RE: Additive plus proportional error model for log-transform data

From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Jakob Ribbing Sent: Thursday, June 02, 2016 6:32 AM To: Abu Helwa, Ahmad Yousef Mohammad - abuay010 Cc: nmusers_at_globomaxnm.com Subject: Re: [NMusers] Additive plus proportional error model for log-transform data Hi Ahmad, The two error models are equivalent (only that with Leonids suggested code, the additive-on-log-transformed error term (TH16) is estimated on variance scale, instead of standard deviation scale (approximate CV). This inflated error rates for very low concentrations is what you get for additive+proportional on the log transformed scale, and I believe that has been discussed on nmusers previously as well, many years ago. You could possibly use a cut-off for when lower IPRE should not lead to higher residual errors, but why not move to additive + proportional for the original concentration scale? Also, this implementation may be unfortunate: Y=(1-FLAG)*IPRE + W*EPS(1) Effectively, when concentration predictions are zero (FLAG=1), e.g. for pre-dose samples or before commence of absorption, then you set the concentration prediction to EXP(1)=3.14 concentration units. Depending on what concentration scale you work on (i.e. if BLQ is much higher than this) it may be OK, but otherwise not. Instead of applying a flag, just set IPRE to a negative value (low in relation to LOG(BLQ)), if you want to stay on the log-transformed scale. I hope this helps to solve your problem. Best regards Jakob Jakob Ribbing, Ph.D. Senior Consultant, Pharmetheus AB Cell/Mobile: +46 (0)70 514 33 77 Jakob.Ribbing_at_Pharmetheus.com<mailto:Jakob.Ribbing_at_Pharmetheus.com> http://www.pharmetheus.com/ Phone, Office: +46 (0)18 513 328 Uppsala Science Park, Dag Hammarskjlds vg 52B SE-752 37 Uppsala, Sweden This communication is confidential and is only intended for the use of the individual or entity to which it is directed. It may contain information that is privileged and exempt from disclosure under applicable law. If you are not the intended recipient please notify us immediately. Please do not copy it or disclose its contents to any other person. On 02 Jun 2016, at 04:27, Abu Helwa, Ahmad Yousef Mohammad - abuay010 <ahmad.abuhelwa_at_mymail.unisa.edu.au<mailto:ahmad.abuhelwa_at_mymail.unisa.edu.au>> wrote: Dear NMusers, I am developing a PK model using log-transformed single-dose oral data. My question relates to using combined error model for log-transform data. I have read few previous discussions on NMusers regarding this, which were really helpful, and I came across two suggested formulas (below) that I tested in my PK models. Both formulas had similar model fits in terms of OFV (OFV using Formula 2 was one unit less than OFV using Formula1) with slightly changed PK parameter estimates. My issue with these formulas is that the model simulates very extreme concentrations (e.g. upon generating VPCs) at the early time points (when drug concentrations are low) and at later time points when the concentrations are troughs. These simulated extreme concentrations are not representative of the model but a result of the residual error model structure. My questions: 1. Is there a way to solve this problem for the indicated formulas? 2. Are the two formulas below equally valid? 3. Is there an alternative formula that I can use which does not have this numerical problem? 4. Any reference paper that discusses this subject? Here are the two formulas: 1. Formula 1: suggested by Mats Karlsson with fixing SIGMA to 1: W=SQRT(THETA(16)**2+THETA(17)**2/EXP(IPRE)**2) 2. Formula 2: suggested by Leonid Gibiansky with fixing SIGMA to 1: W = SQRT(THETA(16)+ (THETA(17)/EXP(IPRE))**2 ) The way I apply it in my model is this: FLAG=0 ;TO AVOID ANY CALCULATIONS OF LOG (0) IF (F.EQ.0) FLAG=1 IPRE=LOG(F+FLAG) W=SQRT(THETA(16)**2+THETA(17)**2/EXP(IPRE)**2) ;FORMULA 1 IRES=DV-IPRE IWRES=IRES/W Y=(1-FLAG)*IPRE + W*EPS(1) $SIGMA 1. FIX Best regards, Ahmad Abuhelwa School of Pharmacy and Medical Sciences University of South Australia- City East Campus Adelaide, South Australia Australia