/****************************************************************/ /* */ /* NAME: NLMLS */ /* TITLE: Joint Modeling of Longitudinal and Survival Data */ /* PRODUCT: STAT */ /* SYSTEM: ALL */ /* KEYS: Longitudinal data, Frailty, Exponential distribution*/ /* KEYS: Joint modeling */ /* PROCS: SORT, MIXED, LIFEREG, NLMIXED */ /* DATA: */ /* */ /* SUPPORT: Oliver Schabenberger UPDATE: */ /* REF: */ /* MISC: Questions, corrections? Send e-mail to */ /* oliver.schabenberger@sas.com */ /****************************************************************/ /*------------------------------------------------------------------- DISCLAIMER: THIS INFORMATION IS PROVIDED BY SAS INSTITUTE INC. AS A SERVICE TO ITS USERS. IT IS PROVIDED "AS IS". THERE ARE NO WARRANTIES, EXPRESSED OR IMPLIED, AS TO MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE REGARDING THE ACCURACY OF THE MATERIALS OR CODE CONTAINED HEREIN. -------------------------------------------------------------------*/ /*-------------------------------------------------------*/ /*---Survival and longitudinal CD4 data ---*/ /* Carlin, B.P. and Louis, T.A. (1996) "Bayes and */ /* Empirical Bayes Methods for Data Analysis", */ /* Boca Raton: Chapman & Hall/CRC Press, Ch. 8.1 */ /* See also */ /* 1. http://www.biostat.umn.edu/~brad/data.html */ /* for data sets */ /* 2. Guo, X. and Carlin, B.P. (2003) "Separate and */ /* Joint Modeling of Longitudinal and Event Time */ /* Data Using Standard Computer Packages" */ /*-------------------------------------------------------*/ data alldata; input t2death death randgrp1 gender1 prevoi1 stratum1 y1-y5; array yy{5} y1-y5; array t{5} (0,2,6,12,18); patient = _n_; do i = 1 to 5; obstime = t{i}; if (yy{i} ne .) then do; cd4 = sqrt(yy{i}); output; end; end; drop i y1-y5 t1-t5; datalines; 16.97 0 0 1 1 -1 114 . 71 89 . 19.00 0 1 1 -1 -1 40 . 66 21 25 18.53 1 1 -1 1 -1 12 13 38 . . 12.70 0 0 1 1 1 15 21 7 3 . 15.13 0 1 1 1 1 53 74 74 45 . 1.90 1 0 -1 1 1 21 . . . . 14.33 0 0 1 1 -1 46 29 20 10 . 9.57 1 1 -1 -1 -1 12 1 0 . . 11.57 1 0 1 1 1 0 33 . . . 16.43 0 1 1 1 -1 147 180 111 56 . 2.40 1 0 1 1 -1 47 . . . . 18.10 0 1 1 -1 -1 185 262 177 91 138 12.23 1 0 1 -1 -1 6 16 6 . . 2.60 1 1 1 -1 -1 4 8 . . . 12.23 0 1 1 1 1 138 97 83 79 . 7.10 1 0 1 1 -1 3 1 26 . . 16.67 0 0 1 -1 -1 43 24 25 25 . 13.70 0 0 1 1 -1 32 29 9 7 . 2.73 1 1 -1 1 -1 9 . . . . 14.40 0 0 1 1 1 363 364 270 279 . 8.07 1 1 1 1 -1 52 29 11 . . 17.40 0 1 1 -1 -1 3 3 2 4 . 12.53 1 1 -1 -1 -1 15 . . . . 20.27 0 0 1 -1 -1 197 255 . 235 206 4.57 1 0 -1 1 1 5 . . . . 20.27 0 1 1 -1 -1 295 394 411 291 185 18.13 0 0 1 -1 -1 17 . 5 2 3 19.57 0 1 1 1 1 285 . . . . 6.13 1 1 1 1 1 21 . . . . 18.87 0 0 -1 -1 -1 33 . 19 . . 16.27 1 0 -1 1 -1 83 112 31 . . 7.17 1 1 1 1 -1 3 . 1 . . 