SPF: A spatial and functional data analytic approach to cell imaging data

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.

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/.

Statistical analysis of multiple regions-of-interest in multiplexed spatial proteomics data

Multiplexed spatial proteomics reveals the spatial organization of cells in tumors, which is associated with important clinical outcomes such as survival and treatment response. This spatial organization is often summarized using spatial summary statistics, including Ripley's K and Besag's L. However, if multiple regions of the same tumor are imaged, it is unclear how to synthesize the relationship with a single patient-level endpoint. We evaluate extant approaches for accommodating multiple images within the context of associating summary statistics with outcomes. First, we consider averaging-based approaches wherein multiple summaries for a single sample are combined in a weighted mean. We then propose a novel class of ensemble testing approaches in which we simulate random weights used to aggregate summaries, test for an association with outcomes, and combine the $P$-values. We systematically evaluate the performance of these approaches via simulation and application to data from non-small cell lung cancer, colorectal cancer, and triple negative breast cancer. We find that the optimal strategy varies, but a simple weighted average of the summary statistics based on the number of cells in each image often offers the highest power and controls type I error effectively. When the size of the imaged regions varies, incorporating this variation into the weighted aggregation may yield additional power in cases where the varying size is informative. Ensemble testing (but not resampling) offered high power and type I error control across conditions in our simulated data sets.

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.

Using random forests to uncover the predictive power of distance-varying cell interactions in tumor microenvironments

Tumor microenvironments (TMEs) contain vast amounts of information on patient's cancer through their cellular composition and the spatial distribution of tumor cells and immune cell populations. Exploring variations in TMEs between patient groups, as well as determining the extent to which this information can predict outcomes such as patient survival or treatment success with emerging immunotherapies, is of great interest. Moreover, in the face of a large number of cell interactions to consider, we often wish to identify specific interactions that are useful in making such predictions. We present an approach to achieve these goals based on summarizing spatial relationships in the TME using spatial K functions, and then applying functional data analysis and random forest models to both predict outcomes of interest and identify important spatial relationships. This approach is shown to be effective in simulation experiments at both identifying important spatial interactions while also controlling the false discovery rate. We further used the proposed approach to interrogate two real data sets of Multiplexed Ion Beam Images of TMEs in triple negative breast cancer and lung cancer patients. The methods proposed are publicly available in a companion R package funkycells.

SpaceANOVA: Spatial Co-occurrence Analysis of Cell Types in Multiplex Imaging Data Using Point Process and Functional ANOVA

Multiplex imaging platforms have enabled the identification of the spatial organization of different types of cells in complex tissue or the tumor microenvironment. Exploring the potential variations in the spatial co-occurrence or colocalization of different cell types across distinct tissue or disease classes can provide significant pathological insights, paving the way for intervention strategies. However, the existing methods in this context either rely on stringent statistical assumptions or suffer from a lack of generalizability. We present a highly powerful method to study differential spatial co-occurrence of cell types across multiple tissue or disease groups, based on the theories of the Poisson point process and functional analysis of variance. Notably, the method accommodates multiple images per subject and addresses the problem of missing tissue regions, commonly encountered due to data-collection complexities. We demonstrate the superior statistical power and robustness of the method in comparison with existing approaches through realistic simulation studies. Furthermore, we apply the method to three real data sets on different diseases collected using different imaging platforms. In particular, one of these data sets reveals novel insights into the spatial characteristics of various types of colorectal adenoma.

Integrating AI-Powered Digital Pathology and Imaging Mass Cytometry Identifies Key Classifiers of Tumor Cells, Stroma, and Immune Cells in Non-Small Cell Lung Cancer

