Proc nlmixed: No valid parameter points were found

[Solène]

Hi,

I simulated a dataset with 500 profiles of a biomarker measured every 3 weeks during 2 years. My structural model is physiological and so a little complex. It can be compared to a biexponentiel function with a time of rupture D. I have 4 fixed effects, 4 random effects (3 are log-transformed and 1 logit-transformed) and a constant residual error on log(Y+1) to estimate. My code is the following:

proc nlmixed data=dataset;

parms mu_A=0.05 mu_B=80 mu_C=0.3 mu_D=140

      omega_A=0.1 omega_B=0.6 omega_C=1.5 omega_D=0.6

      sigma=0.36;

A=mu_A*exp(eta_A);

B=mu_B*exp(eta_B);

C=mu_C/(mu_C+(1-mu_C)*exp(-eta_C));

D=mu_D*exp(eta_D);

YD=0.23*B/(A*(1-C)-0.046+0.23)*exp((A*(1-C)-0.046)*D)+(B-0.23*B/(A*(1-C)-0.046+0.23))*exp(-0.23*D);

if (TIME<D) then Y= 0.23*B/(A*(1-C)-0.046+0.23)*exp((A*(1-C)-0.046)*TIME)+(B-0.23*B/(A*(1-C)-0.046+0.23))*exp(-0.23*TIME) ;

else Y=0.23*B*exp((A*(1-C)-0.046)*D) /(A-0.046+0.23)*exp((A-0.046)*(TIME-D))+(YD-0.23*B*exp((A*(1-C)-0.046)*D)/(A-0.046+0.23))*exp(-0.23*(TIME-D)) ;

lY=log(Y+1);

model logY ~ normal(lY, sigma**2);

random eta_A eta_B eta_C eta_D ~ normal([0,0,0,0], [omega_A**2,

                                                                                                                             0, omega_B**2,

                                                                                                                             0,          0, omega_C**2,

                                                                                                                             0,          0,          0, omega_D**2])  subject=ID;

run;

I would like to use the adaptative Gauss quadrature or Laplace approximation. This code works for the methods FIRO or for non-adaptative Gauss quadrature (but NOAD needs a lot of QPOINTS and takes a long time). But for the adaptative Gauss quadrature, I have the error message: No valid parameter points were found and the initial negative log-likelihood is 1.15792E77. I don’t understand this error since my dataset is simulated given this model and I initialize parameters with the good values. I tried simpler models, notably with only one or two random effects or with smaller omega. Some work, if omegas are enough small, or if only A and B have random effects.

Is my model too complex for SAS? Is there a problem with the rupture time D? Have I too much variability?

My goal is then to write my own likelihood function and to fit real data, so I could not control their variability.

Thanks in advance

[SteveDenham]

Adaptive quadrature gets problematic with multiple random effects and a structured covariance AND complex entry into the model.  That is why the NOAD works, although slowly.  The variance for C looks like the real source of the blow-up, but I don't see a good re-parameterization from the logistic.  Could you "unstructure" the covariance matrix (this means adding six more parameters to optimize), but constrain them somehow.

Check for typos--I see D shows as YD at least once in the else clause.

Consider rescaling time.  The exponentiating can lead to problems.  Another approach would be to model log(time).

Steve Denham

[bienco88]

What I have tried and it helped is that trying to use "good starting values".

I also have simulation data. My model had one RE. And I used the starting values that were quite close to the "true value" (value used in the simulation) but it produced the error "No valid parameter points were found".

I then:

1. Remove the RE, fit the model with initial values qutie close to the true value.

The model converged well. I got the paramter estimates.

2. I used paramter estimates from step 1 as starting values for model with RE, now the initial value for the variance of RE is the value close to one that I used in simulation step.

The model run, but now with warning of "Hessian matrix is full rank but has at least one negative eigenvalue".

I try to vary the initial value of the variance of the RE and finally I got the results without any warnings.