TY - JOUR

T1 - Prediction intervals for all of M future observations based on linear random effects models

AU - Menssen, Max

AU - Schaarschmidt, Frank

N1 - Funding Information: The authors have to thank Clemens Buczilowski for his technical support and Olaf Menssen for fruitful discussions. Furthermore we have to thank the reviewers for reading the manuscript and for their helpful comments. Open Access funding enabled and organized by Projekt DEAL.

PY - 2022/7/3

Y1 - 2022/7/3

N2 - 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

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

KW - Satterthwaite approximation

KW - anti-drug antibody

KW - assay qualification

KW - bootstrap calibration

KW - historical control data

UR - http://www.scopus.com/inward/record.url?scp=85122785428&partnerID=8YFLogxK

U2 - https://doi.org/10.1111/stan.12260

DO - https://doi.org/10.1111/stan.12260

M3 - Article

VL - 76

SP - 283

EP - 308

JO - Statistica Neerlandica

JF - Statistica Neerlandica

SN - 0039-0402

IS - 3

ER -