18.57 0 1 1 1 1 60 43 . . 12 18.50 0 0 1 1 -1 1 . 2 . 7 18.40 0 1 1 -1 -1 157 101 51 47 40 7.67 1 0 1 1 -1 0 . 1 . . 14.87 1 0 1 1 -1 15 9 5 . . 17.87 0 1 -1 -1 -1 280 233 . . . 17.70 0 0 1 -1 -1 100 . 61 20 . 17.40 0 1 1 -1 -1 263 204 . . . 17.37 0 0 1 1 -1 22 11 . 2 . 17.37 0 0 -1 -1 -1 69 . . . . 17.23 0 0 1 -1 -1 272 . . . . 8.47 1 1 1 -1 -1 21 29 12 . . 8.43 1 0 1 1 1 3 . . . . 11.07 1 1 1 -1 -1 39 24 7 . . 11.07 1 0 -1 1 1 16 13 . . . 5.90 1 0 1 1 1 1 2 . . . 2.00 1 1 1 -1 -1 1 . . . . 14.40 0 1 -1 -1 -1 190 207 147 16 . 7.57 1 1 1 1 -1 9 20 . . . 5.57 1 0 1 1 -1 2 0 . . . 4.93 1 0 1 1 1 13 . . . . 16.03 0 0 1 1 1 111 187 130 81 . 12.27 0 0 1 1 -1 6 10 23 4 . 15.03 0 0 1 1 1 48 53 13 20 . 12.20 1 1 1 1 -1 11 32 10 . . 12.27 0 1 1 -1 -1 6 3 3 . . 10.57 1 0 1 1 -1 130 27 33 . . 15.70 1 0 1 1 1 8 . 5 1 . 12.30 0 0 1 1 -1 154 177 . . . 14.17 0 0 1 -1 -1 271 250 125 169 . 12.70 0 0 1 1 1 194 307 142 99 . 7.17 1 1 1 1 -1 32 31 6 . . 2.60 1 1 1 1 1 15 . . . . 15.57 1 1 1 1 1 50 . 21 . . 11.13 1 1 1 1 1 17 . 6 . . 14.17 0 1 1 1 1 192 78 33 11 . 0.77 1 0 1 1 1 5 . . . . 14.07 0 1 1 1 -1 46 61 79 . . 6.00 1 0 1 1 -1 4 5 . . . 13.93 0 0 1 -1 -1 226 187 190 187 . 1.30 1 1 1 1 -1 1 . . . . 13.93 0 1 1 1 -1 21 37 4 8 . 12.67 1 1 1 1 1 110 66 58 . . 13.23 0 0 1 -1 -1 19 19 16 10 . 10.33 1 0 1 1 1 14 1 2 . . 12.47 0 1 1 -1 -1 52 137 104 130 . 12.47 0 0 1 -1 -1 21 31 32 8 . 17.93 0 0 1 -1 -1 120 300 220 272 . 3.13 1 1 1 1 -1 5 5 . . . 18.03 0 1 1 1 1 42 34 15 . 7 4.60 1 1 1 1 1 50 50 . . . 15.97 0 0 1 1 -1 64 15 . . . 14.90 0 1 -1 1 -1 15 54 45 25 . 15.60 0 1 1 1 -1 242 390 264 332 . 10.40 1 0 1 1 1 39 2 24 . . 9.77 1 0 1 1 1 8 30 3 . . 18.13 0 0 1 -1 1 4 11 2 21 19 17.93 0 1 1 -1 -1 199 203 286 255 183 18.13 0 0 1 -1 -1 65 51 46 5 37 18.03 0 1 1 1 1 45 48 60 61 42 17.87 0 0 1 -1 -1 291 314 453 382 273 15.57 0 1 1 1 -1 39 30 21 16 . 17.43 0 0 1 -1 -1 115 90 139 141 . 17.67 0 0 1 -1 -1 224 . 363 262 . 15.10 0 1 1 1 1 40 16 . . . 16.30 0 0 1 1 1 40 26 36 . . 13.03 0 0 1 -1 -1 24 . 3 . . 10.30 1 0 1 1 1 21 35 28 . . 15.03 0 1 1 1 1 176 198 98 22 . 5.10 1 1 1 1 1 6 2 . . . 12.90 0 0 1 -1 -1 13 162 . 42 . 11.03 1 0 1 1 1 15 20 20 . . 11.17 1 0 1 1 -1 11 5 . . . 14.07 0 1 1 -1 -1 275 415 284 308 . 18.40 0 1 1 1 1 50 72 36 . . 1.07 1 0 1 1 1 2 . . . . 4.67 1 0 1 1 1 61 . . . . 12.20 0 1 1 1 1 274 265 . . . 17.83 0 1 1 1 1 28 42 16 . . 16.23 0 0 1 -1 -1 41 30 . . . 12.50 0 1 1 1 1 54 . . . . 10.23 1 1 1 1 -1 4 4 2 . . 15.10 1 0 1 1 1 54 21 . . . 12.50 0 0 1 1 1 29 21 . . . 12.93 0 1 1 1 1 100 . 14 29 . 7.97 1 0 1 1 1 10 . . . . 14.33 0 1 1 -1 -1 156 . 39 . . 3.83 1 1 -1 1 -1 0 . . . . 12.50 0 1 1 -1 -1 59 43 61 25 . 12.20 0 0 1 1 -1 6 4 . . . 12.27 0 0 1 1 -1 71 . . 6 . 12.77 0 1 1 1 -1 27 8 13 18 . 16.47 0 0 1 1 -1 15 3 3 4 . 