Prediction intervals for all of M future observations based on linear random effects models

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Original languageEnglish
Pages (from-to)283-308
Number of pages26
JournalStatistica Neerlandica
Volume76
Issue number3
Early online date19 Dec 2021
Publication statusPublished - 3 Jul 2022

Abstract

In many pharmaceutical and biomedical applications such as assay validation, assessment of historical control data or the detection of anti-drug antibodies, the calculation and interpretation of prediction intervals (PI) is of interest. The present study provides two novel methods for the calculation of prediction intervals based on linear random effects models and REML estimation. Unlike other REML based PI found in literature, both intervals reflect the uncertainty related with the estimation of the prediction variance. The first PI is based on Satterthwaite approximation. For the other PI, a bootstrap calibration approach that we will call quantile-calibration was used. Due to the calibration process this PI can be easily computed for more than one future observation and based on balanced and unbalanced data as well. In order to compare the coverage probabilities of the proposed PI with those of four intervals found in literature, Monte Carlo simulations were run for two relatively complex random effects models and a broad range of parameter settings. The quantile-calibrated PI was implemented in the statistical software R and is available in the predint package

Keywords

    Satterthwaite approximation, anti-drug antibody, assay qualification, bootstrap calibration, historical control data

ASJC Scopus subject areas

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Prediction intervals for all of M future observations based on linear random effects models. / Menssen, Max; Schaarschmidt, Frank.
In: Statistica Neerlandica, Vol. 76, No. 3, 03.07.2022, p. 283-308.

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abstract = "In many pharmaceutical and biomedical applications such as assay validation, assessment of historical control data or the detection of anti-drug antibodies, the calculation and interpretation of prediction intervals (PI) is of interest. The present study provides two novel methods for the calculation of prediction intervals based on linear random effects models and REML estimation. Unlike other REML based PI found in literature, both intervals reflect the uncertainty related with the estimation of the prediction variance. The first PI is based on Satterthwaite approximation. For the other PI, a bootstrap calibration approach that we will call quantile-calibration was used. Due to the calibration process this PI can be easily computed for more than one future observation and based on balanced and unbalanced data as well. In order to compare the coverage probabilities of the proposed PI with those of four intervals found in literature, Monte Carlo simulations were run for two relatively complex random effects models and a broad range of parameter settings. The quantile-calibrated PI was implemented in the statistical software R and is available in the predint package",
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AU - Menssen, Max

AU - Schaarschmidt, Frank

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AB - In many pharmaceutical and biomedical applications such as assay validation, assessment of historical control data or the detection of anti-drug antibodies, the calculation and interpretation of prediction intervals (PI) is of interest. The present study provides two novel methods for the calculation of prediction intervals based on linear random effects models and REML estimation. Unlike other REML based PI found in literature, both intervals reflect the uncertainty related with the estimation of the prediction variance. The first PI is based on Satterthwaite approximation. For the other PI, a bootstrap calibration approach that we will call quantile-calibration was used. Due to the calibration process this PI can be easily computed for more than one future observation and based on balanced and unbalanced data as well. In order to compare the coverage probabilities of the proposed PI with those of four intervals found in literature, Monte Carlo simulations were run for two relatively complex random effects models and a broad range of parameter settings. The quantile-calibrated PI was implemented in the statistical software R and is available in the predint package

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