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# A joint model using PROC NLMIXED

Hello,

I have a problem in fitting the following  joint model for binary and longitudinal outcome using NLMIXED, the concept that I want to predict the probability of developing a medical condition (which is HT in this model ) based on a set of weekly measuremnts of a biomarker (Y). the joint model consists of two parts the first one is a mixed model to summarize the biomarker and a logistic model to obtain the predicted probabilties .

proc nlmixed data=data qpoints=1;
parameters beta0= 2.5 beta1= -0.22
a11= 0.34 a12= -0.01 a22=0.03
alpha0=10 alpha1=10 alpha2=10 s2=0.03;

*the variance covariance matrix;
v11 = a11*a11;
v12 = a11*a12;
v22 = a12*a12 + a22*a22;

*The longitudinal model ;
linplong = (beta0 + u1) + (beta1 + u2)*time;
resid = (y-linplong);

lllong = -0.5*(1.837876 + resid**2 / s2 + log(s2));

*The binary model;
xb=alpha0+alpha1*u1+alpha2*u2;
prob = exp(xb)/(1+exp(xb));
liklhd = (prob**HT)*((1-prob)**(1-HT));
llbin = log(liklhd);

model HT ~ general(lllong + llbin);
random u1 u2 ~ normal([0, 0],[v11,v12,v22]) subject=id;

run;

The above model fails to converge and I get the following error msg

ERROR: No valid parameter points were found

any ideas of what might be wrong in the above code !

The first 5 subjects in the data

id  y  HT time
9 2,1 0 2
9 1,42 0 3
9 1,08 0 4
9 0,95 0 5
9 0,73 0 6
9 0,34 0 7
10 NA 0 2
10 NA 0 3
10 NA 0 4
10 NA 0 5
10 NA 0 6
10 2,15 0 7
11 NA 0 2
11 NA 0 3
11 NA 0 4
11 NA 0 5
11 NA 0 6
11 NA 0 7
12 NA 0 2
12 NA 0 3
12 1,67 0 4
12 1,6 0 5
12 1,51 0 6
12 1,04 0 7
13 NA 0 2
13 NA 0 3
13 NA 0 4
13 0,11 0 5
13 NA 0 6
13 NA 0 7
14 2,56 1 2
14 2,08 1 3
14 1,88 1 4
14 1,79 1 5
14 1,74 1 6
14 NA 1 7
15 NA 1 2
15 NA 1 3
15 NA 1 4
15 2,41 1 5
15 2,43 1 6
15 NA 1 7

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