[NMusers] Combined residual model and IWRES.
Dear All, I'm working on a one-compartment iv model. I have used a model for the IWRES from a discussion from May 2001 (thanks to Mats Karlsson, Niclas Jonsson and Nick Holford), where you use thetas to obtain the sigmas when using a combined residual model: IPRED=F IRES=DV-IPRED IWRES=(DV-IPRED)/SQRT(F*F*THETA(3)*THETA(3)+THETA(4)*THETA(4)) Y=F*(1+THETA(3)*ERR(1))+THETA(4)*ERR(2). where you then fix the sigmas to 1. I obtained the following results for a particular base model: ETA = 3.1628.10.0804 0.163 ETASD = 1.23693 1.42478 ERRSD = 1 1 THETA:se% = 23.932.039.923.3 OMEGA:se% = 18.433.8 SIGMA:se% = 0.0 0.0 I then ran the same model but using the normal code in the $ERROR section to see if there was any difference in the final estimates: IPRED=F IRES=DV-IPRED Y=F*(1+ERR(1))+ERR(2) and obtained these results: THETA = 3.1628.1 ETASD = 1.23693 1.42478 ERRSD = 0.0803741 0.163095 THETA:se% = 23.532.0 OMEGA:se% = 18.533.9 SIGMA:se% = 79.345.9 Here are few questions: 1.Can anyone tell me why the standard errors for the thetas in model 1 and the standard errors for the sigmas in model 2 differ so significantly? 2.Why does the algorithm used to obtain the standard errors for the sigmas differ so much from that used to obtain standard errors for the thetas, and how? 3.What are the implications when then using INTERACTION? 4and finally, which model should i use? Thankyou in advance for any light that can be shed. Best, Paul Westwood.
Re: [NMusers] Combined residual model and IWRES.
sorry for the typo in my first e-mail, I was talking about SIGMAs, not OMEGAs, Below is the corrected version Leonid Paul, In thetas, SE% refers to SE% of SD while in SIGMAs it refers to variances (SD^2). To make them identical, use IWRES=(DV-IPRED)/SQRT(F*F*THETA(3)+THETA(4)) Y=F*(1+SQRT(THETA(3))*ERR(1))+SQRT(THETA(4))*ERR(2). also, if you take the square of SE% in thetas, you will see that it nearly matches SE% for SIGMAs, as it should Leonid -- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web:www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel:(301) 767 5566 Paul Westwood wrote: Dear All, I'm working on a one-compartment iv model. I have used a model for the IWRES from a discussion from May 2001 (thanks to Mats Karlsson, Niclas Jonsson and Nick Holford), where you use thetas to obtain the sigmas when using a combined residual model: IPRED=F IRES=DV-IPRED IWRES=(DV-IPRED)/SQRT(F*F*THETA(3)*THETA(3)+THETA(4)*THETA(4)) Y=F*(1+THETA(3)*ERR(1))+THETA(4)*ERR(2). where you then fix the sigmas to 1. I obtained the following results for a particular base model: ETA = 3.1628.10.0804 0.163 ETASD = 1.23693 1.42478 ERRSD = 1 1 THETA:se% = 23.932.039.923.3 OMEGA:se% = 18.433.8 SIGMA:se% = 0.0 0.0 I then ran the same model but using the normal code in the $ERROR section to see if there was any difference in the final estimates: IPRED=F IRES=DV-IPRED Y=F*(1+ERR(1))+ERR(2) and obtained these results: THETA = 3.1628.1 ETASD = 1.23693 1.42478 ERRSD = 0.0803741 0.163095 THETA:se% = 23.532.0 OMEGA:se% = 18.533.9 SIGMA:se% = 79.345.9 Here are few questions: 1.Can anyone tell me why the standard errors for the thetas in model 1 and the standard errors for the sigmas in model 2 differ so significantly? 2.Why does the algorithm used to obtain the standard errors for the sigmas differ so much from that used to obtain standard errors for the thetas, and how? 3.What are the implications when then using INTERACTION? 4and finally, which model should i use? Thankyou in advance for any light that can be shed. Best, Paul Westwood.
Re: [NMusers] Combined residual model and IWRES.
Dear Paul, You can use the delta method to compute the variance and expected value of a transformation, which is square in your case. given y=theta^2 E(y)=theta^2 Var(y)=Var(theta)+(2*theta)^2 ; the later portion is square of the first derivative of y with respect of theta. In your example theta is the standard deviation whereas error estimate is variance. I did not follow your values very well, so I ran a model with same reparameterization and got following results. theta=2.65, rse=27.2% err=7.04; rse=54.4% theta.1-2.65 rse-27.2 var.theta.1-(rse*theta.1/100)^2 ## = 0.51955 err.1-7.04 rse.err.1-54.4#% var.err.1-(rse.err.1*err.1/100)^2 ## = 14.66 ##now from delta method E(err)=2.65^2 ## 7.025 close to 7.04 var(err)=(2*2.65)^2*0.51955 ## 14.59 close to 14.66 Hope it helps Varun Goel PhD Candidate, Pharmacometrics Experimental and Clinical Pharmacology University of Minnesota Paul Westwood [EMAIL PROTECTED] wrote: Dear All, I'm working on a one-compartment iv model. I have used a model for the IWRES from a discussion from May 2001 (thanks to Mats Karlsson, Niclas Jonsson and Nick Holford), where you use thetas to obtain the sigmas when using a combined residual model: IPRED=F IRES=DV-IPRED IWRES=(DV-IPRED)/SQRT(F*F*THETA(3)*THETA(3)+THETA(4)*THETA(4)) Y=F*(1+THETA(3)*ERR(1))+THETA(4)*ERR(2). where you then fix the sigmas to 1. I obtained the following results for a particular base model: ETA = 3.1628.10.0804 0.163 ETASD = 1.23693 1.42478 ERRSD = 1 1 THETA:se% = 23.932.039.923.3 OMEGA:se% = 18.433.8 SIGMA:se% = 0.0 0.0 I then ran the same model but using the normal code in the $ERROR section to see if there was any difference in the final estimates: IPRED=F IRES=DV-IPRED Y=F*(1+ERR(1))+ERR(2) and obtained these results: THETA = 3.1628.1 ETASD = 1.23693 1.42478 ERRSD = 0.0803741 0.163095 THETA:se% = 23.532.0 OMEGA:se% = 18.533.9 SIGMA:se% = 79.345.9 Here are few questions: 1.Can anyone tell me why the standard errors for the thetas in model 1 and the standard errors for the sigmas in model 2 differ so significantly? 2.Why does the algorithm used to obtain the standard errors for the sigmas differ so much from that used to obtain standard errors for the thetas, and how? 3.What are the implications when then using INTERACTION? 4and finally, which model should i use? Thankyou in advance for any light that can be shed. Best, Paul Westwood. - Never miss a thing. Make Yahoo your homepage.