My-Luong Vuong (1), Geert Verbeke (2), Erwin Dreesen (1)
(1) Department of Pharmaceutical and Pharmacological Sciences, KU Leuven, Leuven, Belgium, (2) Department of Public Health and Primary Care, Leuven Biostatistics and Statistical Bioinformatics Centre, KU Leuven, Leuven, Belgium
Introduction: Missingness of covariate data is a prevalent challenge in pharmacometrics research [1]. Covariate data may be incomplete under three mechanisms: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). MCAR indicates no relationship between missingness and data. MAR occurs when missingness depends only on observed data, MNAR indicates dependence on unobserved data. Covariate missingness adversely affects decisions in drug development and clinical practice, emphasizing the need for proper handling of this issue [2].
Complete case (CC) analysis and single imputation (SI) of the median are missing covariate handling methods usually employed by pharmacometricians [3, 4]. These methods either produce biased results (except under MCAR) or disrupt relationships among covariates, which eventually also leads to bias [4]. Multiple imputation (MI) is a valid approach under both MAR and MCAR and also preserves the relationship between covariates. However, little research was done on the application of MI in pharmacometrics [1]. There is no study comparing the performance of CC, SI, and MI under varying degrees of missing covariate.
Objectives: The objective of our work was to compare the performance of three different methods for handling different extents of covariate missingness in pharmacometrics modelling.
Methods: A clinical dataset describing the pharmacokinetics of warfarin following a single-dose administration to 32 participants was employed [5]. Body weight (WT) was fully observed for all patients, with a median [inter-quartile range – IQR] of 71.7 [61.5-78.5] kg. Besides WT, sex and age are two complete patient characteristics included in the dataset.
A one-compartment population pharmacokinetics (popPK) model parameterised with first-order absorption rate constant (Ka), lag-time (Tlag), volume of distribution (Vd), and clearance (CL) was used to describe total warfarin concentrations. Random effects describe inter-individual variability (IIV) on all four structural pharmacokinetic parameters. Residual variability was modelled using a combined additive and proportional error model. Baseline WT was a covariate on CL and Vd (power function, centred around median).
The R mice_ampute function was used to generate three replicate datasets with ~30%, 50% and 80% missing WT under MAR [6]. For CC analysis, patients with missing WT were removed from the dataset before popPK analysis. For SI, missing WT was imputed with the median of the observed WT to make a complete dataset for analysis. For MI, 30, 50, and 80 complete datasets were generated, corresponding to the respective percentages of missing WT [7]. MI was performed using an imputation model based on all variables present in the dataset. Stochastic imputations were performed using the R mice.impute.norm function [7]. A popPK model was fit to each imputed dataset, after which parameters of converged models were pooled into one final set for inference purposes using Rubin’s rule [3]. Covariate effect parameters obtained from the three methods were compared with the reference model (complete dataset) in terms of typical value (TV) and relative standard error (RSE). All popPK analyses were performed in NONMEM 7.5.
Results: Replicate datasets with WT MAR in 10, 16, and 25 out of total 32 patients (18.8%, 50.0%, and 78.1%) were created. The median (IQR) of the remaining WT were 67 (58–75) kg, 73 (62–79) kg, and 78 (62–82) kg. The parameter estimates of WT on CL and Vd are summarised below.
|
|
100% |
70% |
70% |
70% |
50% |
50% |
50% |
20% |
20% |
20% |
|
WT on CL |
0.597 [38%] |
0.404 [68%] |
0.388 [68%] |
0.636 [47%] |
0.583 [47%] |
0.578 [51%] |
0.613 [46%] |
0.0919 [810%] |
-0.0562 [201%] |
0.321 [159%] |
|
WT on Vd |
0.902 [14%] |
0.982 [16%] |
0.979 [17%] |
1.0857 [14%] |
1.100 [16%] |
1.120 [14%] |
0.847 [23%] |
1.270 [20%] |
1.140 [38%] |
0.969 [32%] |
For MI, the converge rates were 100%, 98% and 91% for the 30%, 50%, and 80% missingness scenarios. Overall, MI estimated the effect of WT on CL most precisely and accurately. Similarly, MI estimated the effect of WT on Vd most accurately with 50% and 80% missing WT, and most precisely with 30% missing WT.
Conclusion: Our analysis showed that MI is generally more precise and accurate than CC and SI in estimating covariate effect. We encourage pharmacometricians to employ MI due to its shown superiority compared with the historic methods.
References:
[1] Johansson Å M et al. AAPS J (2013) 4, 1232-41.
[2] Bräm DS et al. CPT:PSP (2022) 12, 1638-48.
[3] Bonate PL. Pharmacokinetic-Pharmacodynamic Modeling and Simulation: Springer New York, New York; 2011.
[4] Wu H et al. Stat Med (2001) 12, 1755-69.
[5] O’Reilly RA et al. Circulation (1968) 1, 169-77.
[6] Schouten RM et al. JSCS (2018) 15, 2909-30.
[7] Buuren S. Flexible Imputation of Missing Data, Second Edition. New York: Chapman and Hall/CRC; 2018.
Reference: PAGE 32 (2024) Abstr 10814 [www.page-meeting.org/?abstract=10814]
Poster: Methodology - New Modelling Approaches