4 35 28 27 32 27 48 73 66 45 49 21 1 1 2.5 2.6 2.8 2.8 . 17 14 14 13 . 12.1 6.4 6.0 5.0 . 31 31 34 35 . 399 192 176 219 . 22 1 1 2.6 2.3 2.9 2.8 3.1 17 16 14 14 14 7.9 3.3 3.1 3.3 3.2 33 30 40 39 43 240 74 79 103 89 23 1 1 3.2 2.4 2.1 1.8 1.9 19 19 18 19 24 6.3 10.0 13.4 11.4 17.1 26 20 22 21 34 125 95 288 198 178 24 1 1 3.0 3.5 3.3 3.5 3.9 20 19 17 17 18 4.1 26.6 12.1 10.7 8.4 14 29 30 36 37 47 54 33 44 34 25 1 1 1.7 . . . . 15 . . . . 7.4 . . . . 27 . . . . 144 . . . . 26 1 1 2.7 2.6 . . . 17 21 20 . . 24.3 31.4 20.9 . . 25 28 24 . . 145 285 . . . 27 1 1 2.1 2.3 2.4 2.4 2.6 20 16 14 14 13 13.0 10.5 6.9 5.9 5.8 31 24 27 25 22 224 95 71 65 53 28 1 1 2.1 . 2.6 3.4 3.8 15 13 13 12 12 15.7 4.7 3.1 2.8 2.4 31 28 31 39 . 67 78 . 52 39 29 1 1 1.8 1.7 2.3 1.9 1.7 24 22 21 20 21 14.6 11.7 17.1 14.9 10.9 39 34 29 30 24 28 29 34 20 43 30 2 0 2.5 2.3 2.3 2.2 2.1 18 20 22 23 17 11.7 12.7 16.0 16.1 15.1 26 29 27 26 25 157 104 132 115 90 31 2 0 1.8 1.9 1.6 2.6 2.8 24 26 28 23 19 12.6 9.4 8.2 9.9 11.3 28 28 24 30 27 462 500 430 291 140 32 2 0 2.3 2.0 . . . 19 22 . . . 14.7 13.0 . . . 23 26 . . . 136 183 . . . 33 2 0 2.2 2.6 2.5 2.3 2.4 16 16 16 15 15 21.6 15.4 11.7 4.3 3.7 23 27 29 27 28 120 140 162 123 95 34 2 0 2.5 2.4 2.2 . . 17 18 17 . . 13.8 10.2 9.3 . . 30 29 27 . . 87 102 69 . . 35 2 0 2.9 2.6 2.8 3.0 3.7 17 15 14 15 14 22.1 8.7 8.3 6.6 5.5 38 37 39 40 41 131 134 114 117 103 36 2 0 2.0 1.7 . . . 13 13 . . . 9.1 9.9 . . . 25 24 . . . 95 47 . . . 37 2 0 2.7 2.2 3.2 2.9 3.5 15 16 16 15 17 28.2 25.2 35.4 40.8 60.5 38 35 28 25 24 153 117 107 129 87 38 2 0 2.1 1.8 1.6 1.7 . 21 25 25 23 . 12.2 15.9 13.6 19.9 . 23 21 22 24 . 98 127 27 139 . 39 2 1 1.6 1.8 2.2 2.5 2.6 24 20 17 17 16 12.3 7.5 6.6 5.7 4.4 27 27 31 32 27 55 79 107 91 73 40 2 1 2.8 3.2 3.4 3.7 . 19 16 . 16 . 14.5 8.5 4.7 3.8 3.6 30 38 32 36 . 74 137 121 131 149 41 2 1 1.8 2.5 3.3 3.5 3.5 20 16 13 14 14 9.2 5.7 2.8 2.5 1.8 27 29 31 32 32 55 54 37 35 28 42 2 1 2.2 2.6 2.6 2.5 2.6 19 17 16 17 17 13.0 7.0 4.6 4.3 3.6 35 39 37 37 37 100 101 58 105 45 43 2 1 2.7 3.1 3.3 3.1 3.2 17 11 12 12 . 13.4 9.3 4.9 3.7 2.0 30 33 33 33 34 480 167 212 162 69 44 2 1 2.8 2.1 2.3 2.8 2.9 20 15 15 14 14 17.8 24.2 16.8 16.6 10.0 30 24 29 28 26 242 131 89 198 130 45 2 1 2.8 2.3 2.3 2.7 2.3 18 15 15 15 16 17.4 20.0 18.1 16.4 11.7 27 30 28 29 26 181 107 82 87 54 46 3 0 3.2 . . 2.9 2.7 18 17 19 18 16 17.8 17.6 8.5 7.9 6.7 20 26 23 30 30 140 104 122 268 190 47 3 0 2.3 2.6 . . . 20 19 21 . . 15.5 17.3 13.9 . . 25 31 29 . . 29 30 40 . . 48 3 0 2.4 . 