Skip to main content
SpringerLink
Log in

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

  • Original Research Article
  • Published:
Clinical Pharmacokinetics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Kumar A, Roberts D, Wood KE, et al. Duration of hypotension before initiation of effective antimicrobial therapy is the critical determinant of survival in human septic shock. Crit Care Med. 2006;34:1589–96.

    Article  Google Scholar 

  2. Patel N, Scheetz MH, Drusano GL, Lodise TP. Determination of antibiotic dosage adjustments in patients with renal impairment: elements for success. J Antimicrob Chemother. 2010;65(11):2285–90.

    Article  CAS  Google Scholar 

  3. Jamal JA, Mueller BA, Choi GY, Lipman J, Roberts JA. How can we ensure effective antibiotic dosing in critically ill patients receiving different types of renal replacement therapy? Diagn Microbiol Infect Dis. 2015;82:92–103.

    Article  CAS  Google Scholar 

  4. Sime FB, Roberts JA. Antibiotic dosing in critically ill patients receiving renal replacement therapy. Expert Rev Clin Pharmacol. 2016;9:497–9.

    Article  CAS  Google Scholar 

  5. van Lent-Evers NA, Mathot RA, Geus WP, van Hout BA, Vinks AA. Impact of goal-oriented and model-based clinical pharmacokinetic dosing of aminoglycosides on clinical outcome: a cost-effectiveness analysis. Ther Drug Monit. 1999;21:63–73.

    Article  Google Scholar 

  6. Forrest A, Nix DE, Ballow CH, Goss TF, Birmingham MC, Schentag JJ. Pharmacodynamics of intravenous ciprofloxacin in seriously ill patients. Antimicrob Agents Chemother. 1993;37:1073–81.

    Article  CAS  Google Scholar 

  7. Marik PE, Lipman J, Kobilski S, Scribante J. A prospective randomized study comparing once- versus twice-daily amikacin dosing in critically ill adult and paediatric patients. J Antimicrob Chemother. 1991;28:753–64.

    Article  CAS  Google Scholar 

  8. Dellinger RP, Levy MM, Rhodes A, et al. Surviving sepsis campaign: international guidelines for management of severe sepsis and septic shock: 2012. Crit Care Med. 2013;41:580–637.

    Article  Google Scholar 

  9. Roberts DM, Roberts JA, Roberts MS, et al. Variability of antibiotic concentrations in critically ill patients receiving continuous renal replacement therapy: a multicentre pharmacokinetic study. Crit Care Med. 2012;40:1523–8.

    Article  CAS  Google Scholar 

  10. Jamal JA, Udy AA, Lipman J, Roberts JA. The impact of variation in renal replacement therapy settings on piperacillin, meropenem, and vancomycin drug clearance in the critically ill: an analysis of published literature and dosing regimens. Crit Care Med. 2014;42:1640–50.

    Article  Google Scholar 

  11. Roberts JA, Paul SK, Akova M, et al. DALI: Defining Antibiotic Levels in Intensive care unit patients: Are current beta-lactam antibiotic doses sufficient for critically ill patients? Clin Infect Dis 2014;58(8):1072–83.

    Article  CAS  Google Scholar 

  12. Roberts JA, Choi GYS, Joynt GM, et al. SaMpling Antibiotics in Renal Replacement Therapy (SMARRT): an observational pharmacokinetic study in critically ill patients. BMC Infect Dis. 2016;16:103.

    Article  Google Scholar 

  13. Valtonen M, Tiula E, Takkunen O, Backman JT, Neuvonen PJ. Elimination of the piperacillin/tazobactam combination during continuous venovenous haemofiltration and haemodiafiltration in patients with acute renal failure. J Antimicrob Chemother. 2001;48:881–5.

    Article  CAS  Google Scholar 

  14. Capellier G, Cornette C, Boillot A, et al. Removal of piperacillin in critically ill patients undergoing continuous venovenous hemofiltration. Crit Care Med. 1998;26:88–91.

    Article  CAS  Google Scholar 

  15. Mueller SC, Majcher-Peszynska J, Hickstein H, et al. Pharmacokinetics of piperacillin-tazobactam in anuric intensive care patients during continuous venovenous hemodialysis. Antimicrob Agents Chemother. 2002;46:1557–60.

