Clinical Pharmacokinetics

, Volume 58, Issue 2, pp 263–270 | Cite as

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

  • Sanjoy Ketan PaulEmail author
  • Jason A. Roberts
  • Jeffrey Lipman
  • Renae Deans
  • Mayukh Samanta
Original Research Article


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.


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.


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.


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.



JR and JL conceived the SMARRT study, which was subsequently designed by SKP and JR. SKP conceived the methodological idea and the analysis approaches. MS and SKP jointly developed the statistical programmes and conducted analyses. The first draft of the manuscript was developed by SKP and MS, and all authors contributed to the final version of the manuscript. The authors also acknowledge Mr. Julius Agbeve for his contributions to the development and management of the clinical database for the SMARRT study. SKP and JR had full access to all the data in the study, with SKP being the guarantor, taking overall responsibility for the integrity of the data. The University of Melbourne gratefully acknowledges the support from the Australian Government’s National Collaborative Research Infrastructure Strategy (NCRIS) initiative through Therapeutic Innovation Australia. This study was also supported by funding from the National Health and Medical Research Council of Australia (Project Grant APP1044941). JR received salary funding from the National Health and Medical Research Council of Australia, Practitioner Fellowship (APP1117065), and would like to acknowledge funding from the Australian National Health and Medical Research Council for a Centre of Research Excellence Grant (APP1099452).

Compliance with Ethical Standards

Conflicts of interest

Sanjoy Ketan Paul has acted as a consultant and/or speaker for Novartis, GI Dynamics, Roche, AstraZeneca, Guangzhou Zhongyi Pharmaceutical and Amylin Pharmaceuticals LLC, and has received GRANTs in support of investigator and investigator-initiated clinical studies from Merck, Novo Nordisk, AstraZeneca, Hospira, Amylin Pharmaceuticals, Sanofi-Aventis and Pfizer. Jeffrey Lipman declares an unrelated consultancy for MSD. Jason A. Roberts declares unrelated consultancies for bioMerieux, MSD, Astellas, Accelerate Diagnostics, Bayer and Infectopharm over the last 3 years, as well as investigator-initiated Grants from MSD and Cardeas Pharma. Mayukh Samanta and Renae Deans have no conflicts of interest to declare.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Sanjoy Ketan Paul
    • 1
    • 6
    Email author
  • Jason A. Roberts
    • 2
    • 3
    • 4
  • Jeffrey Lipman
    • 2
    • 3
  • Renae Deans
    • 2
  • Mayukh Samanta
    • 5
  1. 1.Melbourne EpiCentreUniversity of Melbourne and Melbourne HealthMelbourneAustralia
  2. 2.Burns Trauma and Critical Care Research Centre, University of Queensland Centre for Clinical ResearchThe University of QueenslandBrisbaneAustralia
  3. 3.Centre for Translational Anti-Infective PharmacodynamicsThe University of QueenslandBrisbaneAustralia
  4. 4.Royal Brisbane and Women’s HospitalBrisbaneAustralia
  5. 5.Clinical Trials and Biostatistics UnitQIMR Berghofer Medical Research InstituteBrisbaneAustralia
  6. 6.The Royal Melbourne HospitalParkvilleAustralia

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