FunSpace: A functional and spatial analytic approach to cell imaging data using entropy measures

Functional protein biomarkers based on distributions of expression levels in single-cell imaging data

MOTIVATION

The intra-tumor heterogeneity of protein expression is well recognized and may provide important information for cancer prognosis and predicting treatment responses. Analytic methods that account for spatial heterogeneity remain methodologically complex and computationally demanding for single-cell protein expression. For many functional proteins, single-cell expressions vary independently of spatial localization in a substantial proportion of the tumor tissues, and incorporation of spatial information may not affect the prognostic value of such protein biomarkers.

RESULTS

We developed a new framework for using the distributions of functional single-cell protein expression levels as cancer biomarkers. The quantile functions of single-cell expressions are used to fully capture the heterogeneity of protein expression across all cancer cells. The quantile index (QI) biomarker is defined as an integral of an unspecified function which may depend linearly or nonlinearly on a tissue-specific quantile function. Linear and nonlinear versions of QI biomarkers based on single-cell expressions of ER, Ki67, TS, and CyclinD3 were derived and evaluated as predictors of progression-free survival or high mitotic index in a large breast cancer dataset. We evaluated performance and demonstrated the advantages of nonlinear QI biomarkers through simulation studies.

AVAILABILITY AND IMPLEMENTATION

The associated R package Qindex is available at https://CRAN.R-project.org/package=Qindex and R package hyper.gam is available at https://github.com/tingtingzhan/hyper.gam. Examples of R code and detailed instructions could be found in vignette quantile-index-predictor (https://CRAN.R-project.org/package=hyper.gam/vignettes/applications.html#quantile-index-predictor).

Benchmarking Spatial Co-Localization Methods for Single-Cell Multiplex Imaging Data with Applications to High-Grade Serous Ovarian and Triple Negative Breast Cancer

Single-cell multiplex imaging (scMI) measures cell locations and phenotypes within a tissue and can be used to understand the tumor microenvironment. In scMI studies, it is often of interest to quantify spatial co-localization of immune cells and its association with clinical outcomes; however, it remains unknown which of the many available spatial indices have adequate power to detect spatial within-sample co-localization and its association with patient outcomes, such as survival. In this study, the performance of six frequentist metrics of spatial co-localization used in scMI studies were evaluated. Simulated data was used to assess the power and type I error of these spatial metrics to detect signficant co-localization. Furthermore, these spatial co-localization methods were applied to two scMI studies - a high-grade serous ovarian cancer (HGSOC) study and triple negative breast cancer (TNBC) study - to detect within-sample co-localization between cell types and their sensitivity to detect differences in survival across samples. In the simulation study, Ripley's K had the greatest power to identify co-localization followed closely by pair correlation g; all other statistics showed little power across all simulation scenarios. In the application of the methods to cancer studies, the results consistently point to pair correlation g and Ripley's K as indices with the most power for detecting significant co-localization in scMI data. Furthermore, pair correlation g, Ripley's K, and the scLMM index were most effective for estimating between-sample associations between level of co-localization and survival.

Detecting Clinically Relevant Topological Structures in Multiplexed Spatial Proteomics Imaging Using TopKAT

Novel multiplexed spatial proteomics imaging platforms expose the spatial architecture of cells in the tumor microenvironment (TME). The diverse cell population in the TME, including its spatial context, has been shown to have important clinical implications, correlating with disease prognosis and treatment response. The accelerating implementation of spatial proteomic technologies motivates new statistical models to test if cell-level images associate with patient-level endpoints. Few existing methods can robustly characterize the geometry of the spatial arrangement of cells and also yield both a valid and powerful test for association with patient-level outcomes. We propose a topology-based approach that combines persistent homology with kernel testing to determine if topological structures created by cells predict continuous, binary, or survival clinical endpoints. We term our method TopKAT (Topological Kernel Association Test) and show that it can be more powerful than statistical tests grounded in the spatial point process model, particularly when cells arise along the boundary of a ring. We demonstrate the properties of TopKAT through simulation studies and apply it to two studies of triple negative breast cancer where we show that TopKAT recovers clinically relevant topological structures in the spatial distribution of immune and tumor cells.

