Divya Brundavanam (1), Mats O. Karlsson (1)
(1) Department of Pharmacy, Uppsala University, Uppsala, Sweden
Objectives:
Randomization of subjects to multiple dose levels in clinical trials enables an unbiased estimation of the dose-response relationship. However, drug exposure is determined by several physiological factors at the subject level which often cannot be randomized. These factors may also influence drug response, thus causing confounding in the exposure-response relationship. This is particularly problematic in exposure-response analyses – which are important to determine dose individualization and when the studied dose range is narrow.
The aim of this study is to examine the confounding bias in estimation of PKPD relationships in randomized dose controlled (RDCT) trials, under multiple designs and modelling approaches.
Methods:
Simulated Data: N subjects, randomly assigned to two dose groups. 100 simulations per design.
(a) Design 1 (N=100): A drug concentration and a response observed following a constant-rate infusion (Rinf = 1 or 2), related by an Emax model. CL and C50 are both simulated as functions of covariates Age~N(45,52) and Score~N(10,42), where Score is unobserved and can cause confounding.
(b) Design 2 (N=5000): A PK Time-to-Event model with Rinf = 1 or 2, where the hazard is dependent on baseline hazard and drug exposure. Baseline hazard and CL are correlated, leading to confounding.
(c) Design 3 (N=53): Repeated measures design based on a PKPD model for moxonidine-noradrenalin [1]. Drug exposure and response were simulated for the 0.2 mg and 0.4 mg arms after repeated dosing, with confounding introduced by a random effect correlation (r=0.9) between CL and C50.
Models: We apply the following approaches (where applicable) to simulated data under each design. Both sequential (2-stage) and simultaneous analyses were explored. X represents observed covariates, and the subscripts IV and RE represent instrumental variable and random effect, respectively.
(i) Unadjusted model (UM)
YPD=g(θPD,ηPD,Cobs(Cipred),X)+ ϵPD
(ii) PKPD Correlated Model (PCM)
YPK=fPCM(θPK,ηPK,Dose,X) + ϵPK
YPD=g(θPD,ηPD, fPCM(θPK,ηPK,Dose,X), X)+ ϵPD, with corr(ηPK,ηPD )≠0
(iii) Double relations model (DRM)
YPK=fDRM (θPK,ηPK,Dose,X)+ϵPK
YPD =YPD,IV +YPD,RE +ϵPD, where
YPD,IV = g(θPD,IV, ηPD,IV, fDRM(θPK,Dose,X), X) and
YPD,RE =g(θPD,RE, ηPD,RE, fDRM(θPK,ηPK,Dose,X), X) – g(θPD,RE, ηPD,RE, fDRM(θPK,Dose,X), X)
(iv) Predictor Substitution (PS) approach [2,3,4]
YPK=f(θPK,ηPK,Dose,X)+ ϵPK
YPD=g(θPD, ηPD, f(θPK,pred,Dose,X), X)+ ϵPD
(v) Control Function (CF) approach [3,5]
YPK=f(θPK,ηPK,Dose,X)+ ϵPK
YPD= g(θPD, ηPD, Cobs, X)+ θres rf +ϵPD, where rf is the residual from the PK model fit.
All simulations, model-fitting and estimation procedures were performed using NONMEM 7.5. Additional data analysis was performed in R 4.3.2.
Results: Model performance was assessed based on bias/standard deviation/root mean squared error (rmse) of the parameter estimates relative to the simulated values, which was 0.5 for C50 in Design 3 and 1 for all other parameters.
Model: parameter (bias, sd, rmse)
Design 1:
UM: C50 (0.238,0.224,0.326) | Emax (0.054,0.043,0.069)
PCM: C50 (-0.024,0.148,0.15) | Emax (-0.006,0.018,0.018)
DRM: C50 (-0.067,0.178,0.19) | Emax (-0.015,0.039,0.041)
PS: C50 (-0.055,0.16,0.168) | Emax (-0.013,0.02,0.023)
CF: C50 (-0.014,0.18,0.18) | Emax (-0.026,0.049,0.055)
Design 2:
UM: h0 (-0.044,0.014,0.046)
DRM: h0 (0.016,0.017,0.023)
PS: h0 (-0.15,0.014,0.15)
CF: h0 (0.018,0.017,0.025)
Design 3:
UM: C50 (-0.001,0.084,0.084) | Emax (-0.001,0.008,0.008)
PCM: C50 (-0.009,0.07,0.07) | Emax (-0.003,0.008,0.008)
DRM: C50 (-0.012,0.084,0.084) | Emax (-0.005,0.012,0.013)
PS: C50 (0.067,0.11,0.128) | Emax (0.006,0.013,0.015)
CF: C50 (-0.028,0.079,0.083) | Emax (-0.008,0.011,0.013)
Conclusions:
Under each design, several of the analysis approaches provided reasonable reduction in estimation bias. In general, estimation of correlation in random effects between exposure and response in the model provided the best results. However, this may not always be applicable (e.g. Design 2) and in practice, identification of the right correlation pattern may be difficult. Among the instrumental variable approaches, CF performs well across designs, whereas PS shows more varied results. We also propose the novel DRM which has the additional advantage of separating out the fixed effects and random effects components of the exposure-response relationship for comparison, and which also performs well across designs.
References
[1] Brynne L. et al. Pharmacodynamic models for the cardiovascular effects of moxonidine in patients with congestive heart failure. Br J Clin Pharmacol (2001) 51: 35-43.
[2] Nedelman, J.R. (2005) On some “disadvantages” of the population approach. The AAPS Journal 7, Article 38.
[3] Wang J. Dose as instrumental variable in exposure-safety analysis using count models. J Biopharm Stat. 2012;22(3):565-81.
[4] Cai B, Small DS, Have TR. Two-stage instrumental variable methods for estimating the causal odds ratio: analysis of bias. Stat Med. 2011 Jul 10;30(15):1809-24.
[5] Terza JV, Basu A, Rathouz PJ. Two-stage residual inclusion estimation: addressing endogeneity in health econometric modeling. J Health Econ. 2008 May;27(3):531-43.
[6] R Core Team (2023). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.
Reference: PAGE 32 (2024) Abstr 11243 [www.page-meeting.org/?abstract=11243]
Poster: Methodology - New Modelling Approaches