I'm looking for help using SAS to fit a Weibull survival model with longitudinal covariate. I modified code I found in SAS documentation: SAS/STAT 9.22 User's Guide Example 61.5 Failure Time and Frailty Model. The objective of the modeling is to determine if the longitudinal covariate is important for explaining variability in survival times, i.e., when the longitudinal covariate goes up more, is there a higher probability of death? However, the code I found in the documentation did not have a longitudinal covariate.
In my code below I attempted to include a longitudinal covariate called longcovar and X1-X3 are other covariates that are constant over time. Aval is the time variable. Although the model is quadratic in the longitudinal covariate shown below, I also looked at quadratic.
proc nlmixed data=final;
parms b0=0 b1=0 b2=0 b3=0 b4=0 b5=0 gamma=1;
bounds gamma > 0.2;
linp = b0 + b1*longcovar + b2* longcovar * longcovar + b3*X1 + b4*X2 + b5*X ;
alpha = exp(-linp);
eps = 1e-8;
if aval > 0 then do;
G_t = exp(-(alpha*aval)**gamma);
g = gamma*alpha*((alpha*aval)**(gamma-1))*G_t;
ll = (CNSR_deatheq0=0)*log(g + eps)
+ (CNSR_deatheq0=1)*log(G_t + eps);
end;
else ll = .;
model aval ~ general(ll);
run;
Question 1: should the time variable (aval) be the time of the observations of longcovar or should it be the time interval value between longcovar observations?
After I used the above code, I added a random effect for subject. Each subject has their own set of covariate values. The change in the code is as follows (but with an overly simple covariance matrix and not showing how the starting values could be updated from the linear model results):
proc nlmixed data=final;
parms b0=0 b1=0 b2=0 b3=0 b4=0 b5=0 gamma=1 logsig=.1;
bounds gamma > 0.2;
linp = b0 + b1*longcovar + b2* longcovar * longcovar + b3*X1 + b4*X2 + b5*X + z;
alpha = exp(-linp);
eps = 1e-8;
if aval > 0 then do;
G_t = exp(-(alpha*aval)**gamma);
g = gamma*alpha*((alpha*aval)**(gamma-1))*G_t;
ll = (CNSR_deatheq0=0)*log(g + eps)
+ (CNSR_deatheq0=1)*log(G_t + eps);
end;
else ll = .;
model aval ~ general(ll);
random z ~ normal(0,exp(2*logsig)) subject=ID;
run;
Question 2: Is the nlmixed code correct for the model specified, i.e., for a Weibull survival model with longitudinal covariate?
Question 3: The algorithm converged for the fixed effects models. I believe the difficulty I had with the random models (nonconvergence and wild parameter values) is due to each subject having different covariate values, i.e., including the random effect z resulted in over-parameterization. Does this seem like a reasonable explanation?
Question 4: The longitudinal covariate was only available for subjects who were censored. If subjects had died, then the measurement could not be taken. We used LOCF as what we believe is a conservative value for the longitudinal covariate knowing that there will be bias, more so for those with larger intervals between the last observation and death. How unreasonable is this (other than as a measure of reasonableness being the size of the time interval)?
