Gamma Frailty Model with Random effects

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Gamma Frailty Model with Random effects

Hi,

I have a particular issue with the exact coding for a gamma frailty model with random effects. I used proc lifereg for the initial parameter values and then entered them into proc nlmixed. I have interval censored data. So my time measured variable is broken into two variables, lower and upper to signify the censoring - the common procedure used in proc lifereg for interval censoring. The issue comes when trying to set up the log likelihood code into proc nlmixed. So far, the code looks like this:

DATA=A;

PARMS gamma 0.55 b0 1.42 b1 -0.74;

*Assigns parameters in the model optionally with initial values.

The estimates from the model without the random frailty effect*

BOUNDS gamma > 0; *The shape parameter for Weibull distribution*

linp = b0 + b1*(MC_group) +z ; *The linear predictor*

alpha = exp(linp);

S_low = exp(-(alpha*time_low)**gamma);

*Conditional survivor function at the lower limit of the

interval;

S_up = exp(-(alpha*time_up)**gamma);

*Conditional survivor function at the upper limit of the

interval;

ll =

MODEL time_low ~ GENERAL(ll);

RANDOM z ~ normal(0,exp(2*logsig)) subject=id out=EB;

*The random effect is normally distributed*

ESTIMATE 'exp(beta)' exp(b1); *Estimating exp(beta);

run;

The bold faced portion is where my code starts to fail. I don't know how to setup that portion of the code.

Regards,

Mike

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