Projection-based testing for mean trajectory differences in two groups of irregularly and sparsely observed functional data has garnered significant attention in the literature because it accommodates a wide spectrum of group differences and (non-stationary) covariance structures. This article presents the derivation of the theoretical power function and the introduction of a comprehensive power and sample size (PASS) calculation toolkit tailored to the projection-based testing method developed by Wang (2021). Our approach accommodates a wide spectrum of group difference scenarios and a broad class of covariance structures governing the underlying processes. Through extensive numerical simulation, we demonstrate the robustness of this testing method by showcasing that its statistical power remains nearly unaffected even when a certain percentage of observations are missing, rendering it 'missing-immune'. Furthermore, we illustrate the practical utility of this test through analysis of two randomized controlled trials of Parkinson's disease. To facilitate implementation, we provide a user-friendly R package fPASS, complete with a detailed vignette to guide users through its practical application. We anticipate that this article will significantly enhance the usability of this potent statistical tool across a range of biostatistical applications, with a particular focus on its relevance in the design of clinical trials.

翻译：针对两组不规则稀疏观测函数数据均值轨迹差异的投影检验方法，因其能适应多种组间差异模式及（非平稳）协方差结构，近年来备受文献关注。本文推导了理论功效函数，并针对Wang (2021)提出的投影检验方法，构建了包含功效与样本量计算（PASS）的综合工具包。该方法能处理广泛的组间差异场景及底层过程协方差结构类别。通过大量数值模拟，我们证明该检验方法具有稳健性：即使观测值缺失一定比例，其统计功效仍几乎不受影响，呈现"缺失免疫"特性。此外，通过分析两项帕金森病随机对照试验数据，我们展示了该检验的实际应用价值。为便于实施，我们提供了用户友好的R语言程序包fPASS，并附有详细的使用指南。预期本文将显著增强这一强力统计工具在生物统计应用中的实用性，尤其在临床试验设计领域具有重要价值。