Performance of methods for handling missing categorical covariate data in population pharmacokinetic analyses

Abstract

In population pharmacokinetic analyses, missing categorical data are often encountered. We evaluated several methods of performing covariate analyses with partially missing categorical covariate data. Missing data methods consisted of discarding data (DROP), additional effect parameter for the group with missing data (EXTRA), and mixture methods in which the mixing probability was fixed to the observed fraction of categories (MIX(obs)), based on the likelihood of the concentration data (MIX(conc)), or combined likelihood of observed covariate data and concentration data (MIX(joint)). Simulations were implemented to study bias and imprecision of the methods in datasets with equal-sized and unbalanced category ratios for a binary covariate as well as datasets with non-random missingness (MNAR). Additionally, the performance and feasibility of implementation was assessed in two real datasets. At either low (10%) or high (50%) levels of missingness, all methods performed similarly well. Performance was similar for situations with unbalanced datasets (3:1 covariate distribution) and balanced datasets. In the MNAR scenario, the MIX methods showed a higher bias in the estimation of CL and covariate effect than EXTRA. All methods could be applied to real datasets, except DROP. All methods perform similarly at the studied levels of missingness, but the DROP and EXTRA methods provided less bias than the mixture methods in the case of MNAR. However, EXTRA was associated with inflated type I error rates of covariate selection, while DROP handled data inefficiently.

Fig. 1

Dataset designs used in the simulation analysis. Black indicates the fraction of male subjects; white indicates females. Left part shows the observed covariate data and right part (grayed out) shows the missing part. Missingness percentage in observed population given between brackets. NonRand probability of missing is 25% for females and 75% for males

Fig. 2

Distribution of bias in CL, balanced dataset. Numbers in the bottom indicate RMSE

Fig. 3

Distribution of bias in covariate effect, balanced dataset. Numbers in the bottom indicate RMSE

Fig. 4

Estimated p _mix, balanced dataset

Fig. 5

“NonRand” dataset: bias in CL (left) and covariate effect size (right)

Fig. 6

Distribution of bias in covariate effect for the datasets with time-varying covariates for MCAR (left) and MNAR (right) scenarios