Evaluating the change in gene expression is a common goal in many research areas, such as in toxicological studies as well as in clinical trials. In practice, the analysis is often based on multiple t-tests evaluated at the observed time points. This severely limits the accuracy of determining the time points at which the gene changes in expression. Even if a parametric approach is chosen, the analysis is often restricted to identifying the onset of an effect. In this paper, we propose a parametric method to identify the time frame where the gene expression significantly changes. This is achieved by fitting a parametric model to the time-response data and constructing a confidence band for its first derivative. The confidence band is derived by a flexible two step bootstrap approach, which can be applied to a wide variety of possible curves. Our method focuses on the first derivative, since it provides an easy to compute and reliable measure for the change in response. It is summarised in terms of a hypothesis test, such that rejecting the null hypothesis means detecting a significant change in gene expression. Furthermore, a method for calculating confidence intervals for time points of interest (e.g. the beginning and end of significant change) is developed. We demonstrate the validity of our approach through a simulation study and present a variety of different applications to mouse gene expression data from a study investigating the effect of a Western diet on the progression of non-alcoholic fatty liver disease.

翻译：评估基因表达变化是毒理学研究和临床试验等多个研究领域的共同目标。实践中，分析通常基于在观测时间点进行多重t检验。这严重限制了确定基因表达发生变化时间点的准确性。即使选择参数化方法，分析也往往局限于识别效应的起始点。本文提出一种参数化方法，用于识别基因表达发生显著变化的时间范围。该方法通过对时间-响应数据拟合参数模型，并为其一阶导数构建置信带来实现。置信带通过灵活的两步自助法推导得出，可适用于多种可能的曲线类型。我们的方法聚焦于一阶导数，因为它为响应变化提供了易于计算且可靠的度量。该方法以假设检验的形式进行总结，拒绝原假设即意味着检测到基因表达的显著变化。此外，本文还开发了计算特定时间点（如显著变化的起始点和结束点）置信区间的方法。我们通过模拟研究证明了该方法的有效性，并以研究西方饮食对非酒精性脂肪肝疾病进展影响的小鼠基因表达数据为例，展示了多种不同的应用场景。