A Robust Statistical Approach to Analyse Population Pharmacokinetic Data in Critically Ill Patients Receiving Renal Replacement Therapy

Background and Aim Current approaches to antibiotic dose determination in critically ill patients requiring renal replacement therapy are primarily based on the assessment of highly heterogeneous data from small number of patients. The standard modelling approaches limit the scope of constructing robust confidence boundaries of the distribution of pharmacokinetics (PK) parameters, especially when the evaluation of possible association of demographic and clinical factors at different levels of the distribution of drug clearance is of interest. Commonly used compartmental models generally construct the inferences through a linear or non-linear mean regression, which is inadequate when the distribution is skewed, multi-modal or effected by atypical observation. In this study, we discuss the statistical challenges in robust estimation of the confidence boundaries of the PK parameters in the presence of highly heterogenous patient characteristics. Methods A novel stepwise approach to evaluate the confidence boundaries of PK parameters is proposed by combining PK modelling with mixed-effects quantile regression (MEQR) methods. Results This method allows the assessment demographic and clinical factors’ effects at any arbitrary quantiles of the outcome of interest, without restricting assumptions on the distributions. The MEQR approach allows us to investigate if the levels of association of the covariates are different at low, medium or high concentration. Conclusions This methodological assessment is deemed as a background initial approach to support the development of a class of statistical algorithm in constructing robust confidence intervals of PK parameters which can be used for developing an optimised antibiotic dosing guideline for critically ill patients requiring renal replacement therapy.