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Further Evaluation of Covariate Analysis using Empirical Bayes Estimates in Population Pharmacokinetics: the Perception of Shrinkage and Likelihood Ratio Test

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Abstract

Covariate analysis based on population pharmacokinetics (PPK) is used to identify clinically relevant factors. The likelihood ratio test (LRT) based on nonlinear mixed effect model fits is currently recommended for covariate identification, whereas individual empirical Bayesian estimates (EBEs) are considered unreliable due to the presence of shrinkage. The objectives of this research were to investigate the type I error for LRT and EBE approaches, to confirm the similarity of power between the LRT and EBE approaches from a previous report and to explore the influence of shrinkage on LRT and EBE inferences. Using an oral one-compartment PK model with a single covariate impacting on clearance, we conducted a wide range of simulations according to a two-way factorial design. The results revealed that the EBE-based regression not only provided almost identical power for detecting a covariate effect, but also controlled the false positive rate better than the LRT approach. Shrinkage of EBEs is likely not the root cause for decrease in power or inflated false positive rate although the size of the covariate effect tends to be underestimated at high shrinkage. In summary, contrary to the current recommendations, EBEs may be a better choice for statistical tests in PPK covariate analysis compared to LRT. We proposed a three-step covariate modeling approach for population PK analysis to utilize the advantages of EBEs while overcoming their shortcomings, which allows not only markedly reducing the run time for population PK analysis, but also providing more accurate covariate tests.

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Acknowledgments

There is no conflict of interest. Dr. Min Yuan is supported by the National Science Foundation of China (NSFC), Grant No. 11271346 and the Fundamental Research Funds for the Central Universities (No.WK0010000052).

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Author notes

    Authors and Affiliations

    1. Janssen Research and Development, 920 Route 202, Raritan, New Jersey, 08869, USA

      Xu Steven Xu & Jose Pinheiro

    2. School of public health administration, Anhui Medical University, Hefei, China

      Min Yuan

    3. University of Florida, Gainesville, Florida, USA

      Haitao Yang

    4. Bristol-Myers Squibb, Princeton, New Jersey, USA

      Yan Feng

    5. Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China

      Jinfeng Xu

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    1. Xu Steven Xu
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    2. Min Yuan
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    3. Haitao Yang
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    4. Yan Feng
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    5. Jinfeng Xu
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    Corresponding author

    Correspondence to Xu Steven Xu.

    Additional information

    Xu Steven Xu and Min Yuan contributed equally to this work.

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    Supplementary Fig. 1

    Comparison of root mean square error between likelihood ratio test (LRT) and EBEs. The size of each symbol is scaled based on the number of successful runs for the corresponding simulation scenario. (GIF 19 kb)

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    Xu, X.S., Yuan, M., Yang, H. et al. Further Evaluation of Covariate Analysis using Empirical Bayes Estimates in Population Pharmacokinetics: the Perception of Shrinkage and Likelihood Ratio Test. AAPS J 19, 264–273 (2017). https://doi.org/10.1208/s12248-016-0001-4

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    • DOI: https://doi.org/10.1208/s12248-016-0001-4

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