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

Abstract

The tumor microenvironment (TME), which characterizes the tumor and its surroundings, plays a critical role in understanding cancer development and progression. Recent advances in imaging techniques enable researchers to study spatial structure of the TME at a single-cell level. Investigating spatial patterns and interactions of cell subtypes within the TME provides useful insights into how cells with different biological purposes behave, which may consequentially impact a subject’s clinical outcomes. We utilize a class of well-known spatial summary statistics, the K-function and its variants, to explore inter-cell dependence as a function of distances between cells. Using techniques from functional data analysis, we introduce an approach to model the association between these summary spatial functions and subject-level outcomes, while controlling for other clinical scalar predictors such as age and disease stage. In particular, we leverage the additive functional Cox regression model (AFCM) to study the nonlinear impact of spatial interaction between tumor and stromal cells on overall survival in patients with non-small cell lung cancer, using multiplex immunohistochemistry (mIHC) data. The applicability of our approach is further validated using a publicly available multiplexed ion beam imaging (MIBI) triple-negative breast cancer dataset.

A Spatial Omnibus Test (SPOT) for Spatial Proteomic Data

“…We then compared SPOT to existing methods. We considered SPF [13] and FunSpace [14] as alternative approaches. These methods allow for a range of radii and treat the spatial summary measure evaluated at each radius as a functional covariate.…”

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

“…For a formal inference, cell types are randomly switched and empirical p -values based on permutation test are considered. Recently, a more rigorous framework based on the homogeneous multitype Poisson point process (PPP) or complete spatial randomness and independence (CSRI) , has been considered by different groups of researchers. − In essence, these methods utilize various spatial summary functions, such as Ripley’s K , L , g , and mark connection function (MCF), that are formulated using the assumptions of homogeneous PPP and have slightly varying interpretations. As an example, for a pair of cell types ( m , m ′), the bivariate K function [ K mm ′ ( r )] calculates the ratio of the observed number of cells to the expected number of cells of type m ′ within a distance r of a typical cell of type m , relative to a hypothetical completely random distribution of cell types.…”

“…Such a simplification of the summary functions, however, discards granular information and thus might be suboptimal in practical scenarios, as demonstrated in our simulation studies. A key improvement was proposed by Vu et al 28 who incorporated the MCF over a range of r , to the additive functional Cox model, 36 as a functional covariate to study association with time-to-event outcomes. However, unlike SpicyR, Vu et al’s 28 approach cannot be readily used to study differential spatial co-occurrence across clinical groups, which is the focus of our manuscript and does not accommodate more than one image per subject.…”

“…A key improvement was proposed by Vu et al 28 who incorporated the MCF over a range of r , to the additive functional Cox model, 36 as a functional covariate to study association with time-to-event outcomes. However, unlike SpicyR, Vu et al’s 28 approach cannot be readily used to study differential spatial co-occurrence across clinical groups, which is the focus of our manuscript and does not accommodate more than one image per subject. Additionally, the multiplexed images may have missing regions in them due to some parts of the tissue getting sliced or washed away.…”

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

“…By analyzing these patterns, ecologists can infer crucial information about species interactions, habitat preferences, and the influence of environmental factors on distribution. Such statistics have also been widely adopted by researchers investigating the tumor microenvironment [22][23][24]. More bespoke methods have also been developed, such as those in which a "neighborhood composition" vector is calculated for each cell [16,[25][26][27].…”