Artificial intelligence (AI)-powered approaches are becoming increasingly used as histopathologic tools to extract subvisual features and improve diagnostic workflows. On the other hand, hi-plex approaches are widely adopted to analyze the immune ecosystem in tumor specimens. Here, we aimed at combining AI-aided histopathology and imaging mass cytometry (IMC) to analyze the ecosystem of non-small cell lung cancer (NSCLC). An AI-based approach was used on hematoxylin and eosin (H&E) sections from 158 NSCLC specimens to accurately identify tumor cells, both adenocarcinoma and squamous carcinoma cells, and to generate a classifier of tumor cell spatial clustering. Consecutive tissue sections were stained with metal-labeled antibodies and processed through the IMC workflow, allowing quantitative detection of 24 markers related to tumor cells, tissue architecture, CD45+ myeloid and lymphoid cells, and immune activation. IMC identified 11 macrophage clusters that mainly localized in the stroma, except for S100A8+ cells, which infiltrated tumor nests. T cells were preferentially localized in peritumor areas or in tumor nests, the latter being associated with better prognosis, and they were more abundant in highly clustered tumors. Integrated tumor and immune classifiers were validated as prognostic on whole slides. In conclusion, integration of AI-powered H&E and multiparametric IMC allows investigation of spatial patterns and reveals tissue relevant features with clinical relevance.

SIGNIFICANCE

Leveraging artificial intelligence-powered H&E analysis integrated with hi-plex imaging mass cytometry provides insights into the tumor ecosystem and can translate tumor features into classifiers to predict prognosis, genotype, and therapy response.

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.

DIMPLE: An R package to quantify, visualize, and model spatial cellular interactions from multiplex imaging with distance matrices

A major challenge in the spatial analysis of multiplex imaging (MI) data is choosing how to measure cellular spatial interactions and how to relate them to patient outcomes. Existing methods to quantify cell-cell interactions do not scale to the rapidly evolving technical landscape, where both the number of unique cell types and the number of images in a dataset may be large. We propose a scalable analytical framework and accompanying R package, DIMPLE, to quantify, visualize, and model cell-cell interactions in the TME. By applying DIMPLE to publicly available MI data, we uncover statistically significant associations between image-level measures of cell-cell interactions and patient-level covariates.

Investigating Ecological Interactions in the Tumor Microenvironment using Joint Species Distribution Models for Point Patterns

The tumor microenvironment (TME) is a complex and dynamic ecosystem that involves interactions between different cell types, such as cancer cells, immune cells, and stromal cells. These interactions can promote or inhibit tumor growth and affect response to therapy. Multitype Gibbs point process (MGPP) models are statistical models used to study the spatial distribution and interaction of different types of objects, such as the distribution of cell types in a tissue sample. Such models are potentially useful for investigating the spatial relationships between different cell types in the tumor microenvironment, but so far studies of the TME using cell-resolution imaging have been largely limited to spatial descriptive statistics. However, MGPP models have many advantages over descriptive statistics, such as uncertainty quantification, incorporation of multiple covariates and the ability to make predictions. In this paper, we describe and apply a previously developed MGPP method, the saturated pairwise interaction Gibbs point process model , to a publicly available multiplexed imaging dataset obtained from colorectal cancer patients. Importantly, we show how these methods can be used as joint species distribution models (JSDMs) to precisely frame and answer many relevant questions related to the ecology of the tumor microenvironment.

LOCATOR: feature extraction and spatial analysis of the cancer tissue microenvironment using mass cytometry imaging technologies

Motivation

Recent advances in highly multiplexed imaging have provided unprecedented insights into the complex cellular organization of tissues, with many applications in translational medicine. However, downstream analyses of multiplexed imaging data face several technical limitations, and although some computational methods and bioinformatics tools are available, deciphering the complex spatial organization of cellular ecosystems remains a challenging problem.

Results

To mitigate this problem, we develop a novel computational tool, LOCATOR (anaLysis Of CAncer Tissue micrOenviRonment), for spatial analysis of cancer tissue microenvironments using data acquired from mass cytometry imaging technologies. LOCATOR introduces a graph-based representation of tissue images to describe features of the cellular organization and deploys downstream analysis and visualization utilities that can be used for data-driven patient-risk stratification. Our case studies using mass cytometry imaging data from two well-annotated breast cancer cohorts re-confirmed that the spatial organization of the tumour-immune microenvironment is strongly associated with the clinical outcome in breast cancer. In addition, we report interesting potential associations between the spatial organization of macrophages and patients' survival. Our work introduces an automated and versatile analysis tool for mass cytometry imaging data with many applications in future cancer research projects.

