Re: comparing theta's

From: Pascal Girard <pg@upcl.univ-lyon1.fr> Date: Thu, 25 Mar 1999 16:02:18 +0100 Subject: Re: comparing theta's Peter, You mean you have: * 3 groups of data with (almost) same type of patients (same average values of <<known>> covariates), same dose and same regimen. * Each 3 data sets has been succesfully fitted with exactly the same structral PK, interindividual and intra-individual random effect models. * TH1 TH2 and TH3 are the structural vectors of PK parameter estimates in the 3 groups respectively; * OM1, OM2 and OM3 are the interindividual variance matrices estimates; * S1, S2 and S3 are the intra-individual variance matrices estimates. * Finally you also have the precision of the estimates COV1=variance(TH1,OM1,S1), COV2 and COV3, given by $COV. Let suppose that individuals have been placed in one of the 3 groups at random. So you may want to test, with significant level x%, hypothesis like: H0: TH1 = TH2 = TH3 versus H1: TH1!=TH2 or TH1!=TH3 or TH2!=TH3 I think you will have to distinguish different cases: 1. COV1 # COV2 # COV3 # ZERO with # meaning almost equal, and ZERO a covariance matrix. This is the (unrealistic) case where your parameter are estimated without errors. 1.1. OM1, OM2 and OM3 are diagonal. You can perform classical t-tests on each separate elements of vector TH1, TH2 and TH3, just being careful with the multiplicity of the tests. 1.2. OM1, OM2 and OM3 are not diagonal. You will have to do what statisticians call a multivariate ANOVA. It is usually performed with individual data. I am not sure you can perform it with only the NONMEM outputs: you probably need the NONMEM objective functions, the S1, S2 and S3, but maybe other quantities that are not classically output by NONMEM. Tricky, but not unfeasible. 2. COV1 !=ZERO or COV2 !=ZERO or COV3 !=ZERO This is the realistic case where your parameter are estimated with a non negligible error. Here it is becoming really tricky because you will need to introduce this error in your test: and I really personnaly don't see how you are going to do it! Unfortunately this is the most frequent case!! So given all this, I would advise you to try to get the individual data, fit them altogether with your common model, then introduce the covariate GROUP on certain parameters (e.g. on CL, V, or interindividual variances ...) , and just perform a likelihood ratio test and graphical comparisons, to see if the fit is improved. I'm not sure it helps, but it is how I personnally see this business! Pascal Girard ------------------------------------------------------------------- Service Pharmacologie Clinique PG@upcl.univ-lyon1.fr BP 3041,162, avenue Lacassagne Tel : +33 (0)4 78 78 57 26 69394 LYON Cedex 03 FRANCE Fax : +33 (0)4 78 78 57 19