Mar Ribera Armengol (1), Maria Luisa Sardu (2), Akash Khandelwal (3)
(1) UCB Pharma, Slough, UK, (2) UCB Pharma, Milano, Italy, (3) UCB Biosciences Gmbh, Monheim, Germany
Background & Objectives: Pharmacometric models often address causal questions, specifically examining the impact of changing an independent variable (X) on the outcome (Y). In population modelling, covariate analysis traditionally involves a two-step process: (1) pre-selecting correlated covariates for inclusion in the analysis, and (2) testing and incorporating these covariates using full fixed effect models, full random effect models, or stepwise-covariate modelling. However, in step 1, causal considerations are often overlooked, potentially leading to biased estimates of covariate effects in the final model. While covariates are typically treated as independent variables (X), they can also act as confounders [1], influencing both covariate and outcome, such that, a triangular relationship exists between covariate, confounder, and outcome. In the context of Exposure-Response (ER) analysis, certain covariates may confound the relationship between exposure and response. Ignoring these confounders can result in incorrect conclusions regarding the impact of exposure on response. The objective of the current analysis is to assess the impact of inclusion/exclusion of confounders in ER and Population PK covariate analysis.
Methods: Population PK: A one-compartment oral population PK model (CL/F = 1L/h, ka = 1 h-1, V/F = 10 L) [2] with creatinine clearance (CRCL) as a covariate on the outcome clearance (CL) and body weight (BW) as a confounder on CL was considered (True model 1). In a second model, CL was only assumed to be dependent on BW (True model 2). Different scenarios were simulated, including or excluding a relationship between covariate and outcome, with different correlation levels between confounder and covariate, (i.e. 0.3, 0.5, 0.7 and 0.9).
Exposure-Response: A logistic regression model was employed to describe the outcome (probabilities of response). Different true models were considered: in the first the response was assumed to depend on both AUC infinity (exposure) and Lactate dehydrogenase (LDH) (confounder), whereas in the second one the response was only assumed dependent on the confounder. Multiple scenarios were simulated, encompassing different levels of strength in the relationships between exposure and response (i.e. 0.25 and 2), confounder and exposure (i.e. 0.3, 0.5, 0.7 and 0.9) and confounder and response (i.e. 0.25 and 4).
500 datasets with 100 individuals each were simulated for population PK and ER studies. All simulations and estimations were performed using PsN [3] SSE. The models were assessed in terms of Type I and Type II errors as well as bias in the parameter estimates.
Results: Population PK: When there is no relationship between the covariate (CRCL) and the outcome (CL), but a high correlation exists between the confounder (BW)-covariate and confounder-outcome, the Type I error rate is 9.2%. This means there is a risk of falsely detecting a CRCL-CL relationship. In cases with low correlation between confounder-covariate and confounder-outcome, the Type I error rate is lower (4.2-5%). However, the CRCL-parameter estimate is positively biased.
When there is a positive relationship between CRCL and CL, and a positive correlation between confounder-covariate and confounder-outcome, the exclusion of the covariate results in a Type II error rate of ~90%. While the CRCL-parameter estimate can be either positively or negatively biased, depending on the correlation level between BW-CRCL.
Exposure-Response: In scenario 1 (weak relationships between exposure-response, confounder-exposure, and confounder-response), the exclusion of the exposure results in a Type II error rate of 66.6%, making it difficult to detect an exposure-response relationship.
In scenario 2 (exposure-response relationship is strong but the correlation between confounder-exposure and confounder-response is weak) the Type II error rate is 0%, therefore, lower than in scenario 1. Consequently, this implies that the true model is always preferred.
Conclusions: This work proposes a valuable approach to quantitatively assess the role and impact of confounders in ER and Population PK covariate analysis within the framework of causal inference. In order to accurately assess the impact of a particular covariate or exposure, it is important to condition the model on the confounder to draw unbiased conclusions.
References:
[1] Rogers JA, Maas H, Pitarch AP. An Introduction To Causal Inference For Pharmacometricians. CPT Pharmacometrics Syst Pharmacol. (2023) 12:27-40.
[2] Lavielle, Marc, and Benjamin Ribba. Enhanced Method for Diagnosing Pharmacometric Models: Random Sampling from Conditional Distributions. Pharmaceutical research (2016) 33(12):2979-2988.
[3] Lindbom, L., Pihlgren, P. & Jonsson, E.N. PsN-Toolkit–a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM. Comput. Methods. Programs. Biomed. (2005) 79 (3):241–257.
Reference: PAGE 32 (2024) Abstr 10954 [www.page-meeting.org/?abstract=10954]
Poster: Methodology - Covariate/Variability Models