Robert H. Leary, Michael R. Dunlavey, and Jason Chittenden
Pharsight Corporation
Objectives: In the most usual form of NLME bootstrapping for parameter uncertainty estimation, each replicate data set is constructed by pooling Nsub (=total number of subjects) random selections of individual data sets with equal probability 1/Nsub on each individual. In effect, the bootstrap replicates are the concatenation of Nsub samples from a mixture distribution of individual data sets with equal probabilities on each such set. An intriguing analogy occurs in the optimal NLME estimation solution via EM methods – the fixed effects parameters in the optimal solution are the means, and the random effect parameters the variance/covariances, of the mixture distribution of posteriors with equal probabilities 1/Nsub. This suggests a very fast method for bootstrapping – rather than construct a large number of bootstrap data sets and solve the estimation problem separately for each one, simply solve the base case problem with each individual represented exactly once, and then bootstrap the resulting posteriors. All that is required is to save the means and variance/covariance matrices of each posterior from the base case, and then perform a rather small amount of very fast linear algebra to get parameter estimates for each bootstrap replicate.
Methods: The posterior EM bootstrap methodology was implemented within the Pharsight Phoenix NLME parametric QRPEM method for 1000 simulated data sets from a simple IV bolus model. For each data set, fixed and random effect parameter values were computed for 10000 bootstrap replicates in less than 3 seconds total time using the EM posterior method. Coverage analyses were performed for the posterior estimates relative to the known true values used to simulate the data to evaluate the quality of confidence limits.
Results: Coverage was remarkably accurate for essentially all confidence probability levels for fixed effects estimates, somewhat less so for random effect estimates.
Conclusions: EM posterior bootstrapping appears a viable methodology for computing confidence limits and standard errors, particularly for fixed effects.
Reference: PAGE 22 (2013) Abstr 2797 [www.page-meeting.org/?abstract=2797]
Poster: Estimation methods