20.23 0 0 1 -1 -1 63 30 22 4 . 15.47 1 1 1 1 -1 25 163 113 59 . 3.20 1 1 1 1 1 14 . . . . 13.50 0 0 1 1 -1 21 15 5 . . 19.20 0 0 1 -1 -1 197 154 135 110 31 12.23 0 1 -1 -1 -1 130 582 . . . 17.80 0 0 1 -1 -1 16 37 10 8 . 16.70 0 0 1 1 1 37 26 0 8 . 13.87 1 1 1 1 -1 10 12 9 . . 16.30 0 0 1 -1 -1 50 40 20 10 . 16.23 0 0 1 -1 -1 109 42 18 . . 20.40 0 1 1 -1 -1 89 19 43 9 6 11.30 1 1 1 -1 -1 52 15 26 . . 18.60 0 0 1 -1 -1 42 23 30 11 15 13.20 1 1 1 1 1 7 . 1 . . 10.93 1 1 1 1 -1 10 0 5 . . 17.17 0 1 1 -1 -1 232 221 166 141 . 16.40 1 0 1 1 1 117 17 . 55 . 16.23 0 1 1 -1 -1 288 268 150 298 . 16.03 0 0 1 -1 -1 168 226 129 144 . 16.03 0 0 1 1 1 169 149 93 45 . 14.63 1 0 1 1 -1 12 16 0 . . 15.27 0 1 1 -1 -1 126 246 153 140 . 14.83 0 1 1 -1 -1 136 112 . 86 . 14.60 0 0 1 -1 -1 1 3 0 0 . 10.23 1 1 1 -1 -1 91 37 . . . 13.83 0 0 1 -1 -1 280 . 319 . . 14.13 0 0 1 -1 -1 160 115 57 69 . 13.13 0 1 1 -1 -1 46 31 8 10 . 13.03 0 1 1 1 -1 5 3 3 7 . 6.63 1 1 1 1 1 0 . . . . 18.37 0 1 1 -1 -1 246 333 . 232 177 16.20 0 1 1 -1 -1 224 . 204 141 . 13.47 0 1 1 -1 -1 240 360 . 310 . 13.20 0 0 -1 1 -1 198 172 . 286 . 18.17 0 0 1 1 1 66 89 81 18 . 15.57 0 1 1 1 1 40 15 34 5 . 5.43 1 1 1 1 1 10 30 . . . 10.30 1 1 1 1 1 30 . . . . 18.37 0 0 1 -1 -1 120 160 120 130 80 17.80 1 0 1 1 1 50 . 20 10 . 17.80 0 1 1 -1 -1 47 110 63 20 . 16.63 1 0 1 1 1 20 10 20 . . 17.37 0 0 1 1 -1 30 40 95 50 . 15.90 0 0 1 -1 -1 80 50 60 10 . 17.33 0 0 1 1 1 30 4 40 10 . 9.37 1 1 1 1 1 76 110 . . . 16.97 0 0 1 -1 -1 250 . 210 220 . 17.10 0 0 1 -1 -1 30 40 40 320 . 9.37 1 0 1 1 1 100 40 . . . 15.80 0 0 1 1 1 140 105 . 89 . 15.50 0 0 1 1 1 20 20 10 20 . 15.10 0 0 1 -1 -1 270 290 220 240 . 11.93 1 1 1 1 -1 40 20 30 . . 14.63 0 0 1 -1 -1 190 90 130 80 . 3.13 1 1 1 1 1 40 . . . . 14.57 0 1 1 -1 -1 40 80 20 20 . 14.33 0 0 1 1 -1 70 40 30 0 . 13.93 0 1 1 -1 -1 180 260 160 180 . 13.37 0 1 1 1 1 0 . 60 70 . 13.23 0 0 1 -1 -1 190 280 130 200 . 12.97 0 0 1 -1 -1 270 370 360 350 . 14.87 0 1 1 1 -1 7 4 6 287 . 1.83 0 1 1 1 -1 370 . . . . 13.73 0 0 1 1 -1 24 3 11 7 . 16.93 0 1 -1 1 -1 144 237 242 119 . 16.17 0 1 1 1 1 13 27 . 19 . 12.27 0 1 1 -1 -1 104 174 194 . . 12.53 0 0 1 1 1 25 0 9 23 . 12.77 0 1 1 -1 -1 110 250 170 80 . 1.70 1 1 1 1 -1 20 . . . . 2.17 0 0 1 -1 -1 130 . . . . 12.30 0 1 1 -1 -1 160 230 300 200 . 12.23 0 1 1 -1 -1 190 300 150 240 . 12.23 0 0 1 1 -1 20 10 0 4 . 7.03 1 1 1 1 1 5 0 . . . 3.30 1 0 -1 1 1 59 . . . . 11.60 1 1 -1 1 1 5 14 5 . . 12.20 0 1 -1 1 -1 28 . 46 . . 4.33 1 1 1 1 1 6 5 . . . 17.57 0 0 1 -1 -1 107 126 72 14 . 4.53 1 1 1 1 1 23 . . . . 13.73 0 0 1 1 1 4 5 4 9 . 18.80 0 1 1 1 1 32 39 46 30 34 18.57 0 1 1 -1 -1 143 154 264 176 . 2.47 1 0 1 1 1 14 8 . . . 12.43 0 0 1 -1 -1 273 383 263 369 . 12.30 1 1 1 1 1 72 20 9 . . 11.90 1 0 1 1 -1 77 19 . . . 