# LorDist: a novel method for calculating the distance based on functional data analysis with application to longitudinal microbial data

## TL;DR

LorDist is a new method for analyzing longitudinal microbiome data that better captures temporal patterns and improves detection of biological differences.

## Contribution

LorDist introduces a novel distance calculation method using functional data analysis for longitudinal microbiome studies.

## Key findings

- LorDist performs robustly even with up to 60% sparsity and varying sequencing depths.
- LorDist outperforms existing methods in capturing meaningful differences in longitudinal microbiome data.
- LorDist successfully analyzed real-world datasets related to inflammatory bowel disease and infant gut development.

## Abstract

Longitudinal human microbial data offer insights into microbiome dynamics over time. Traditional methods usually overlook temporal relationships among samples from the same subject. Here, we presented the Longitudinal Microbial Data Distance (LorDist) method, which uses functional data fitting to construct a distance matrix integrating information from the same subject at different time points. Simulation data showed that LorDist handled well up to 60% sparseness and worked robustly with various sequencing depths and time points. Empirical data analysis demonstrated that LorDist excels in capturing differences across subjects with longitudinal microbiome data. LorDist presented the potential of longitudinal microbial data in addressing temporal autocorrelation and distinguishing phenotypes.

Longitudinal analysis of the human microbiome is critical for understanding its dynamic role in health and disease. However, current analytical approaches struggle to address key challenges, such as data sparsity and irregular sampling, inherent to time-series microbiome studies. Here, we developed longitudinal microbial data distance (LorDist), an innovative method leveraging functional data analysis to model temporal microbial dynamics with enhanced precision. Compared to existing methods, LorDist consistently outperforms in discerning biologically meaningful group differences, even in highly sparse data sets or under fluctuating sequencing depths. Our findings demonstrate LorDist’s robust performance on real-world data sets involving inflammatory bowel disease and infant gut development. By explicitly preserving the temporal structure inherent in microbiome data, LorDist enables robust detection of subtle yet critical biological shifts, paving the way for improved diagnostics and personalized therapeutic strategies in microbiome science.