Janošová Markéta, Katina Stanislav, Hanes Jozef
Department of Mathematics and Statistics, Masaryk University Faculty of Science, Brno, Czech Republic.
Slovak Academy of Sciences Institute of Neuroimmunology, Bratislava, Slovakia.
Pharmacol Res Perspect. 2025 Feb;13(1):e70048. doi: 10.1002/prp2.70048.
Laboratory measurements used for safety assessments in clinical trials are subject to the limits of the used laboratory equipment. These limits determine the range of values which the equipment can accurately measure. When observations fall outside the measurable range, this creates a problem in estimating parameters of the normal distribution. It may be tempting to use methods of estimation that are easy to implement, however selecting an incorrect method may lead to biased estimates (under- or overestimation) and change the research outcomes, for example, incorrect result of two-sample test about means when comparing two populations or biased estimation of regression line. In this article, we consider the use of four methods: ignoring unmeasured observations, replacing unmeasured observations with a multiple of the limit, using a truncated normal distribution, and using a normal distribution with censored observations. To compare these methods we designed a simulation study and measured their accuracy in several different situations using relative error , ratio , and mean square errors of both parameters. Based on the results of this simulation study, if the amount of observations outside of measurable range is below 40%, we recommend using a normal distribution with censored observations in practice. These recommendations should be incorporated into guidelines for good statistical practice. If the amount of observations outside of measurable range exceeds 40%, we advise not to use the data for any statistical analysis. To illustrate how the choice of method can affect the estimates, we applied the methods to real-life laboratory data.
临床试验中用于安全性评估的实验室测量受所用实验室设备的限制。这些限制决定了设备能够准确测量的值的范围。当观测值落在可测量范围之外时，这会在估计正态分布参数时产生问题。可能会倾向于使用易于实施的估计方法，然而选择错误的方法可能会导致有偏差的估计（低估或高估）并改变研究结果，例如，在比较两个总体时两样本均值检验的错误结果或回归线的有偏差估计。在本文中，我们考虑使用四种方法：忽略未测量的观测值、用极限值的倍数替换未测量的观测值、使用截断正态分布以及使用带有删失观测值的正态分布。为了比较这些方法，我们设计了一项模拟研究，并使用相对误差、比率以及两个参数的均方误差在几种不同情况下测量了它们的准确性。基于这项模拟研究的结果，如果超出可测量范围的观测值数量低于40%，我们建议在实际中使用带有删失观测值的正态分布。这些建议应纳入良好统计实践指南。如果超出可测量范围的观测值数量超过40%，我们建议不要将这些数据用于任何统计分析。为了说明方法的选择如何影响估计，我们将这些方法应用于实际的实验室数据。
