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A Bayesian Adjustment for Multiplicative Measurement Errors for a Calibration Problem with Application to a Stem Cell Study

Authors

  • Peng Zhang,

    Corresponding author
    1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
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  • Juxin Liu,

    1. Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E6, Canada
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  • Jianghu Dong,

    1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
    2. Department of Medicine, University of Alberta, Edmonton, Alberta T6G 2B7, Canada
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  • Jelena L. Holovati,

    1. Department of Laboratory Medicine and Pathology, University of Alberta, Edmonton, Alberta T6G 2B7, Canada
    2. Hematopoietic Stem Cell Laboratory, Canadian Blood Services, Edmonton, Alberta T6G 2R8, Canada
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  • Brenda Letcher,

    1. Hematopoietic Stem Cell Laboratory, Canadian Blood Services, Edmonton, Alberta T6G 2R8, Canada
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  • Locksley E. McGann

    1. Department of Laboratory Medicine and Pathology, University of Alberta, Edmonton, Alberta T6G 2B7, Canada
    2. Hematopoietic Stem Cell Laboratory, Canadian Blood Services, Edmonton, Alberta T6G 2R8, Canada
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email: pengz@ualberta.ca

Abstract

Summary We develop a Bayesian approach to a calibration problem with one interested covariate subject to multiplicative measurement errors. Our work is motivated by a stem cell study with the objective of establishing the recommended minimum doses for stem cell engraftment after a blood transplant. When determining a safe stem cell dose based on the prefreeze samples, the postcryopreservation recovery rate enters in the model as a multiplicative measurement error term, as shown in the model (2). We examine the impact of ignoring measurement errors in terms of asymptotic bias in the regression coefficient. According to the general structure of data available in practice, we propose a two-stage Bayesian method to perform model estimation via R2WinBUGS (Sturtz, Ligges, and Gelman, 2005, Journal of Statistical Software12, 1–16). We illustrate this method by the aforementioned motivating example. The results of this study allow routine peripheral blood stem cell processing laboratories to establish recommended minimum stem cell doses for transplant and develop a systematic approach for further deciding whether the postthaw analysis is warranted.

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