RE: Ordinal data model: Incorporation of variability & assessment of predictive performance

From: [email protected] <[email protected]> On Behalf Of Eduard Schmulenson Sent: den 5 februari 2019 11:04 To: [email protected] Subject: [NMusers] Ordinal data model: Incorporation of variability & assessment of predictive performance Dear all, I am currently trying to model the transitions between four adverse event grades (0-3) using a continuous-time Markov modeling approach. I have included a dose effect as well as a time effect on the transition constants. Overall, the parameters are well estimated and the VPC looks also quite good. However, the model does not have any IIV or other variability incorporated, so no individual predictions can be made. I have tried different approaches to include variability: - Six different etas: a) One eta per transition constant without a block structure (this has resulted in rounding errors), b) with a full block structure (see Lacroix BD et al. CPT PSP 2014), also with rounding errors and c) with two OMEGA BLOCK(3) structures which solely include "forward" and "backward" transition constants, respectively (also with rounding errors). - Two different etas: One mutual eta on "forward" and "backward" transition constants (shrinkage values of ~ 40 and 60%, respectively, which do not lower after including the dose effect. The impact of time cannot be estimated anymore) - Just one eta on every transition constant (shrinkage value of 46% which slightly increases after including the dose and time effect. The etas were added as exponential variables. Other tested covariates were not significant or resulted in run errors when a bootstrap was performed. Are there any other possibilities to incorporate variability in this type of model? Or is it solely a data-dependent issue? You can find the control stream (without any IIV) below. My second question is about the assessment of predictive performance in the same model. One can compare the observed proportions of an adverse event grade vs. the simulated probability or the observed vs. simulated grade. Is there a meaningful error which I can calculate in order to assess bias and precision? Would be a median prediction error and a median absolute prediction error appropriate for this type of data? And what kind of error would you suggest when one has to calculate a relative error which would include a division by 0? Thank you very much in advance. Best regards, Eduard ########################################## $ABB COMRES = 1 $SUBROUTINES ADVAN6 TOL = 4 $MODEL NCOMP = 4 COMP = (G0) ; No AE COMP = (G1) ; Mild AE COMP = (G2) ; Moderate AE COMP = (G3) ; Severe AE $PK IF(NEWIND.NE.2) THEN PSDV = 0 COM(1) = 0 ENDIF PRSP = PSDV ; Previous DV IF(PRSP.EQ.1) COM(1) = 0 IF(PRSP.EQ.2) COM(1) = 1 IF(PRSP.EQ.3) COM(1) = 2 IF(PRSP.EQ.4) COM(1) = 3 F1 = 0 F2 = 0 F3 = 0 F4 = 0 IF(COM(1).EQ.0) F1 = 1 IF(COM(1).EQ.1) F2 = 1 IF(COM(1).EQ.2) F3 = 1 IF(COM(1).EQ.3) F4 = 1 TVK01 = THETA(1) K01 = TVK01*EXP(ETA(1)) TVK12 = THETA(2) K12 = TVK12 TVK23 = THETA(3) K23 = TVK23 TVK10 = THETA(4) K10 = TVK10 TVK21 = THETA(5) K21 = TVK21 TVK32 = THETA(6) K32 = TVK32 TVKT = THETA(8) KT = TVKT $DES K01F = K01*EXP(KT*T) ; Time effect K12F = K12*EXP(KT*T) K23F = K23*EXP(KT*T) K10B = K10*EXP(THETA(7)*(DOSEDAY-3000)) ; Dose effect K21B = K21*EXP(THETA(7)*(DOSEDAY-3000)) K32B = K32*EXP(THETA(7)*(DOSEDAY-3000)) DADT(1) = K10B*A(2) - K01F*A(1) ; Grade 0 DADT(2) = K01F*A(1) + K21B*A(3) - A(2)*(K10B + K12F) ; Grade 1 DADT(3) = K12F*A(2) + K32B*A(4) - A(3)*(K21B + K23F) ; Grade 2 DADT(4) = K23F*A(3) - K32B*A(4) ; Grade 3 $ERROR Y = 1 IF(DV.EQ.1.AND.CMT.EQ.0) Y = A(1) IF(DV.EQ.2.AND.CMT.EQ.0) Y = A(2) IF(DV.EQ.3.AND.CMT.EQ.0) Y = A(3) IF(DV.EQ.4.AND.CMT.EQ.0) Y = A(4) P0 = A(1) P1 = A(2) P2 = A(3) P3 = A(4) ; Cumulative probabilities CUP0 = P0 CUP1 = P0 + P1 CUP2 = P0 + P1 + P2 CUP3 = P0 + P1 + P2 + P3 ; Start of simulation block IF(ICALL.EQ.4) THEN IF(CMT.EQ.0) THEN CALL RANDOM (2,R) IF(R.LE.CUP0) DV = 1 IF(R.GT.CUP0.AND.R.LE.CUP1) DV = 2 IF(R.GT.CUP1.AND.R.LE.CUP2) DV = 3 IF(R.GT.CUP2) DV = 4 ENDIF ENDIF ; End of simulation block PSDV=DV $THETA ... $OMEGA 0 FIX $COV PRINT=E ;$SIM (7776) (8877 UNIFORM) ONLYSIM NOPREDICTION $EST METHOD=1 LAPLACIAN LIKE SIG=2 PRINT=1 MAX=9999 NOABORT [cid:[email protected]][unnamed] _____________________ Eduard Schmulenson, M.Sc. Apotheker/Pharmacist Klinische Pharmazie Pharmazeutisches Institut Universität Bonn An der Immenburg 4 D-53121 Bonn Tel.: +49 228 73-5242 [email protected]<mailto:[email protected]> När du har kontakt med oss på Uppsala universitet med e-post så innebär det att vi behandlar dina personuppgifter. För att läsa mer om hur vi gör det kan du läsa här: http://www.uu.se/om-uu/dataskydd-personuppgifter/ E-mailing Uppsala University means that we will process your personal data. For more information on how this is performed, please read here: http://www.uu.se/en/about-uu/data-protection-policy