RE: Simulation vs. actual data

From: "Perez Ruixo, Juan Jose [PRDBE]" JPEREZRU@PRDBE.jnj.com Subject: RE: [NMusers] Simulation vs. actual data Date: Wed, July 13, 2005 7:40 am Nick, Your interpretation of the process described to generate a tolerance interval is correct. In theory, I think it's better approach to sample from a non-parametric bootstrap distribution than just "sampling from the covariance matrix of the estimate in addition to the variance-covariance matrix for OMEGA and SIGMA". I agree it's easier to use the prediction interval than the tolerance interval. Also, the theoretical advantage of the tolerance interval in some cases could not be relevant (low uncertainty), but in some other it could be the only choice (high uncertainty). My suggestion is to test (on case by case basis) both intervals, and if both give similar results then move forward with the prediction interval, otherwise use the tolerance interval. At risk of getting me out of the tolerance interval of my wife :-), I did some simulations at home to answer your questions. However, I used other datasets where I had a model with between and within subject variability in several parameters. The model was built with the dataset A, and the 80% prediction and tolerance intervals were calculated for each concentration in the dataset B. The prediction and the tolerance intervals contained 81.4% and 79.4% of the observations, respectively. Probably both numbers are very similar because RSE for fixed and random effects are lower than 15% and 40%, respectively. Therefore, in this case (low uncertainty) I would continue the simulation and/or evaluation work without considering the uncertainty. At this stage, I don't have any example where I can show you the tolerance interval is superior to prediction interval in terms of predictive performance. Perhaps, anyone else may have it and would be very interesting to see the results and the consequences. One interesting thing I learned from this exercise is that tolerance interval can be narrower than prediction interval. One potential reason is that the estimates for two random effects fall in the upper part of the non-parametric bootstrap distribution for the same parameter, but below the 90% confidence interval. So, when the uncertainty is considered, more subproblems are simulated with lower variability and as a consequence, the tolerance interval is narrower. Finally, I also wonder if anyone in the nmuser list would like to share any experience with prediction/tolerance intervals for categorical data. I guess the way to calculate those intervals is a bit more complex With respect to your comment on the allometric scaling, as you know allometric model are empirical and not all equations relate directly to physiology. In fact, body weight and brain weight has been commonly used to predict the clearance of drugs in humans (Mahmood I, et al. Xenobiotica 1996). In particular, body weigh and brain weight has been recently used to predict from animal to human the clearance of protein drugs, such rhuEPO and EPO-beta (Mahmood I. J Pharm Sci. 2004). I agree that brain is not an important clearance organ for EPO, however brain weight was tested on the basis of Sacher equation, which relates body weight and brain weight to the maximum lifetime potential (MLP). MLP is a measurement of the chronological time for a particular species, necessary for a particular physiological event to occur. The shorter the MLP, the faster the biological cycles occur. One may for instance consider the drug elimination as the physiological event to occur and, then MLP (or brain weight) could be used to explain the difference in drug clearance across species with similar body weight. In fact, the brain weight in rabbit (0.56% of body weight) is lower than the brain weight in monkey (1.80% of body weight). So, given the same body weight for both species (see figure 3 of the paper), then MLP in rabbits is shorter relative to monkeys (0.76 x 105 h versus 1.62 x 105 h) and, therefore, the PEG-EPO clearance in rabbits is faster as compared to monkeys. The reference model we reported is a simple allometric model based on body weight alone. From the RSE, you can see that 95%CI were not different from the theoretical value. Even in the final model you can derive the "real" exponent of body weight for CL. In order to do that, it is needed to consider the effect of brain weight because of its proportionality to body weight, within a particular species. Therefore, 1.030 (apparent exponent of weight) cannot be directly compared to 0.75, without taking into account the exponent of brain weight. Doing so, 1.030 - 0.345 = 0.685 is obtained as the "real" exponent of weight, which is very similar to the expected 0.75. I understand the real exponent of body weight is 0.75. Regards, Juanjo.