2.8 2.4 2.7 14 15 14 14 14 20.0 15.5 18.3 14.1 17.5 41 28 25 27 30 133 159 78 66 80 49 3 1 2.8 2.8 7.9 3.0 3.5 15 15 13 12 12 11.1 10.6 6.7 3.9 2.6 33 33 37 39 39 58 45 47 35 30 50 3 1 2.3 2.6 2.2 2.6 2.6 17 16 18 17 18 44.1 42.6 38.0 36.6 33.0 28 30 27 27 29 77 78 72 61 57 51 3 1 3.3 2.8 2.5 3.3 2.6 19 12 12 11 12 5.4 1.8 1.2 1.2 1.0 33 39 45 49 48 415 46 72 43 34 52 3 1 2.2 2.2 . . . 17 20 . . . 30.3 26.4 . . . 30 29 . . . 100 85 . . . 53 4 0 3.1 . . . . 15 14 14 14 13 23.1 15.0 6.9 4.9 3.6 38 33 33 36 42 115 180 170 136 . 54 4 0 3.0 2.7 2.8 . . 17 15 15 16 . 38.7 40.0 32.2 35.5 29.5 31 28 24 34 29 385 175 163 305 460 55 4 0 2.2 2.5 2.9 2.5 2.5 18 18 18 17 . 9.4 6.8 6.0 4.6 4.1 21 24 26 27 . 162 135 56 51 68 56 4 0 2.8 2.4 2.6 2.5 . 14 15 15 14 . 29.2 29.1 33.5 30.2 . 28 28 30 31 . 86 95 122 128 . 57 4 0 2.5 2.7 3.2 3.8 3.1 20 16 17 . . 24.0 22.0 25.0 22.5 13.0 36 37 42 42 35 163 310 575 850 465 58 4 1 2.2 . 3.3 3.6 3.6 20 16 14 14 14 7.2 3.5 2.5 2.3 2.5 40 41 45 47 47 141 72 77 66 66 59 4 1 2.1 . 3.2 2.4 2.8 20 18 16 15 16 28.1 16.5 15.6 7.9 6.9 27 35 25 24 33 232 150 85 121 325 60 4 1 2.4 2.1 2.4 2.6 . 16 17 17 15 13 13.2 6.7 7.3 5.0 4.5 35 35 34 35 . 145 67 44 87 72 61 4 1 3.0 2.6 2.6 3.2 3.3 17 14 14 14 13 33.5 34.0 9.9 6.6 4.4 21 29 26 24 25 213 113 188 127 112 62 4 1 2.4 2.8 3.0 . . 17 16 16 . . 17.8 10.7 7.7 . . 24 27 29 . . 73 66 169 . . 63 4 1 2.2 2.6 . . . 16 13 . . . 22.5 13.5 . . . 26 27 . . . 120 192 . . . 64 4 1 2.1 2.3 2.2 3.1 3.4 22 20 18 18 18 19.0 12.9 8.7 11.5 11.0 25 27 27 28 30 89 70 47 38 48 65 4 1 2.2 2.2 2.4 . . 17 16 15 . . 18.0 12.3 11.1 . . 33 34 33 . . 188 101 102 . . 66 4 1 2.7 2.5 3.4 3.0 3.1 18 16 14 15 . 27.0 12.3 9.2 5.2 3.7 36 35 37 34 . 166 128 107 25 16 ; run; proc print data=alc_hep; id subject center treatment; var bilirubin0-bilirubin4; title 'Alcoholic Hepatitis Data Set'; run; proc gplot data=alc_hep; plot bilirubin4*bilirubin0=treatment/vaxis=axis1 haxis=axis2 nolegend frame; axis1 label=(a=90 'Visit 4 Bilirubin'); axis2 label=('Visit 0 Bilirubin'); symbol1 value=x color=black; symbol2 value=o color=black; title2 'Scatterplot of Visit 4 vs. Visit 0 Measurements'; run; proc gplot data=alc_hep; plot bilirubin4*center=treatment/vaxis=axis1 haxis=axis2 nolegend frame; axis1 label=(a=90 'Visit 4 Bilirubin'); axis2 offset=(20) label=('Clinical Center') minor=none major=(number=4); symbol1 value=x color=black; symbol2 value=o color=black; title2 'Scatterplot of Visit 4 Measurements vs. Clinical Center'; run; proc glm data=alc_hep; class center treatment; model bilirubin4=center treatment bilirubin0 treatment*center treatment*bilirubin0; title2 'ANCOVA for determining interactions'; run; proc glm data=alc_hep; class center treatment; model bilirubin4=center treatment bilirubin0; means treatment; lsmeans treatment/stderr pdiff; title2 'ANCOVA'; run;