13.37 0 1 1 -1 -1 95 234 216 98 . 17.67 0 0 1 1 1 94 53 29 5 . 9.93 1 1 1 1 -1 165 . 35 . . 12.27 1 1 1 1 -1 6 18 . . . 18.33 0 0 1 1 -1 281 207 160 71 62 17.67 0 0 1 1 -1 17 10 . . . 11.20 1 1 1 1 -1 7 15 11 . . 18.13 0 1 1 -1 -1 109 92 85 . 68 18.57 0 0 1 -1 -1 222 136 . 179 . 17.93 0 1 1 -1 -1 6 10 8 5 11 16.23 0 0 1 -1 -1 10 8 3 . . 17.20 0 1 -1 1 -1 21 17 8 . . 11.47 1 1 1 1 -1 10 . . . . 10.70 1 0 1 1 1 0 21 . . . 2.17 1 0 1 1 -1 13 . . . . 2.70 1 0 1 1 -1 14 . . . . 12.67 0 1 1 1 -1 9 . 10 30 . 12.70 0 1 1 1 -1 11 7 14 16 . 17.03 1 0 1 1 1 53 27 . . . 14.70 1 0 1 -1 -1 131 129 122 66 . 13.30 1 1 1 1 1 3 7 . . . 13.87 0 1 1 -1 -1 216 249 14 139 . 10.87 1 1 1 1 1 8 7 . . . 16.73 0 1 1 1 -1 37 30 21 16 . 13.20 0 0 1 -1 -1 200 . 203 209 . 13.90 0 0 1 -1 -1 32 57 13 7 . 15.37 0 0 1 -1 -1 67 40 32 54 . 15.97 0 0 1 -1 -1 235 . 134 53 . 7.93 1 0 1 1 -1 43 55 . . . 16.00 0 1 1 1 -1 35 19 11 . . 15.60 0 1 1 -1 -1 228 235 29 294 . 14.63 0 1 1 -1 -1 109 124 88 . . 14.43 1 1 1 1 1 11 . . . . 14.10 0 0 1 -1 -1 82 . . . . 14.07 0 0 1 1 1 112 9 5 . . 12.47 0 1 -1 -1 -1 181 110 . . . 12.67 0 0 1 1 1 76 18 11 7 . 12.33 0 0 1 1 1 152 168 144 68 . 12.20 0 0 1 1 1 7 8 5 2 . 16.17 0 0 1 -1 -1 230 253 17 170 . 15.53 0 0 -1 1 1 2 3 2 4 . 14.40 0 0 1 1 1 1 2 1 1 . 12.70 0 0 1 1 -1 9 22 8 11 . 19.27 0 0 -1 -1 -1 281 300 368 202 130 4.53 1 1 -1 1 -1 5 . . . . 20.67 0 0 1 1 -1 12 35 34 14 14 3.37 1 0 1 1 -1 277 84 . . . 12.23 0 1 1 1 1 4 3 1 1 . 19.27 0 0 -1 1 1 2 2 2 2 . 14.20 0 1 1 -1 -1 254 284 291 204 . 12.23 0 0 1 1 -1 51 75 78 . . 9.80 1 1 1 1 1 6 2 1 . . 14.20 0 1 1 1 -1 19 27 34 12 . 12.73 0 0 -1 1 -1 16 10 3 4 . 12.73 0 1 1 -1 -1 2 6 1 1 . 12.63 1 1 1 1 -1 8 12 4 . . 10.03 1 0 1 1 1 17 4 7 . . 13.27 0 1 1 -1 -1 11 8 . 5 . 19.77 0 1 1 -1 -1 41 52 30 1 . 19.53 0 1 1 1 1 54 39 23 14 19 18.37 0 1 1 1 1 16 . 10 2 4 15.93 0 1 1 -1 -1 70 35 49 26 . 5.03 1 1 1 1 1 10 . . . . 20.27 0 0 1 -1 -1 10 10 4 . . 12.93 0 1 1 1 1 8 9 6 9 . 11.00 1 0 1 1 -1 12 . 6 . . 19.57 0 0 1 1 1 10 8 3 7 . 8.13 1 1 1 1 -1 17 3 1 . . 21.40 0 1 1 1 1 15 5 1 1 . 21.13 0 1 1 1 1 31 26 27 12 . 21.13 0 1 1 1 -1 40 9 . . . 5.53 1 1 1 1 -1 44 30 . . . 3.57 1 0 1 1 1 40 6 . . . 2.57 1 1 1 1 1 12 . . . . 12.27 0 1 1 1 1 80 35 47 3 . 19.57 0 1 1 -1 -1 99 200 152 191 . 13.90 0 0 1 1 1 8 . . 5 . 1.43 1 0 -1 1 -1 3 . . . . 12.20 0 0 1 1 -1 34 34 36 13 . 15.97 0 1 1 -1 -1 60 33 37 14 . 17.83 0 0 1 1 -1 38 17 12 55 . 12.37 1 0 1 1 1 31 22 10 . . 8.80 1 0 1 1 1 34 13 9 . . 16.20 0 1 1 1 1 11 11 3 . . 9.57 1 1 1 1 1 77 51 37 . . 10.63 1 1 1 1 -1 9 21 . . . 13.87 0 1 1 -1 -1 122 112 77 72 . 13.43 0 0 1 -1 -1 273 129 163 154 . 13.03 0 0 1 1 1 81 52 26 . . 12.33 0 1 1 1 1 10 7 14 10 . 12.30 0 0 -1 1 1 4 . 6 . . 12.07 1 0 1 1 1 35 . 11 4 . 12.33 0 0 1 -1 -1 65 58 22 15 . 