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Evaluation and Comparison of Simple Multiple Model, Richer Data Multiple Model, and Sequential Interacting Multiple Model (IMM) Bayesian Analyses of Gentamicin and Vancomycin Data Collected From Patients Undergoing Cardiothoracic Surgery

Macdonald, Iona MSc; Staatz, Christine E PhD†‖; Jelliffe, Roger W MD; Thomson, Alison H PhD*†§

doi: 10.1097/FTD.0b013e318161a38c
Original Article

This study compared the abilities of three Bayesian algorithms-simple multiple model (SMM) using a single creatinine measurement; richer data multiple model (RMM) using all creatinine measurements; and the sequential interacting multiple model (IMM)-to describe gentamicin and vancomycin concentration-time data from patients within a cardiothoracic surgery unit who had variable renal function. All algorithms start with multiple sets of discrete parameter support points obtained from nonparametric population modeling. The SMM and RMM Bayesian algorithms then estimate their Bayesian posterior probabilities by conventionally assuming that the estimated parameter distributions are fixed and unchanging throughout the period of data analysis. In contrast, the IMM sequential Bayesian algorithm permits parameter estimates to jump from one population model support point to another, as new data are analyzed, if the probability of a different support point fitting the more recent data is more likely. Several initial IMM jump probability settings were examined-0.0001%, 0.1%, 3%, and 10%-and a probability range of 0.0001% to 50%. The data sets comprised 550 gentamicin concentration measurements from 135 patients and 555 vancomycin concentration measurements from 139 patients. The SMM algorithm performed poorly with both antibiotics. Improved precision was obtained with the RMM algorithm. However, the IMM algorithm fitted the data with the highest precision. A 3% jump probability gave the best estimates. In contrast, the IMM 0.0001% to 50% range setting performed poorly, especially for vancomycin. In summary, the IMM algorithm described and tracked drug concentration data well in these clinically unstable patients. Further investigation of this new approach in routine clinical care and optimal dosage design is warranted.

From the *Pharmacy Department, Western Infirmary, Glasgow, UK; †Division of Cardiovascular and Medical Sciences, University of Glasgow, Glasgow, UK; ‡Laboratory of Applied Pharmacokinetics, School of Medicine, University of Southern California, Los Angeles, California; and §Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, Glasgow, UK.

Received for publication July 9, 2007; accepted November 5, 2007.

Present address: ¶Pharmacy Department, Gartnavel General Hospital, Glasgow, UK; and ‖School of Pharmacy, University of Queensland, Brisbane, Australia.

The MM-USCPACK software was developed with support from National Institutes of Health grants GM-068968 and EB-005803. CES was supported by a National Health and Medical Research Council, Neil Hamilton Fairley Fellowship.

Correspondence: Iona Macdonald, MSc, Pharmacy Department, Gartnavel General Hospital, 1053 Great Western Road, Glasgow, UK (e-mail:

© 2008 Lippincott Williams & Wilkins, Inc.