# Quantile index predictors using R package hyper.gam

## TL;DR

The paper introduces an R package called hyper.gam for analyzing single-cell protein expression data to derive functional biomarkers.

## Contribution

The novel contribution is a supervised learning framework using quantile functions for biomarker discovery in single-cell data.

## Key findings

- The hyper.gam package converts single-cell data into quantile functions for biomarker estimation.
- The package provides tools for estimating integrand surfaces and exploring them visually.
- It is designed for heterogeneous protein expression analysis but is applicable to other single-cell data types.

## Abstract

Evaluation of single-cell protein expression from immunohistochemistry images is used increasingly in biomedical research. Many proteins are used solely for phenotyping cells in the tumor microenvironment. Other proteins with meaningfully quantitative expression levels provide so-called functional protein biomarkers. There is still a limited number of methods and software tools available for utilizing the entire distributions of single-cell expression levels.

We present the R package hyper.gam, providing a supervised learning framework for deriving biomarkers based on single-cell distribution quantiles. The single-cell data are first converted into sample quantile functions, which are then used as predictors in scalar-on-function regression models to estimate the integrand surface. The estimated integrand surface defines the quantile index predictors based on the single-cell expression levels in a new test set. The package features a user-friendly interface and visual tools enabling exploration of the estimated integrand surfaces. Our tools are motivated by the need for biomarkers, taking into account heterogeneous protein expression levels in a tissue, but they can be applied to other types of single-cell data.

R package hyper.gam and vignette are available at https://CRAN.R-project.org/package=hyper.gam and https://CRAN.R-project.org/package=hyper.gam/vignettes/applications.html.