9.60 1 0 1 1 1 7 4 6 . . 15.97 0 0 1 -1 -1 180 238 171 65 . 11.30 1 0 1 1 1 4 8 3 . . 20.87 0 0 1 -1 -1 93 142 . 15 . 13.90 1 0 -1 -1 -1 297 122 89 40 . 18.97 0 0 1 -1 -1 300 330 290 270 340 4.97 1 0 1 1 -1 13 10 . . . 18.17 0 1 1 1 1 8 15 17 12 8 18.07 1 0 1 1 1 3 3 8 6 3 15.93 0 1 1 1 1 7 9 2 . . 18.37 0 1 1 1 1 273 152 65 38 21 15.97 0 1 1 1 -1 137 121 146 138 . 17.70 0 0 1 -1 -1 42 . . . . 3.63 1 1 1 1 1 8 . . . . 3.97 1 0 1 -1 -1 62 . . . . 17.37 0 1 1 1 -1 3 4 3 4 . 10.07 1 0 1 1 1 13 7 3 . . 17.00 0 0 1 1 1 37 17 20 1 . 11.67 1 0 1 1 1 6 3 1 . . 17.20 0 1 1 -1 -1 128 . 24 15 . 6.13 1 1 1 -1 -1 64 28 . . . 2.03 1 1 1 1 1 2 . . . . 16.47 0 1 1 -1 -1 125 147 203 113 . 16.23 0 0 1 1 1 18 30 22 . . 16.03 0 0 1 -1 -1 21 . 8 7 . 15.77 0 0 1 1 -1 47 56 . . . 7.40 1 1 1 1 -1 5 5 4 . . 10.80 1 0 1 1 1 11 12 8 . . 12.57 0 0 -1 -1 -1 184 138 37 . . 1.13 1 1 -1 1 1 12 . . . . 13.20 0 0 1 1 1 7 10 9 4 . 13.47 0 1 -1 -1 -1 40 29 28 20 . 13.90 0 0 -1 1 -1 100 145 88 45 . 13.93 0 1 -1 -1 -1 113 116 173 126 . 14.60 0 1 1 1 -1 74 56 29 27 . 14.43 0 0 -1 -1 -1 161 176 . 30 . 1.07 1 0 1 1 -1 5 . . . . 7.17 1 0 1 1 -1 31 24 31 . . 15.33 0 1 1 1 1 233 269 182 71 . 15.57 0 1 1 1 -1 63 71 16 16 . 12.23 0 1 1 1 1 247 289 219 . . 11.50 1 1 1 1 1 10 20 . . . 12.23 0 0 1 -1 -1 291 367 323 267 . 12.27 0 0 -1 -1 -1 30 41 22 16 . 12.23 0 0 1 1 -1 5 . . . . 12.53 0 1 1 1 -1 108 475 284 151 . 6.30 1 1 1 -1 -1 13 15 . . . 0.47 1 1 -1 -1 -1 341 . . . . 4.10 1 1 1 1 1 6 6 . . . 12.23 0 0 1 1 1 7 12 9 0 . 8.17 1 1 1 1 -1 23 54 . . . 20.50 0 1 1 1 1 27 33 18 5 12 19.80 0 1 1 1 -1 52 48 84 63 20 6.90 1 1 1 1 1 0 . 15 . . 3.43 1 0 1 1 1 0 . . . . 7.97 1 0 1 1 -1 4 10 0 . . 15.33 1 1 1 1 -1 14 . . 0 . 5.37 1 0 1 -1 -1 48 143 . . . 13.90 0 0 1 -1 -1 49 77 . 90 . 3.20 1 0 1 1 -1 5 2 . . . 17.83 0 1 1 -1 -1 63 110 55 26 . 19.93 0 0 1 1 1 6 0 . 5 . 18.63 1 0 1 1 1 8 0 . . . 8.47 1 0 1 1 1 10 . 7 . . 16.87 0 0 1 -1 -1 237 306 286 276 . 11.93 1 1 1 -1 -1 66 70 . . . 18.77 0 0 1 1 1 155 104 . 184 . 7.83 1 1 1 -1 -1 281 . . . . 1.63 1 1 1 1 1 0 . . . . 13.50 0 0 -1 -1 -1 201 238 240 418 . 6.07 1 1 1 1 1 6 0 . . . 8.30 1 1 1 1 -1 20 12 12 . . 19.80 0 0 1 1 -1 27 20 11 . . 13.60 1 0 1 1 -1 110 57 41 . . 17.23 0 0 1 1 1 37 40 . . . 16.50 0 0 1 -1 -1 3 5 1 . . 13.40 0 1 -1 -1 -1 176 207 383 161 . 17.63 0 0 1 1 1 217 90 97 9 . 8.33 1 0 1 1 1 84 39 . . . 10.70 1 0 1 1 -1 22 14 6 . . 12.53 0 0 1 1 1 8 29 16 7 . 9.67 1 1 1 -1 -1 80 51 . . . 12.20 0 0 1 1 1 224 194 125 . . 18.17 0 1 1 1 -1 13 19 . 3 2 7.70 1 0 1 -1 -1 96 53 . . . 8.73 1 0 1 1 1 10 17 9 . . 2.13 1 1 1 1 -1 30 . . . . 13.00 0 0 1 1 -1 57 55 . 11 . 11.63 1 1 1 1 1 2 3 11 . . 3.00 1 0 1 1 -1 19 . . . . 12.70 0 1 1 1 -1 39 14 16 . . 16.93 0 1 1 -1 -1 288 323 357 369 . 9.63 1 0 1 1 1 15 11 3 . . 