Availability and implementation

Datasets and codes of LOCATOR are publicly available at https://github.com/RezvanEhsani/LOCATOR.

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

Spatial heterogeneity in the tumor microenvironment (TME) plays a critical role in gaining insights into tumor development and progression. Conventional metrics typically capture the spatial differential between TME cellular patterns by either exploring the cell distributions in a pairwise fashion or aggregating the heterogeneity across multiple cell distributions without considering the spatial contribution. As such, none of the existing approaches has fully accounted for the simultaneous heterogeneity caused by both cellular diversity and spatial configurations of multiple cell categories. In this article, we propose an approach to leverage spatial entropy measures at multiple distance ranges to account for the spatial heterogeneity across different cellular organizations. Functional principal component analysis (FPCA) is applied to estimate FPC scores which are then served as predictors in a Cox regression model to investigate the impact of spatial heterogeneity in the TME on survival outcome, potentially adjusting for other confounders. Using a non-small cell lung cancer dataset (n = 153) as a case study, we found that the spatial heterogeneity in the TME cellular composition of CD14+ cells, CD19+ B cells, CD4+ and CD8+ T cells, and CK+ tumor cells, had a significant non-zero effect on the overall survival (p = 0.027). Furthermore, using a publicly available multiplexed ion beam imaging (MIBI) triple-negative breast cancer dataset (n = 33), our proposed method identified a significant impact of cellular interactions between tumor and immune cells on the overall survival (p = 0.046). In simulation studies under different spatial configurations, the proposed method demonstrated a high predictive power by accounting for both clinical effect and the impact of spatial heterogeneity.

Quantile Index Biomarkers Based on Single-Cell Expression Data

Current histocytometry methods enable single-cell quantification of biomolecules in tumor tissue sections by multiple detection technologies, including multiplex fluorescence-based immunohistochemistry or in situ hybridization. Quantitative pathology platforms can provide distributions of cellular signal intensity (CSI) levels of biomolecules across the entire cell populations of interest within the sampled tumor tissue. However, the heterogeneity of CSI levels is usually ignored, and the simple mean signal intensity value is considered a cancer biomarker. Here we consider the entire distribution of CSI expression levels of a given biomolecule in the cancer cell population as a predictor of clinical outcome. The proposed quantile index (QI) biomarker is defined as the weighted average of CSI distribution quantiles in individual tumors. The weight for each quantile is determined by fitting a functional regression model for a clinical outcome. That is, the weights are optimized so that the resulting QI has the highest power to predict a relevant clinical outcome. The proposed QI biomarkers were derived for proteins expressed in cancer cells of malignant breast tumors and demonstrated improved prognostic value compared with the standard mean signal intensity predictors. The R package Qindex implementing QI biomarkers has been developed. The proposed approach is not limited to immunohistochemistry data and can be based on any cell-level expressions of proteins or nucleic acids.

SpaceANOVA: Spatial co-occurrence analysis of cell types in multiplex imaging data using point process and functional ANOVA

Motivation

Multiplex imaging platforms have enabled the identification of the spatial organization of different types of cells in complex tissue or tumor microenvironment (TME). Exploring the potential variations in the spatial co-occurrence or co-localization of different cell types across distinct tissue or disease classes can provide significant pathological insights, paving the way for intervention strategies. However, the existing methods in this context either rely on stringent statistical assumptions or suffer from a lack of generalizability.

Results

We present a highly powerful method to study differential spatial co-occurrence of cell types across multiple tissue or disease groups, based on the theories of the Poisson point process (PPP) and functional analysis of variance (FANOVA). Notably, the method accommodates multiple images per subject and addresses the problem of missing tissue regions, commonly encountered in such a context due to the complex nature of the data-collection procedure. We demonstrate the superior statistical power and robustness of the method in comparison to existing approaches through realistic simulation studies. Furthermore, we apply the method to three real datasets on different diseases collected using different imaging platforms. In particular, one of these datasets reveals novel insights into the spatial characteristics of various types of precursor lesions associated with colorectal cancer.

Availability

The associated R package can be found here, https://github.com/sealx017/SpaceANOVA.