# Sample size estimation for local hypothesis testing of functional data in medical studies: method comparison, recommendations, and a web application

## TL;DR

This paper compares methods for calculating sample sizes in medical studies using functional data and provides a web tool to help researchers plan their studies effectively.

## Contribution

The paper introduces a web application and provides guidelines for sample size estimation in functional data analysis, addressing a gap in medical research.

## Key findings

- Different inferential methods and data characteristics lead to varying sample size requirements for achieving target statistical power.
- Classical scalar approaches can underestimate required sample sizes when applied to functional data.
- A web-based tool was developed to assist researchers in performing a priori power analysis for functional data.

## Abstract

Recent medical studies have shown an increasing interest in inferential methods for analysing functional data, while statistical power analysis for sample size planning for such data is less explored. As a result, researchers often rely on classical scalar approaches to estimate sample size, despite working with functional data. This can substantially underestimate the required sample sizes. Moreover, there are no guidelines to assist researchers in planning, conducting, and reporting sample size estimation for studies analysing functional data.

Two functional data sets from medical sciences are used in a simulation study to explore a functional approach for sample size planning. These data represent two distinct patterns in mean function differences. Six well-known local inferential methods are evaluated for two-population comparisons of functional data. The evaluation focuses on the sample sizes required to achieve the target statistical power, under different data characteristics and assuming equal group sizes and stationary noise in the data generation process. We have also developed an interactive web-based application that helps researchers in performing a priori power analysis by allowing them to explore how changes in data characteristics affect statistical power, and consequently, the required sample size.

Our comparison revealed distinct patterns in the estimated sample sizes for different data characteristics and inferential methods. Even when based on the same baseline data, the required sample sizes to achieve a target statistical power of 0.80 differed noticeably, ranging from very small to moderately large sample sizes, depending on the mean function pattern, underlying noise characteristics, and inferential approach.

Overall, our results emphasise the importance of appropriate sample size planning and inferential method selection for valid inference in medical studies that include functional data analysis. Based on these findings, we provide guidance for researchers to follow, from study design conception through to reporting.

The online version contains supplementary material available at 10.1186/s12874-026-02772-w.