Quantification of spatial tumor heterogeneity in immunohistochemistry staining images

Abstract

Motivation

Quantitative immunofluorescence is often used for immunohistochemistry quantification of proteins that serve as cancer biomarkers. Advanced image analysis systems for pathology allow capturing expression levels in each individual cell or subcellular compartment. However, only the mean signal intensity within the cancer tissue region of interest is usually considered as biomarker completely ignoring the issue of tumor heterogeneity.

Results

We propose using immunohistochemistry image-derived information on the spatial distribution of cellular signal intensity (CSI) of protein expression within the cancer cell population to quantify both mean expression level and tumor heterogeneity of CSI levels. We view CSI levels as marks in a marked point process of cancer cells in the tissue and define spatial indices based on conditional mean and conditional variance of the marked point process. The proposed methodology provides objective metrics of cell-to-cell heterogeneity in protein expressions that allow discriminating between different patterns of heterogeneity. The prognostic utility of new spatial indices is investigated and compared to the standard mean signal intensity biomarkers using the protein expressions in tissue microarrays incorporating tumor tissues from 1000+ breast cancer patients.

Availability and Implementation: The R code for computing the proposed spatial indices is included as supplementary material

 

Supplementary information

Supplementary data are available at Bioinformatics online.

1 Introduction

It is well established that there is substantial intra-tumoral cell-to-cell heterogeneity in levels of proteins, protein modifications, ribonucleic acids and metabolites. Extensive efforts focus on analyzing tumor marker levels in single-cell assays, e.g. by multiplexed flow cytometry, single cell nucleic acid sequencing or combinations (Irish et al., 2004; Krutzik and Nolan, 2006; Stoeckius et al., 2017; Tirosh et al., 2016). However, assays performed on dissociated cancer cells lack spatial information, while immunohistochemistry (IHC) images capture spatial heterogeneity.

Thus far, spatial analyses of IHC images have focused on morphological patterns (e.g. Doyle et al., 2008; Lewis et al., 2014), metrics of topological organization (e.g. Cheng et al., 2018; Kothari et al., 2013), distance-based metrics of interaction between cancer cells and their microenvironment (e.g. Keren et al., 2018; Maley et al., 2015; Nawaz and Yuan, 2016), and models for spatial arrangements of cancer cells (Heindl et al., 2015; Jones-Todd et al., 2019). Meanwhile, an objective and interpretable metric of spatial heterogeneity of single cell signal intensities in IHC images is still lacking.

The standard quantitative assessment of proteins levels in IHC images have been facilitated by computing the Mean Signal Intensity (MSI) within the tumor region of interest, e.g. cancer cell or stromal compartments. Newer generations of integrated scanning and image analysis systems for pathology (e.g. see Garcia-Rojo, 2012) incorporate advances in machine learning and improved segmentation algorithms and enable measurement of analytes in individual cells and subcellular compartments such as nuclei or membranes. However, mainstream approaches continue to neglect valuable quantitative information related to spatial distribution of Cell Signal Intensity (CSI) levels by reducing data to the standard MSI metric or classifying cells into positive or negative for the target protein.

Here, we propose new objective metrics of spatial distribution of CSI levels of proteins or other analytes and demonstrate the utility of these metrics for developing predictors of clinical outcomes. We view CSI levels as marks in a marked point pattern (MPP) (Stoyan and Stoyan, 1994) of cancer cells and consider conditional mean and conditional variance of marks in MPP (Schlather, 2001; Schlather et al., 2004). Since conditional mean and conditional variance of MPP are functions of the distance between the points, we propose spatial indices defined as the areas under the conditional mean or variance curves in the interval from 0 to some d_max and standardize by dividing by d_max. The resulting standardized area under the conditional mean curve (AUcMean) is an aggregate measure of average CSI in the range $(0,d_{\text{max}})$. It has the same meaning as the MSI but averages CSIs in cells with inter-point distances in $(0,d_{\text{max}})$. The standardized area under the conditional variance curve (AUcVar) is a novel aggregate measure of CSI signal heterogeneity in the range $(0,d_{\text{max}})$. For large enough numbers of tissue samples, parameter d_max can be optimized using the standard training and validation or cross-validation strategy. For limited numbers, a natural way of selecting d_max may be based on tissue morphology (the size of the islands of cancer cells) or expected size of the clusters that matter from the biological point of view.

To shorten the notation, the dependence on d_max is omitted further unless actual value is reported.

A simulation study was conducted to demonstrate that the proposed spatial indices AUcMean and AUcVar can discriminate between commonly observed types of tumor heterogeneity of CSIs. The proposed spatial indices are continuous metrics, but it is possible to use them either as continuous or dichotomized biomarkers. Here, we illustrate the use of AUcMean and AUcVar as either continuous or dichotomized biomarkers. Dichotomized IHC biomarkers are often preferred because pathologists do not expect that monotone increase in raw measures implies monotone increase in the hazard or odds of a clinical outcome.

The proposed approach was applied to derive AUcMean and AUcVar biomarkers based on the cell proliferation related protein Ki67 and transcription factor TWIST1. The CSI levels of these proteins were quantified in quantitative immunofluorescence (QIF)-IHC images of tissue cores in tissue microarrays (TMAs) from 1000+ breast cancer patients. For Ki67 and TWIST1, the primary interest was on dichotomized AUcMean and AUcVar biomarkers as predictors of progression-free survival (PFS). The prognostic utility of dichotomized Ki67 and TWIST1 biomarkers with optimized d_max was investigated and compared to the standard MSI. In addition, continuous versions of AUcMean and AUcVar were evaluated as PFS predictors across the biologically meaningful range of d_max from nearest neighbor cell distance and up to the size of commonly observed cancer cell islands.