15.07 1 1 1 1 -1 43 13 . . . 9.93 1 1 1 1 1 14 14 10 . . 16.50 0 1 1 -1 -1 125 . . . . 16.97 0 1 1 1 1 7 7 3 11 . 14.40 0 1 1 1 -1 14 9 10 7 . 6.60 1 1 1 1 1 2 8 . . . 12.53 0 0 1 1 -1 11 7 8 0 . 5.23 1 0 1 1 -1 5 7 . . . 13.00 0 1 1 1 1 46 47 35 25 . 3.40 1 0 -1 1 -1 3 2 . . . 16.03 0 0 1 -1 -1 132 90 60 23 . 12.20 1 1 1 1 1 84 57 54 . . 6.87 1 1 1 1 1 26 . . . . 15.03 0 1 1 -1 -1 239 200 89 51 . 1.03 1 0 1 1 -1 4 . . . . 14.10 0 0 1 1 -1 29 23 35 . . 10.60 1 1 1 -1 -1 21 113 5 . . 4.20 1 1 1 -1 -1 166 . . . . 13.60 0 1 1 -1 -1 273 87 359 285 . 13.00 0 0 1 1 -1 181 . . . . 13.50 0 1 1 1 -1 2 4 2 0 . 13.20 0 0 1 1 1 28 43 28 28 . 13.20 0 0 1 1 -1 70 60 66 49 . 9.73 1 1 1 -1 -1 76 105 40 . . 13.60 0 0 1 -1 -1 78 . . . . 20.63 0 1 1 -1 -1 75 132 . . . 1.43 1 0 1 1 1 36 . . . . 12.43 0 0 1 1 -1 12 6 16 13 . 8.00 1 0 -1 1 1 40 . 28 . . 12.47 0 0 1 1 -1 16 50 17 5 . 2.47 1 0 1 1 1 5 . . . . 9.07 1 1 1 1 1 3 12 . . . 14.13 1 1 1 1 1 56 45 9 8 . 15.17 1 0 1 1 -1 66 78 50 32 . 17.70 0 0 1 -1 -1 65 96 60 91 . 16.63 1 1 1 -1 -1 272 240 234 98 . 14.30 0 0 1 1 1 60 24 90 76 . 12.43 0 1 -1 -1 -1 105 272 375 150 . 7.30 1 1 1 1 -1 36 32 42 . . 5.57 1 0 1 1 1 24 4 . . . 17.20 0 0 1 1 1 300 270 143 160 . 7.73 1 0 1 -1 -1 20 18 10 . . 19.80 0 0 1 -1 -1 13 14 6 7 7 16.47 0 1 1 1 -1 42 20 30 18 . 13.50 0 0 1 1 -1 27 42 6 6 . 11.50 1 1 1 1 1 7 9 21 . . 12.47 1 1 1 -1 -1 70 63 30 . . 5.07 1 1 1 1 -1 159 73 . . . 12.70 1 1 1 1 1 14 16 5 . . 19.03 0 1 1 1 1 138 140 154 120 126 7.93 0 1 1 1 -1 169 144 84 . . 19.07 1 0 1 1 1 40 36 . 10 . 0.90 1 1 -1 1 1 40 . . . . 19.70 0 1 1 -1 -1 24 15 5 5 3 13.10 1 0 1 -1 -1 21 12 24 102 . 20.87 0 0 1 -1 -1 6 24 . . . 17.27 1 0 1 1 1 10 20 14 3 . 13.37 0 1 1 1 -1 190 136 . . . 9.33 1 1 1 -1 -1 220 400 240 . . 12.30 0 1 1 1 1 247 300 220 242 . 10.23 1 1 1 1 1 9 30 10 . . 3.30 1 1 1 1 1 3 21 . . . 14.33 0 1 1 -1 -1 7 10 6 7 . 2.00 1 0 1 1 -1 24 . . . . 13.30 1 1 1 1 1 10 6 12 . . 15.07 0 0 -1 1 -1 9 10 . . . 3.90 1 0 1 1 1 30 5 . . . ; proc sort data=alldata; by patient obstime; data alldata; set alldata; by patient; last = last.patient; run; title1 'The first 100 observations of the joint data'; proc print data=alldata(obs=100) noobs; var patient cd4 t2death obstime randgrp1 gender1 prevoi1 stratum1 last; run; /*-------------------------------------------------------*/ /*---Fit the longitudinal part with PROC MIXED ---*/ /*---The FA0(2) structure will yield parameter estimates */ /* identical to the Cholesky root of an unstructured */ /* variance-covariance matrix. This is the parameteri- */ /* zation chosen below in NLMIXED. */ /* For comparison with NLMIXED below we choose ML esti- */ /* mation. The MIXED default would be REML. */ /*-------------------------------------------------------*/ title1 