Documentation Example 1 for PROC NLMIXED
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/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: nlmex1 */
/* TITLE: Documentation Example 1 for PROC NLMIXED */
/* One-Compartment Model with Pharmacokinetic Data */
/* PRODUCT: STAT */
/* SYSTEM: ALL */
/* KEYS: Continuous, normal response */
/* Correlated random effects */
/* PROCS: NLMIXED */
/* DATA: Theophylline data, Pinheiro and Bates (1995) */
/* */
/* SUPPORT: Oliver Schabenberger */
/* REF: */
/* MISC: */
/****************************************************************/
data theoph;
input subject time conc dose wt;
datalines;
1 0.00 0.74 4.02 79.6
1 0.25 2.84 4.02 79.6
1 0.57 6.57 4.02 79.6
1 1.12 10.50 4.02 79.6
1 2.02 9.66 4.02 79.6
1 3.82 8.58 4.02 79.6
1 5.10 8.36 4.02 79.6
1 7.03 7.47 4.02 79.6
1 9.05 6.89 4.02 79.6
1 12.12 5.94 4.02 79.6
1 24.37 3.28 4.02 79.6
2 0.00 0.00 4.40 72.4
2 0.27 1.72 4.40 72.4
2 0.52 7.91 4.40 72.4
2 1.00 8.31 4.40 72.4
2 1.92 8.33 4.40 72.4
2 3.50 6.85 4.40 72.4
2 5.02 6.08 4.40 72.4
2 7.03 5.40 4.40 72.4
2 9.00 4.55 4.40 72.4
2 12.00 3.01 4.40 72.4
2 24.30 0.90 4.40 72.4
3 0.00 0.00 4.53 70.5
3 0.27 4.40 4.53 70.5
3 0.58 6.90 4.53 70.5
3 1.02 8.20 4.53 70.5
3 2.02 7.80 4.53 70.5
3 3.62 7.50 4.53 70.5
3 5.08 6.20 4.53 70.5
3 7.07 5.30 4.53 70.5
3 9.00 4.90 4.53 70.5
3 12.15 3.70 4.53 70.5
3 24.17 1.05 4.53 70.5
4 0.00 0.00 4.40 72.7
4 0.35 1.89 4.40 72.7
4 0.60 4.60 4.40 72.7
4 1.07 8.60 4.40 72.7
4 2.13 8.38 4.40 72.7
4 3.50 7.54 4.40 72.7
4 5.02 6.88 4.40 72.7
4 7.02 5.78 4.40 72.7
4 9.02 5.33 4.40 72.7
4 11.98 4.19 4.40 72.7
4 24.65 1.15 4.40 72.7
5 0.00 0.00 5.86 54.6
5 0.30 2.02 5.86 54.6
5 0.52 5.63 5.86 54.6
5 1.00 11.40 5.86 54.6
5 2.02 9.33 5.86 54.6
5 3.50 8.74 5.86 54.6
5 5.02 7.56 5.86 54.6
5 7.02 7.09 5.86 54.6
5 9.10 5.90 5.86 54.6
5 12.00 4.37 5.86 54.6
5 24.35 1.57 5.86 54.6
6 0.00 0.00 4.00 80.0
6 0.27 1.29 4.00 80.0
6 0.58 3.08 4.00 80.0
6 1.15 6.44 4.00 80.0
6 2.03 6.32 4.00 80.0
6 3.57 5.53 4.00 80.0
6 5.00 4.94 4.00 80.0
6 7.00 4.02 4.00 80.0
6 9.22 3.46 4.00 80.0
6 12.10 2.78 4.00 80.0
6 23.85 0.92 4.00 80.0
7 0.00 0.15 4.95 64.6
7 0.25 0.85 4.95 64.6
7 0.50 2.35 4.95 64.6
7 1.02 5.02 4.95 64.6
7 2.02 6.58 4.95 64.6
