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**A combined efficient design for biomarker data subject to a limit of detection due to measuring instrument sensitivity.**
*(English)*
Zbl 1234.62149

Summary: Pooling specimens, a well-accepted sampling strategy in biomedical research, can be applied to reduce the cost of studying biomarkers. Even if the cost of a single assay is not a major restriction in evaluating biomarkers, pooling can be a powerful design that increases the efficiency of estimation based on data that is censored due to an instrument’s lower limit of detection (LLOD). However, there are situations when the pooling design strongly aggravates the detection limit problem. To combine the benefits of pooled assays and individual assays, hybrid designs that involve taking a sample of both pooled and individual specimens have been proposed. We examine the efficiency of these hybrid designs in estimating parameters of two systems subject to a LLOD: (1) normally distributed biomarkers with normally distributed measurement errors and pooling errors; (2) Gamma distributed biomarkers with double exponentially distributed measurement errors and pooling errors. A three-assay design and a two-assay design with replicates are applied to estimate the measurement and pooling errors. The maximum likelihood method is used to estimate the parameters. We found that the simple one-pool design, where all assays but one are random individuals and a single pooled assay includes the remaining specimens, under plausible conditions, is very efficient and can be recommended for practical use.

### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62N02 | Estimation in survival analysis and censored data |

62N01 | Censored data models |

65C60 | Computational problems in statistics (MSC2010) |

### Keywords:

measurement error; pooling; limit of detection; cost-efficient design; three-assay design; two-assay design; duplicate; one-pool design### Software:

VGAM
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XMLCite

\textit{E. F. Schisterman} et al., Ann. Appl. Stat. 5, No. 4, 2651--2667 (2011; Zbl 1234.62149)

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