Programming the statistical procedures from SAS

Biased estimation in PROC NLMIXED

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Biased estimation in PROC NLMIXED

Hello everyone,

I am doing simulation to compare a couple of methods. I simulate survival data from the one-level parametric frailty model with Weibull baseline hazard, normally distributed clusters. I generate 500 of these datasets at the same time in the dataset "Survival_MultiLevel". Each of these 500 datasets is recognizable by "sample_id". Clusters are, also, determined by "cluster_id". I have two covariates as well.

Since I used to get errors when using the codes posted on SAS website to model parameteric frailty models in NLMIXED, I wrote the loglikelihood in this way. These initial values also help no to get over-flow values. "qpoints = 30" also helps to get more precise estimated. I used to qpoints = 5, qpoints = 10 and ... and I used to get worst estimates. In a word, many "NOTE"s and "ERROR"s led me to use the following codes. These codes work perfectly and I get very appealing results for estimation of b1 and b2. However, estimations of logsig, rho and b0 are very biased.

  ods output on;

proc nlmixed data=Survival_MultiLevel qpoints = 30 noad;

  by sample_id;

  bounds rho > 0 ;

  parms rho = 2 b1 = 0 b2 = 0 logsig = .5 b0 = 0;

  eta = b0 + b1 * covariate1 + b2 * covariate2 + W;

  lambda = exp(eta);

  log_S_t = -lambda * (survival_t ** rho);

  log_h = (censor_flag&j = 1) * (eta + log(rho) + (rho - 1) * log(survival_t));

  ll = log_h + log_S_t;

  model survival_t ~ general(ll);

  random W ~ normal(0, exp(2 * logsig)) subject = cluster_id ;

  ods select off;

  ods output ParameterEstimates = data&j;

  run;

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