I have a project where, despite being able to implement some parametric models in LIFEREG, it is somewhat more convenient to do it in NLMIXED. Verifying that this technique works, I tried implementing a pretty bog standard Weibull AFT as follows:
data work.data;
call streaminit(123);
do i = 1 to 1000;
x = rand('BERN', 0.10); *10% exposed;
t1 = rand('Weibull', 1, 20*(exp(-0.500*x)));
t2 = t1;
weight = 1;
output;
end;
run;
PROC NLMIXED data=work.data fd;
parms alpha=1 f0=-1 f1=0;
bounds alpha>0;
*Rate of x;
lam=exp(-(f0*alpha+f1*alpha*x));
*Density of x;
ff1=alpha*lam*t1**(alpha-1)*exp(-lam*t1**alpha);
*log Likelihood;
logl=log(ff1);
*Weighted log Likelihood;
wlogl=logl*weight;
model t1~general(wlogl);
ods exclude iterhistory parameters;
run; quit; run;
proc lifereg data=work.data;
model (t1, t2) = x / D=WEIBULL;
weight weight; run;
This works swimmingly. Both LIFEREG and NLMIXED produce the same estimates, and all is right in the world. Testing it for a Log-Normal AFT model however using the following modifications doesn't work so well:
PROC NLMIXED data=work.data fd;
parms sigma=1 g0=-1 g1=0;
bounds sigma>0;
*Rate of X;
mu=exp(g0+g1*x);
*Density of X;
fg1 = exp(-0.5*((log(t1)-mu)/sigma)**2)/((t1*(2*CONSTANT('PI'))**0.5)*sigma);
*log Likelihood;
logl=log(fg1);
*Weighted log Likelihood;
wlogl=logl*weight;
estimate "RT NDD" exp(g1);
model x~general(wlogl);
ods exclude iterhistory parameters;
run;
proc lifereg data=work.data;
model (t1, t2) = x / D=Lnormal;
weight weight;run;
Here, while both models estimate the scale as the same number (1.2676), the estimates for the intercept (g0) and x (g1) are wildly off. In NLMIXED they are 0.8747 and -0.1419 respectively, while in LIFEREG they are 2.3981 and -0.3172.
Any idea what's going on?
