Re: Bayesian fits

From: Nick Holford <n.holford@auckland.ac.nz> Subject: Re: [NMusers] Bayesian fits Date: Thu, 08 Nov 2001 09:47:54 +1300 Paul, > I think I understand that to use a group ("population") of subjects with > full or limited sampling to determine mean values of THETA and of the > individual ETAs, one would use the FOCE method: > METHOD=CONDITIONAL (or "1"), which would provide tempering of extreme > estimates of individual ETAs from the patient data in the input file. While I agree with you that FOCE may indeed provide better estimates of THETA et al. this is something of a red herring because the use of this particular estimation method is not *necessary* in order to get Bayesian individual estimates. > My > understanding is that the initial estimates of THETA and of ETA are indeed > estimates, and that they provide no understanding of the final estimates of > THETAs and ETAs. (Please correct me if I misunderstand this) I have found it personally helpful to take care to distinguish between a prior data set (and the estimates, population or individual, that arise from it) and the current data set (and its population and individual estimates). In the situation described below (MAXEVAL=0 method), the initial population estimates (from prior data) are identical to the final population estimates but the individual estimates are for the current data individuals. > However, it is not clear to me how to code the control stream when previous > data regarding the estimates of THETA and ETA are known, so that the > evaluation of the local patient data includes for example the THETA and > variance (ETA) estimates of published PK parameters as well as including > the new data from the more recent data set being evaluated. Can someone > shed light on this? I think you are describing the case where you have prior population estimates but do not have the data e.g. you are using literature estimates. You have a current data set (perhaps just one observation in a single subject and wish to obtain individual estimates from the current data based only on the prior population estimates. This is the usual situation when applied to dose forecasting using target concentration intervention (aka therapeutic drug monitoring). The current data individual estimates are called maximum a posteriori (MAP) Bayesian estimates. The suggestions made e.g. by Ruedi Port, show how to obtain these using the MAXEVAL=0 technique. If you use FO estimation then you need to use the POSTHOC option. If you use FOCE you do not need to specify POSTHOC. In both cases you need to include the parameters in the $TABLE output in order to see the MAP Bayesian individual estimates. There are 2 other approaches you might consider to obtain current data individual estimates. They both rely on updating the prior population estimates by merging information from the prior and current data to obtain a new set of population estimates which are then used to compute MAP Bayesian estimates for the current data set individuals. Note the critical difference from the MAXEVAL=0 method is that MAXEVAL is not used to stop estimation of the population estimates. A new set of population estimates is obtained using these methods. The 2 approaches are: 1. Pooled Data: This is straightforward assuming you have the prior data. Simply pool the prior and current data sets and estimate parameters using the pooled data. Use FO+POSTHOC or FOCE as before to get the MAP Bayesian individual estimates plus as a bonus an updated set of population parameters. 2. Hierarchical Bayesian: This has been discussed several times before on nmusers e.g. http://www.cognigencorp.com/nonmem/nm/99aug052000.html, but recent threads are hard to find. (I note that the Cognigen hosted web page http://www.cognigencorp.com/nonmem/nm/ says "The last update was February 8, 2000." but also says that the archive has "Postings from 3/31/95 - 8/31/01" but I cannot find anything later than 98apr042001.html using their search engine. Looks like 4 Apr 2001 is the posterior Bayesian estimate of the Feb 8 2000 prior and 31 August 2001 (not quite) current data :-) ). The hierarchical Bayesian (aka NONMEM PRIOR) approach uses the prior population parameters *with estimates of their uncertainty* (both together constitute the Bayesian "prior" distribution) and the current data to obtain Bayesian posterior estimates of the population parameters. The popln parameters will be updated (unlike the MAXEVAL=0 method) even though the only data that is used is from the current data set. The individual parameters are still MAP Bayesian estimates but based on the updated population (Bayesian posterior) estimates. Note that this method is unsupported by the NONMEM Project Group (and I assume also by nmconsult@globomaxnm). Bottom line, if you have the prior data then my own preference is to pool the data. I consider this the gold standard because it is totally based on the actual data you have rather than on various assumptions about the uncertainty of the prior estimates that are implicit in the hierarchical Bayesian approach. -- Nick Holford, Divn Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/