RE: Confidence intervals of PsN bootstrap output

Hello all, Sorry to enter the conversation late. (I deleted prior posts to keep from exceeding the length limit). I certainly agree with that nonparametric bootstrap procedures need consideration and interpretation of output. I feel that such procedures lead to difficulty (as described by many of the previous emails) when the design is unbalanced (especially when severely so) and only a few individuals supply data which supports estimation of a covariate or structural parameter. For example, it might be in a sparse PK setting that only a few subjects had samples in the absorption phase. Sampling with replacement might lead some datasets with fewer subjects with absorption data than in the original dataset. This might lead to erratic behavior (for example Ka going to large unlikely value) during estimation and hence a multimodal distribution of the estimates. An example of this for parametric simulation is in Kimko and Duffull (eds), Simulation for Clinical Design (2003), Evaluation of Random Sparse Designs for a Population Pharmacokinetic Study: Assessement of Power and Bias Using Simulation, Hutmacher and Kowalksi. There, some random sample designs lead to large estimates of Ka - this did not affect CL or V however - pairwise scatterplots were used to demonstrate this (as Mark Gastonguay suggested in his thread to do). In such cases, it might be confidence intervals for the nonparametric bootstrap are too wide - valid at the nominal level, but inaccurate. With respect to dealing with boundary constraints and the non-parametric bootstrap, upfront thought I think can lead to less arbitrariness. Do the CI's reflect similar findings based on likelihood profiling (LP) or likelihood ratio tests (LRT)? For example, it might require more thought to reconcile a bootstrap procedure that yielded 15% of your Emax's be 0 if your LRT for Emax was > 10 points or the 95% CI based on LP did not include 0, for example. By allowing the 0 in the constraints an explicit assumption is made that one is unclear that Emax is greater than 0, and thus the modeler is allowing a point mass at 0 to exist, which is a difficult distribution statistically to deal with. One must contemplate whether this makes sense in the overall clinical interpretation. If it does not, then perhaps EMAX = exp(theta(X)) should be used to ensure that EMAX is not equal to 0 ever. Reparameterization can be done for just about any parameter to ensure a 'valid' estimate and I would suggest to do this (a sort of likelihood-based prior knowledge manifestation) than to arbitrarily pick which estimates from the bootstrap to use. Even OMEGA matrices can be parameterized to ensure non-positive semi-definite matrices, which might help in certain situations. I would also be careful if the nonparametric bootstrap CI's are different from the COV step CI's as this indicates that something is unknown with respect to estimation or inference. In the case of small sample size and non-realistic clinical inference, I would suggest a more formal Bayesian analysis which pre-specifies the analysts assumptions regarding the probability or viability of certain estimates (can be influenced by the prior). Best regards, Matt