RE: $OMEGA blocks and log-likelihood profiling

From: Nick Holford Subject: RE:[NMusers] $OMEGA blocks and log-likelihood profiling Date: Sat, June 5, 2004 4:52 am Mats, thank you for re-emphasising my earlier assertion. So everyone can make their own judgement of the similarity of the bootstrap average and stdev obtained with all runs, minimization successful runs and covariance step successful runs here are the parameters of a 2 compartment model (BSV* are sqrt(OMEGA), CVAG and SDAG are sqrt(SIGMA), R12 and R34 are correlations of random effects of CL and V and V2 and Q) plus some covariate parameters. Param avg-all avg-sxs avg-cov sd-all sd-sxs sd-cov CL 4.70 4.68 4.64 0.12 0.13 0.11 Vss 30.8 31.1 30.6 1.75 1.68 1.68 CLNR 1.12 1.12 1.11 0.24 0.25 0.30 CLR 3.56 3.56 3.53 0.23 0.24 0.27 V1 19.52 19.53 19.53 0.26 0.25 0.22 Q 1.02 1.01 1.00 0.11 0.10 0.09 V2 11.28 11.29 11.03 1.52 1.52 1.66 BSVCL 0.30 0.29 0.29 0.017 0.016 0.019 BSVV1 0.24 0.24 0.24 0.014 0.014 0.013 BSVQ 0.82 0.82 0.84 0.081 0.076 0.076 BSVV2 1.17 1.20 1.17 0.22 0.21 0.21 CVAG 0.16 0.16 0.16 0.006 0.006 0.005 SDAG 0.14 0.14 0.15 0.025 0.024 0.020 R12 0.55 0.55 0.55 0.059 0.064 0.058 R34 0.90 0.91 0.90 0.085 0.082 0.052 KAGECR 111.9 111.8 112.4 5.88 6.39 7.63 FSEXCR 0.82 0.82 0.82 0.033 0.032 0.027 KAGERF 119.0 119.1 118.4 8.05 7.95 7.25 FCPRLO 0.70 0.70 0.71 0.030 0.031 0.031 I don't contend that NONMEM's asymptotic standard errors are useless. But failure of the $COV step is not a reliable sign that the parameters are not trustworthy (see above). Equally I believe that success of the $COV step implies little more than good (numerical) luck. The SE estimates of the $COV step are a cheap and quick way of understanding something about estimation uncertainty but when they disagree with the bootstrap values I prefer the bootstrap. Nick -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/