'Longitudinal Model - MIXED'; proc mixed data=alldata noclprint covtest method=ml; class patient; model cd4 = obstime obstime*randgrp1 gender1 prevoi1 stratum1 / s; random intercept obstime / subject=patient type=fa0(2); ods output covparms=cp; ods output solutionf=solf; run; /*-------------------------------------------------------*/ /*---Fit the survival part of the model ---*/ /*-------------------------------------------------------*/ title2 'Survival Model - LIFEREG'; proc lifereg data=alldata(where=(last=1)); model t2death*death(0)=randgrp1 gender1 prevoi1 stratum1 /dist=exponential; ods output ParameterEstimates=survpe(rename=(Parameter=SurvEffect)); run; /*-------------------------------------------------------*/ /* Combine the estimates from the separate models */ /* You can use this data set for comparison with the */ /* estimates in the joint model and to provide */ /* starting values in the joint model */ /*-------------------------------------------------------*/ data SeparateEstimates; set solf cp survpe; length Parameter $5; select ; when ( Effect = 'Intercept' ) Parameter = 'bl0' ; when ( Effect = 'obstime' ) Parameter = 'bl1' ; when ( Effect = 'obstime*randgrp1' ) Parameter = 'bl2' ; when ( Effect = 'gender1' ) Parameter = 'bl3' ; when ( Effect = 'prevoi1' ) Parameter = 'bl4' ; when ( Effect = 'stratum1' ) Parameter = 'bl5' ; when ( CovParm = 'FA(1,1)' ) Parameter = 'a11' ; when ( CovParm = 'FA(2,1)' ) Parameter = 'a12' ; when ( CovParm = 'FA(2,2)' ) Parameter = 'a22' ; when ( CovParm = 'Residual' ) Parameter = 's2' ; when ( SurvEffect= 'Intercept' ) Parameter = 'bs0' ; when ( SurvEffect= 'randgrp1' ) Parameter = 'bs1' ; when ( SurvEffect= 'gender1' ) Parameter = 'bs2' ; when ( SurvEffect= 'prevoi1' ) Parameter = 'bs3' ; when ( SurvEffect= 'stratum1' ) Parameter = 'bs4' ; otherwise Parameter = ''; end; if Parameter ne ''; keep Parameter Estimate StdErr; rename Estimate=SeparateEstimate StdErr=SeparateStdErr; run; /*-------------------------------------------------------*/ /*---Model XI in Carlin and Guo ---*/ /* Fit by maximum likelihood with NLMIXED. */ /* Marginal log likelihood is computed by Gaussian */ /* quadrature. */ /*-------------------------------------------------------*/ title1 'Joint Model - NLMIXED'; proc nlmixed data=alldata; /*---All parameters not assigned starting values ---*/ /*---explicitly are assigned the default value (1)---*/ parameters r1=0.13; /*---Compute log likelihood contribution of the ---*/ /*---survival data part when the last observaion---*/ /*---of a subject is reached ---*/ /*---NOTE: This parameterization yields estimates ---*/ /*--- equivalent to those in LIFEREG ---*/ if (last) then do; linpsurv = bs0 + bs1*randgrp1 + bs2*gender1 + bs3*prevoi1 + bs4*stratum1 + r1*u0 + r2*u1; alpha = exp(-linpsurv); G_t = exp(-alpha*t2death); g = alpha*G_t; llsurv = (death=1)*log(g) + (death=0)*log(G_t); end; else llsurv=0; /*---Cholesky parameterization of the random effects ---*/ /*---variance matrix. ---*/ /*---This ensures that the variance-covariance matrix---*/ /*---of the random effects is non-negative definite ---*/ v11 = a11*a11; v12 = a11*a12; v22 = a12*a12 + a22*a22; /*---Compute the contribution of the longitudinal---*/ /*---part. Every observation in the data set ---*/ /*---makes a contribution. Notice that conditional--*/ /*---on the random effects we have independent ---*/ /*---Gaussian contributions ---*/ linplong = (bl0 + u0) + (bl1 + u1)*obstime + bl2*obstime*randgrp1 + bl3*gender1 + bl4*prevoi1 + bl5*stratum1; resid = (cd4-linplong); if (abs(resid) > 1.3E100) or (s2 < 1e-12) then do; lllong = -1e20; end; else do; lllong = -0.5*(1.837876 + resid**2 / s2 + log(s2)); end; /*---Any numeric variable in the data set can be used---*/ /*---as the response in the MODEL statement. It has ---*/ /*---no bearing on the results ---*/ model last ~ general(lllong + llsurv); random u0 u1 ~ normal([0, 0],[v11,v12,v22]) subject=patient; /*---Compute median of the patient-specific ---*/ /*---survival distributions ---*/ predict (1/alpha)* log(2) out=median; /*---Compute the variances and covariance of the random---*/ /*---effects and obtain their std. errors by the delta ---*/ /*---method ---*/ estimate 'Var[U0]' v11; estimate 'Cov[U0,U1]' v12; estimate 'Var[U1]' v22; ods output ParameterEstimates=JointEstimates; run; /*-------------------------------------------------------*/ /*---Compare estimates in joint and separate models ---*/ /*-------------------------------------------------------*/ proc sort data=SeparateEstimates; by Parameter; proc sort data=JointEstimates; by Parameter; data Estimates; merge SeparateEstimates JointEstimates; by Parameter; run; title1 'Estimates and Standard Errors from Separate and Joint Analysis'; proc print data=Estimates label; label SeparateEstimate = 'MLE in separate models' SeparateStdErr = 'Asymptotic Std. Error of MLE in separate models' Estimate = 'MLE in joint model' StandardError = 'Asymptotic Std. Error of MLE in joint model'; var SeparateEstimate SeparateStdErr Estimate StandardError; id Parameter; run; /*-------------------------------------------------------*/ /*---Extract predicted patient-specific median ---*/ /*-------------------------------------------------------*/ title1 'Patient Specific Modes and Medians for Patients 450 and 454'; title2 'With Standard Errors and Confidence Intervals'; proc print data=median(where=( ((patient=450) or (patient=454)) and (last=1))); var patient pred stderrpred lower upper; run; title1;