7 3.48 7.09 4.95 64.6
7 5.00 6.66 4.95 64.6
7 6.98 5.25 4.95 64.6
7 9.00 4.39 4.95 64.6
7 12.05 3.53 4.95 64.6
7 24.22 1.15 4.95 64.6
8 0.00 0.00 4.53 70.5
8 0.25 3.05 4.53 70.5
8 0.52 3.05 4.53 70.5
8 0.98 7.31 4.53 70.5
8 2.02 7.56 4.53 70.5
8 3.53 6.59 4.53 70.5
8 5.05 5.88 4.53 70.5
8 7.15 4.73 4.53 70.5
8 9.07 4.57 4.53 70.5
8 12.10 3.00 4.53 70.5
8 24.12 1.25 4.53 70.5
9 0.00 0.00 3.10 86.4
9 0.30 7.37 3.10 86.4
9 0.63 9.03 3.10 86.4
9 1.05 7.14 3.10 86.4
9 2.02 6.33 3.10 86.4
9 3.53 5.66 3.10 86.4
9 5.02 5.67 3.10 86.4
9 7.17 4.24 3.10 86.4
9 8.80 4.11 3.10 86.4
9 11.60 3.16 3.10 86.4
9 24.43 1.12 3.10 86.4
10 0.00 0.24 5.50 58.2
10 0.37 2.89 5.50 58.2
10 0.77 5.22 5.50 58.2
10 1.02 6.41 5.50 58.2
10 2.05 7.83 5.50 58.2
10 3.55 10.21 5.50 58.2
10 5.05 9.18 5.50 58.2
10 7.08 8.02 5.50 58.2
10 9.38 7.14 5.50 58.2
10 12.10 5.68 5.50 58.2
10 23.70 2.42 5.50 58.2
11 0.00 0.00 4.92 65.0
11 0.25 4.86 4.92 65.0
11 0.50 7.24 4.92 65.0
11 0.98 8.00 4.92 65.0
11 1.98 6.81 4.92 65.0
11 3.60 5.87 4.92 65.0
11 5.02 5.22 4.92 65.0
11 7.03 4.45 4.92 65.0
11 9.03 3.62 4.92 65.0
11 12.12 2.69 4.92 65.0
11 24.08 0.86 4.92 65.0
12 0.00 0.00 5.30 60.5
12 0.25 1.25 5.30 60.5
12 0.50 3.96 5.30 60.5
12 1.00 7.82 5.30 60.5
12 2.00 9.72 5.30 60.5
12 3.52 9.75 5.30 60.5
12 5.07 8.57 5.30 60.5
12 7.07 6.59 5.30 60.5
12 9.03 6.11 5.30 60.5
12 12.05 4.57 5.30 60.5
12 24.15 1.17 5.30 60.5
;
proc nlmixed data=theoph;
parms beta1=-3.22 beta2=0.47 beta3=-2.45
s2b1 =0.03 cb12 =0 s2b2 =0.4 s2=0.5;
cl = exp(beta1 + b1);
ka = exp(beta2 + b2);
ke = exp(beta3);
pred = dose*ke*ka*(exp(-ke*time)-exp(-ka*time))/cl/(ka-ke);
model conc ~ normal(pred,s2);
random b1 b2 ~ normal([0,0],[s2b1,cb12,s2b2]) subject=subject;
run;
/* Cholesky-root parameterization as in Pinheiro and Bates (1995) */
proc nlmixed data=theoph;
parms ll1=-1.5 l2=0 ll3=-0.1 beta1=-3 beta2=0.5 beta3=-2.5 ls2=-0.7;
s2 = exp(ls2);
l1 = exp(ll1);
l3 = exp(ll3);
s2b1 = l1*l1*s2;
cb12 = l2*l1*s2;
s2b2 = (l2*l2 + l3*l3)*s2;
cl = exp(beta1 + b1);
ka = exp(beta2 + b2);
ke = exp(beta3);
pred = dose*ke*ka*(exp(-ke*time)-exp(-ka*time))/cl/(ka-ke);
model conc ~ normal(pred,s2);
random b1 b2 ~ normal([0,0],[s2b1,cb12,s2b2]) subject=subject;
run;
