The file 'rats.dat' contains the rat data described in Section 6 of the paper. The data set has 4 columns: 1 : defines the treatment groups ('con' = control, 'hig' = high dose, 'low' = low dose) 2 : identification number of the rat 3 : age of the rat (in days) at which a specific measurement was taken 4 : the response of interest (in pixels) The linear mixed model (9) in Section 6 of the paper, with random intercepts and slopes, can be fitted in SAS, using the following program : /* Input of the data */ data rats; infile 'a:\rats.dat'; /* specify path ! */ input treat $ rat age y; run; /* Logarithmic transformation of the time-axis */ data rats; set rats; t = log(1+(age-45)/10); run; /* Fitting the linear mixed model */ proc mixed data = test method=ml; class treat rat; model y = treat*t / solution; random intercept t / type=un subject=rat; run; con 3 50 75.00666637 con 3 60 78.568441502 con 3 70 79.924964811 con 3 80 80.777472107 con 5 50 67.955868032 con 6 50 76.006578663 con 6 60 78.294316524 con 6 70 81.215762017 con 9 50 70.830784268 con 9 60 74.953318806 con 9 70 75.166481892 con 9 80 77.665951356 con 9 90 82.734515167 con 11 50 71.847059787 con 11 60 75.133215025 con 11 70 76.216796049 con 20 50 72.835430939 con 20 60 78.568441502 con 20 70 80.603970126 con 20 80 82.073138115 con 22 50 70.72481884 con 22 60 74.813100457 con 22 70 75.166481892 con 22 80 77.006493233 con 22 90 81.024687596 con 22 100 78.492037813 con 22 110 81.841309862 con 23 50 74.51845409 con 24 50 73.4982993 con 24 60 75.591004756 con 24 70 77.935871074 con 24 80 79.195959493 con 24 90 81.024687596 con 24 100 82.462112512 con 24 110 86.284413424 con 25 50 69.641941386 con 25 60 74.094534211 con 25 70 78.390050389 con 26 50 74.027022093 con 26 60 77.524189773 con 26 70 81.83520025 con 26 80 81.633326528 con 43 50 70.292247083 con 43 60 76.026311235 con 43 70 77.833154889 con 43 80 79.511005528 con 43 90 80.280757346 con 44 50 70.802542327 con 44 60 75.286120899 con 44 70 78.390050389 con 44 80 80.919713297 con 44 90 79.605276207 con 44 100 80.622577483 con 44 110 82.661962232 con 47 50 66.843099868 con 47 60 73 con 47 70 74.652528423 con 47 80 77.466121627 con 47 90 77.103826105 con 48 50 70.604532432 con 48 60 74.953318806 con 48 70 78.409183136 con 48 80 78.600254453 con 48 90 80.721744282 con 48 100 82.800966178 con 48 110 83.006023878 hig 1 50 69.339743293 hig 1 60 73.246160309 hig 1 70 77.388629656 hig 1 80 78.102496759 hig 1 90 76.485292704 hig 1 100 77.801028271 hig 1 110 79.056941504 hig 7 50 70.802542327 hig 7 60 75 hig 7 70 76.843997814 hig 7 80 81.024687596 hig 7 90 80.603970126 hig 7 100 82.800966178 hig 7 110 83.815273071 hig 12 50 74.276510419 hig 12 60 77.781745931 hig 12 70 79.906195004 hig 12 80 84.646323015 hig 14 50 71.119617547 hig 14 60 74.404300951 hig 14 70 75.451971479 hig 49 50 69.462219947 hig 49 60 74.686009399 hig 49 70 75.742986474 hig 49 80 78.243210568 hig 49 90 77.155686764 hig 49 100 77.466121627 hig 49 110 80.280757346 hig 50 50 73.246160309 hig 50 60 74.652528423 hig 50 70 76.843997814 hig 50 80 80.280757346 hig 50 90 80.603970126 hig 50 100 82.377181306 hig 50 110 83.408632647 hig 51 50 68.883960397 hig 51 60 72.917761897 hig 51 70 76.059187479 hig 51 80 79.202272695 hig 52 50 71.421285343 hig 52 60 76.843997814 hig 52 70 77.665951356 hig 