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Projection-based testing for mean trajectory differences in two groups ofirregularly and sparsely observed functional data has garnered significantattention in the literature because it accommodates a wide spectrum of groupdifferences and (non-stationary) covariance structures. This article presentsthe derivation of the theoretical power function and the introduction of acomprehensive power and sample size (PASS) calculation toolkit tailored to theprojection-based testing method developed by Wang (2021). Our approachaccommodates a wide spectrum of group difference scenarios and a broad class ofcovariance structures governing the underlying processes. Through extensivenumerical simulation, we demonstrate the robustness of this testing method byshowcasing that its statistical power remains nearly unaffected even when acertain percentage of observations are missing, rendering it 'missing-immune'.Furthermore, we illustrate the practical utility of this test through analysisof two randomized controlled trials of Parkinson's disease. To facilitateimplementation, we provide a user-friendly R package fPASS, complete with adetailed vignette to guide users through its practical application. Weanticipate that this article will significantly enhance the usability of thispotent statistical tool across a range of biostatistical applications, with aparticular focus on its relevance in the design of clinical trials.

Power and sample size calculation of two-sample projection-based testing for sparsely observed functional data