    Article  CAS  Google Scholar 

  16. van der Werf TS, Mulder PO, Zijlstra JG, Uges DR, Stegeman CA. Pharmacokinetics of piperacillin and tazobactam in critically ill patients with renal failure, treated with continuous veno-venous hemofiltration (CVVH). Intensive Care Med. 1997;23:873–7.

    Article  Google Scholar 

  17. Bilgrami I, Roberts JA, Wallis SC, et al. Meropenem dosing in critically ill patients with sepsis recieving high volume continuous veno-venous hemofiltration. Antimicrob Agents Chemother. 2010;54:2974–8.

    Article  CAS  Google Scholar 

  18. Tegeder I, Neumann F, Bremer F, Brune K, Lotsch J, Geisslinger G. Pharmacokinetics of meropenem in critically ill patients with acute renal failure undergoing continuous venovenous hemofiltration. Clin Pharmacol Ther. 1999;65:50–7.

    Article  CAS  Google Scholar 

  19. Thalhammer F, Schenk P, Burgmann H, et al. Single-dose pharmacokinetics of meropenem during continuous venovenous hemofiltration. Antimicrob Agents Chemother. 1998;42:2417–20.

    Article  CAS  Google Scholar 

  20. Ververs TF, van Dijk A, Vinks SA, et al. Pharmacokinetics and dosing regimen of meropenem in critically ill patients receiving continuous venovenous hemofiltration. Crit Care Med. 2000;28:3412–6.

    Article  CAS  Google Scholar 

  21. Giles LJ, Jennings AC, Thomson AH, Creed G, Beale RJ, McLuckie A. Pharmacokinetics of meropenem in intensive care unit patients receiving continuous veno-venous hemofiltration or hemodiafiltration. Crit Care Med. 2000;28:632–7.

    Article  CAS  Google Scholar 

  22. Krueger WA, Schroeder TH, Hutchison M, Hoffmann E, Dieterich HJ, Heininger A, et al. Pharmacokinetics of meropenem in critically ill patients with acute renal failure treated by continuous hemodiafiltration. Antimicrob Agents Chemother. 1998;42:2421–4.

    Article  CAS  Google Scholar 

  23. Valtonen M, Tiula E, Backman JT, Neuvonen PJ. Elimination of meropenem during continuous veno-venous haemofiltration and haemodiafiltration in patients with acute renal failure. J Antimicrob Chemother. 2000;45:701–4.

    Article  CAS  Google Scholar 

  24. DelDot ME, Lipman J, Tett SE. Vancomycin pharmacokinetics in critically ill patients receiving continuous venovenous haemodiafiltration. Br J Clin Pharmacol. 2004;58:259–68.

    Article  CAS  Google Scholar 

  25. Joy MS, Matzke GR, Frye RF, Palevsky PM. Determinants of vancomycin clearance by continuous venovenous hemofiltration and continuous venovenous hemodialysis. Am J Kidney Dis. 1998;31:1019–27.

    Article  CAS  Google Scholar 

  26. Macias WL, Mueller BA, Scarim SK. Vancomycin pharmacokinetics in acute renal failure: preservation of nonrenal clearance. Clin Pharmacol Ther. 1991;50:688–94.

    Article  CAS  Google Scholar 

  27. Boereboom FT, Ververs FF, Blankestijn PJ, Savelkoul TJ, van Dijk A. Vancomycin clearance during continuous venovenous haemofiltration in critically ill patients. Intensive Care Med. 1999;25:1100–4.

    Article  CAS  Google Scholar 

  28. Santre C, Leroy O, Simon M, et al. Pharmacokinetics of vancomycin during continuous hemodiafiltration. Intensive Care Med. 1993;19:347–50.

    Article  CAS  Google Scholar 

  29. Davies SP, Azadian BS, Kox WJ, Brown EA. Pharmacokinetics of ciprofloxacin and vancomycin in patients with acute renal failure treated by continuous haemodialysis. Nephrol Dial Transplant. 1992;7:848–54.

    CAS  PubMed  Google Scholar 

  30. Roberts DM, Roberts JA, Roberts MS, et al. Variability of antibiotic concentrations in critically ill patients receiving continuous renal replacement therapy: a multicentre pharmacokinetic study. Crit Care Med. 2012;40(5):1523–8.