52 80 81.83520025 hig 52 90 81.4002457 hig 52 100 83.408632647 hig 52 110 84.72307832 hig 53 50 70.455659815 hig 53 60 72.124891681 hig 53 70 75.451971479 hig 53 80 78.600254453 hig 53 90 77.336925204 hig 53 100 79.881161734 hig 53 110 80.802227692 hig 54 50 67.601775125 hig 54 60 70.661163308 hig 54 70 74.202425836 hig 56 50 69.310893805 hig 56 60 73.925638313 hig 56 70 75.471849056 hig 56 80 77.781745931 hig 57 50 72.201108025 hig 57 60 76.006578663 hig 57 70 77.07788269 hig 57 80 80.156097709 hig 57 90 81.39410298 hig 57 100 83.486525859 hig 57 110 82.661962232 hig 59 50 70.837842994 hig 60 50 70.213958726 hig 60 60 75.432088663 hig 60 70 77.420927403 hig 60 80 79.056941504 hig 60 90 77.233412459 hig 60 100 81.024687596 hig 60 110 83.528438271 hig 62 50 71.700767081 hig 62 60 74.813100457 hig 63 50 68.476273263 hig 63 60 75.471849056 hig 63 70 76.40026178 hig 63 80 78.230428862 hig 63 90 78.549347547 hig 63 100 80.280757346 hig 63 110 81.39410298 hig 64 50 70.802542327 hig 64 60 73.409808609 hig 64 70 75.604232686 hig 64 80 78.644770964 hig 64 90 79.025312401 hig 64 100 80.603970126 hig 64 110 81.884064384 low 8 50 71.700767081 low 8 60 78.816241981 low 10 50 71.281133549 low 10 60 78.492037813 low 10 70 82.492423895 low 10 80 82.377181306 low 10 90 84.811555816 low 10 100 84.291162052 low 10 110 83.862983491 low 13 50 66.603303221 low 13 60 70.604532432 low 13 70 72.069410987 low 13 80 73.878278269 low 13 90 75.822160349 low 13 100 78.243210568 low 13 110 79.649231007 low 16 50 72.718635851 low 16 60 81.565924258 low 16 70 82.134036794 low 16 80 83.006023878 low 16 90 83.737685662 low 16 100 84.899941107 low 16 110 86.833173384 low 17 50 73.246160309 low 17 60 80.956778592 low 17 70 78.409183136 low 17 80 81.271151093 low 17 90 83.408632647 low 27 50 70.455659815 low 27 60 78.409183136 low 27 70 79.404030124 low 27 80 80.802227692 low 27 90 82.661962232 low 27 100 82.8794305 low 27 110 85.702975444 low 28 50 70.178344238 low 30 50 72.249567473 low 30 60 75.432088663 low 31 50 70.830784268 low 31 60 75.802374633 low 31 70 80 low 31 80 81.633326528 low 31 90 82.006097334 low 31 100 80.808415403 low 31 110 82.680106434 low 32 50 70.178344238 low 32 60 72.470683728 low 32 70 75.822160349 low 32 80 76.609398901 low 33 50 69.115844783 low 33 60 74.330343737 low 33 70 76.850504227 low 33 80 77.006493233 low 33 90 78.51751397 low 33 100 81.688432474 low 34 50 73.006848994 low 34 60 77.524189773 low 34 70 77.201036262 low 34 80 82.800966178 low 34 90 81.320354156 low 34 100 83.408632647 low 35 50 75.073297516 low 35 60 78.0320447 low 35 70 80.156097709 low 35 80 83.006023878 low 35 90 82.219219164 low 35 100 84.053554357 low 35 110 84.876380696 low 37 50 69.77105417 low 37 60 74.404300951 low 37 70 76.609398901 low 37 80 77.388629656 low 37 90 82.419657849 low 37 100 80.280757346 low 37 110 82.661962232 low 38 50 71.561162651 low 38 60 78.006409993 low 38 70 81.6884325 low 38 80 79.32212806 low 39 50 74.027022093 low 39 60 75.471849056 low 39 70 79.511005528 low 39 80 80.448741444 low 40 50 70.3449445 low 40 60 76.843997814 low 40 70 76.694197955 low 40 80 81.024687596 low 40 90 81.344944526 low 41 50 73.246160309 low 41 60 78.236819976 low 41 70 79.649231007 low 41 80 80.212218521 low 41 90 84.811555816 low 41 100 82.328609851 low 41 110 85.211501571