Spatial cell graph analysis reveals skin tissue organization characteristic for cutaneous T cell lymphoma

Cutaneous T-cell lymphomas (CTCLs) are non-Hodgkin lymphomas caused by malignant T cells which migrate to the skin and lead to rash-like lesions which can be difficult to distinguish from inflammatory skin conditions like atopic dermatitis (AD) and psoriasis (PSO). To characterize CTCL in comparison to these differential diagnoses, we carried out multi-antigen imaging on 69 skin tissue samples (21 CTCL, 23 AD, 25 PSO). The resulting protein abundance maps were then analyzed via scoring functions to quantify the heterogeneity of the individual cells' neighborhoods within spatial graphs inferred from the cells' positions in the tissue samples. Our analyses reveal characteristic patterns of skin tissue organization in CTCL as compared to AD and PSO, including a combination of increased local entropy and egophily in T-cell neighborhoods. These results could not only pave the way for high-precision diagnosis of CTCL, but may also facilitate further insights into cellular disease mechanisms.

mxfda: a comprehensive toolkit for functional data analysis of single-cell spatial data

Summary

Technologies that produce spatial single-cell (SC) data have revolutionized the study of tissue microstructures and promise to advance personalized treatment of cancer by revealing new insights about the tumor microenvironment. Functional data analysis (FDA) is an ideal analytic framework for connecting cell spatial relationships to patient outcomes, but can be challenging to implement. To address this need, we present mxfda, an R package for end-to-end analysis of SC spatial data using FDA. mxfda implements a suite of methods to facilitate spatial analysis of SC imaging data using FDA techniques.

Availability and implementation

The mxfda R package is freely available at https://cran.r-project.org/package=mxfda and has detailed documentation, including four vignettes, available at http://juliawrobel.com/mxfda/.

Computational methods and biomarker discovery strategies for spatial proteomics: a review in immuno-oncology

Advancements in imaging technologies have revolutionized our ability to deeply profile pathological tissue architectures, generating large volumes of imaging data with unparalleled spatial resolution. This type of data collection, namely, spatial proteomics, offers invaluable insights into various human diseases. Simultaneously, computational algorithms have evolved to manage the increasing dimensionality of spatial proteomics inherent in this progress. Numerous imaging-based computational frameworks, such as computational pathology, have been proposed for research and clinical applications. However, the development of these fields demands diverse domain expertise, creating barriers to their integration and further application. This review seeks to bridge this divide by presenting a comprehensive guideline. We consolidate prevailing computational methods and outline a roadmap from image processing to data-driven, statistics-informed biomarker discovery. Additionally, we explore future perspectives as the field moves toward interfacing with other quantitative domains, holding significant promise for precision care in immuno-oncology.

A Spatial Omnibus Test (SPOT) for Spatial Proteomic Data

MOTIVATION

Spatial proteomics can reveal the spatial organization of immune cells in the tumor immune microenvironment. Relating measures of spatial clustering, such as Ripley's K or Besag's L, to patient outcomes may offer important clinical insights. However, these measures require pre-specifying a radius in which to quantify clustering, yet no consensus exists on the optimal radius which may be context-specific.

RESULTS

We propose a SPatial Omnibus Test (SPOT) which conducts this analysis across a range of candidate radii. At each radius, SPOT evaluates the association between the spatial summary and outcome, adjusting for confounders. SPOT then aggregates results across radii using the Cauchy combination test, yielding an omnibus P-value characterizing the overall degree of association. Using simulations, we verify that the type I error rate is controlled and show SPOT can be more powerful than alternatives. We also apply SPOT to ovarian and lung cancer studies.

AVAILABILITY AND IMPLEMENTATION

An R package and tutorial are provided at https://github.com/sarahsamorodnitsky/SPOT.

A Spatial Omnibus Test (SPOT) for Spatial Proteomic Data

Spatial proteomics can reveal the spatial organization of immune cells in the tumor immune microenvironment. Relating measures of spatial clustering, such as Ripley's K or Besag's L, to patient outcomes may offer important clinical insights. However, these measures require pre-specifying a radius in which to quantify clustering, yet no consensus exists on the optimal radius which may be context-specific. We propose a SPatial Omnibus Test (SPOT) which conducts this analysis across a range of candidate radii. At each radius, SPOT evaluates the association between the spatial summary and outcome, adjusting for confounders. SPOT then aggregates results across radii using the Cauchy combination test, yielding an omnibus p-value characterizing the overall degree of association. Using simulations, we verify that the type I error rate is controlled and show SPOT can be more powerful than alternatives. We also apply SPOT to an ovarian cancer study. An R package and tutorial is provided at https://github.com/sarahsamorodnitsky/SPOT.