    Article  CAS  Google Scholar 

  31. Nielsen EI, Friberg LE. Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs. Pharmacol Rev. 2013;65:1053–90.

    Article  Google Scholar 

  32. Upton RN, Mould DR. Basic concepts in population modeling, simulation, and model-based drug development: part 3. Introduction to pharmacodynamic modeling methods. CPT Pharmacometrics Syst Pharmacol 2014;3:e88.

  33. Beal SL, Sheiner LB. NONMEM User Guides (I-VIII). San Francisco: University of California at San Francisco; 1998.

    Google Scholar 

  34. Koenker R. Quantile regression. Cambridge: Cambridge University Press; 2005.

    Book  Google Scholar 

  35. Galarza Morales C, Bandyopadhyay D, Lachos VH Quantile Regression for Linear Mixed Models: A Stochastic Approximation EM approach. Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas; 2015;2.

  36. Beyerlein A. Quantile regression: opportunities and challenges from a user’s perspective. Am J Epidemiol. 2014;180:330–1.

    Article  Google Scholar 

  37. Tian Y, Li EQ, Tian M. Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates. Comput Stat. 2016;31:1031–57.

    Article  Google Scholar 

  38. Geraci M. Linear quantile mixed models: the lqmm package for laplace quantile regression. J Stat Softw. 2014;57:29.

    Article  Google Scholar 

  39. Smith LB, Fuentes M, Gordon-Larsen P, Reich BJ. Quantile regression for mixed models with an application to examine blood pressure trends in China. Ann Appl Stat. 2015;9:1226–46.

    Article  Google Scholar 

  40. Geraci M, Bottai M. Linear quantile mixed models. Stat Comput. 2014;24:461–79.

    Article  Google Scholar 

  41. Lim HS, Chong YP, Noh YH, Jung JA, Kim YS. Exploration of optimal dosing regimens of vancomycin in patients infected with methicillin-resistant Staphylococcus aureus by modeling and simulation. J Clin Pharm Ther. 2014;39:196–203.

    Article  CAS  Google Scholar 

  42. Bohler J, Donauer J, Keller F. Pharmacokinetic principles during continuous renal replacement therapy: drugs and dosage. Kidney Int 1999;56(Supplement 72):S24–8.

    Article  Google Scholar 

  43. Bugge JF. Pharmacokinetics and drug dosing adjustments during continuous venovenous hemofiltration or hemodiafiltration in critically ill patients. Acta Anaesthesiol Scand. 2001;45:929–34.

    Article  CAS  Google Scholar 

  44. Li AM, Gomersall CD, Choi G, Tian Q, Joynt GM, Lipman J. A systematic review of antibiotic dosing regimens for septic patients receiving continuous renal replacement therapy: do current studies supply sufficient data? J Antimicrob Chemother. 2009;64:929–37.

    Article  CAS  Google Scholar 

Download references

Acknowledgements

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).

Author information

Authors and Affiliations

  1. Melbourne EpiCentre, University of Melbourne and Melbourne Health, Melbourne, VIC, Australia

    Sanjoy Ketan Paul

  2. Burns Trauma and Critical Care Research Centre, University of Queensland Centre for Clinical Research, The University of Queensland, Brisbane, QLD, Australia

    Jason A. Roberts, Jeffrey Lipman & Renae Deans

  3. Centre for Translational Anti-Infective Pharmacodynamics, The University of Queensland, Brisbane, QLD, Australia

    Jason A. Roberts & Jeffrey Lipman

  4. Royal Brisbane and Women’s Hospital, Brisbane, QLD, Australia

    Jason A. Roberts

  5. Clinical Trials and Biostatistics Unit, QIMR Berghofer Medical Research Institute, Brisbane, QLD, Australia

    Mayukh Samanta

  6. The Royal Melbourne Hospital, City Campus, 7 East, Main Building, Grattan Street, Parkville, VIC, 3050, Australia

    Sanjoy Ketan Paul

Authors
  1. Sanjoy Ketan Paul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jason A. Roberts
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jeffrey Lipman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Renae Deans
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mayukh Samanta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sanjoy Ketan Paul.

Ethics declarations

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Paul, S.K., Roberts, J.A., Lipman, J. et al. A Robust Statistical Approach to Analyse Population Pharmacokinetic Data in Critically Ill Patients Receiving Renal Replacement Therapy. Clin Pharmacokinet 58, 263–270 (2019). https://doi.org/10.1007/s40262-018-0690-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40262-018-0690-1

Search

Navigation