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 restricted maximum likelihood (REML) estimation. Unlike other REML-based PI found in the 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 the 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.

中文翻译：

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基于线性随机效应模型的所有 M 个未来观测值的预测区间

在许多制药和生物医学应用中，例如化验验证、历史对照数据的评估或抗药物抗体的检测，预测区间 (PI) 的计算和解释是令人感兴趣的。本研究为基于线性随机效应模型和限制最大似然 (REML) 估计的预测区间计算提供了两种新方法。与文献中发现的其他基于 REML 的 PI 不同，这两个区间都反映了与预测方差估计相关的不确定性。第一个 PI 基于 Satterthwaite 近似。对于另一个 PI，我们称之为分位数校准的自举校准方法被使用了。由于校准过程，这个 PI 可以很容易地计算出来，用于未来不止一次的观察，也可以基于平衡和不平衡的数据。为了将提议的 PI 的覆盖概率与文献中发现的四个区间的​​覆盖概率进行比较，对两个相对复杂的随机效应模型和广泛的参数设置进行了蒙特卡罗模拟。分位数校准的 PI 在统计软件 R 中实现，可在 predint 包中获得。