Figure 1 shows representative images of Ki67 QIF-IHC (A–D) with the corresponding marked point patterns (E–H). In the images, the red color reflects the intensity of the Ki67 signal, the green color shows the cancer cells and the blue color shows the cell nuclei. The points in MPPs represent the locations of cancer cell nucleus centroids, and the size of the plotting circle is proportional to ${10}^{-3}\times \mathit{CSI}$ in the corresponding cell nucleus. High-signal clusters are readily visualized in MPP plots F-G, while the corresponding red colored spots are more obscure by visual assessment in the images B-C. Corresponding estimates of cMean(d) and cVar(d) of log-transformed Ki67 CSI signals are shown in Figure 1(I–L). Combination of dichotomized Ki67 AUcMean and AUcVar yielded stronger prognostic marker as compared to MSI alone or either spatial biomarker alone in the multivariable model controlling for the standard clinico-pathological risk factors.

Fig. 1.

Representative examples of Ki67 QIF-IHC images (A–D) with the corresponding marked point patterns (E–H) and estimates of cMean(d) and cVar(d) (I–L). The centers of the plotting circles in (E–H) are at the cancer cell centroids, the radii of the plotting circles are proportional to the Ki67 expression. The green and red lines represent the means and variances of the marginal distribution of log-transformed Ki67 expression, respectively

Figure 2 shows examples of TWIST1 QIF-IHC images (A, B) with the corresponding marked point patterns (C, D) and kernel smoothed estimates of cMean(d) and cVar(d) (E, F). These examples demonstrate that two tumors with similar TWIST1 cMean(d) levels may have substantially different cVar(d). For TWIST1, only dichotomized AUcVar retained prognostic value in the multivariable model controlling for the standard clinico-pathological risk factors. Thus, TWIST1 exemplifies a protein for which measure of tumor heterogeneity in CSI levels has potentially higher prognostic value as compared to the average levels.

Fig. 2.

Representative examples of QIF-IHC images of TWIST1 expression (A, B) with the corresponding marked point patterns (C, D) and estimates of cMean(d) and cVar(d) (E, F). The centers of the plotting circles in (C, D) are at the cancer cell centroids, the radii of the plotting circles are proportional to the TWIST1 expression. The green and red lines represent the means and variances of the marginal distribution of log-transformed TWIST1 expression, respectively

Previously proposed applications of point processes framework to IHC data utilized primarily the methods developed for multi-type point processes with categorical marks. The application of multitype point processes requires manual annotation by trained pathologist of each cell as positive or negative for the protein of interest. This labor-intense process is not practical for tissue samples with thousands of cells.

In recent work, Edsgard et al. (2018) used the framework of the marked point processes to develop a software tool that identifies genes with statistically significant spatial expression trends by performing permutation tests of independence between marks and their location (the null hypothesis of independent marking). In contrast, our objective was to develop an approach to quantify spatial heterogeneity in CSI levels and to identify potential outcome predictors based on heterogeneity measures. Our approach is appropriate regardless of dependence or independence between the spatial pattern of cells and CSI levels. For Ki67 and TWIST1 CSIs considered here, independence between marks and cell locations was supported for some tissue cores, but for large numbers of tissue cores, the independence assumption was not appropriate. Using the test proposed by Edsgard et al. (2018) with mark correlation test statistics and $\alpha =0.05$, the null hypothesis of independence was rejected for Ki67 in 39% of the tissue cores and for TWIST1 in 45% of the tissue cores.

2 Approach

We use marked point processes framework for development of spatial biomarkers that capture the average levels and heterogeneity of CSI patterns in the tumor. The CSI levels are viewed as marks associated with points in the point pattern of centroids of nuclei or entire cancer cells.

We now define the basic notation required for the methods description. A spatial point process is a random pattern of points, both the number of points and their locations being random. Let P be a spatial point process observed in a bounded region $D\subset {\mathit{R}}^2$. Each observed point pattern of centroids of nuclei, cytoplasms or entire cells is viewed as one random realization of P. Let $N_P(B)$ be the count function of P, which is the number of points falling into any Borel set $B\subset D,$ and $\left|B\right|$ be the Lebesgue measure of B. For ${\mathbf{u}}_1,\dots {\mathbf{u}}_k\in P,$ the kth order intensity function is defined by ${\lambda }_k\left({\mathbf{u}}_1,\dots ,{\mathbf{u}}_k\right)=\underset{\left|\mathbf{d}{\mathbf{u}}_1\right|···\left|\mathbf{d}{\mathbf{u}}_{\mathbf{k}}\right|\to 0}{\lim }\left\{\frac{E\left[N\left(d{\mathbf{u}}_1\right)···N\left(d{\mathbf{u}}_k\right)\right]}{\left|d{\mathbf{u}}_1\right|···\left|d{\mathbf{u}}_k\right|}\right\}$, where $E[X]$ stands for expected value of the random variable X. Assuming that the intensity functions exist for $k\le 2$, the first order intensity ${\lambda }_1\left(\mathbf{u}\right)$ is strictly positive but not necessarily constant. The pair correlation function is defined as $\rho \left(\mathbf{u},\mathbf{v}\right)={\lambda }_2\left(\mathbf{u},\mathbf{v}\right){\left[{\lambda }_1\left(\mathbf{u}\right){\lambda }_1\left(\mathbf{v}\right)\right]}^{-1}$ The point process P is called stationary if ${\lambda }_1\left(\mathbf{u}\right)\equiv \lambda$ (constant intensity). Also, P is called the second-order intensity reweighted stationary (Baddeley et al., 2000) if $\rho \left(\mathbf{u},\mathbf{v}\right)$ is translation invariant, i.e. $\rho \left(\mathbf{u},\mathbf{v}\right)=\rho \left(\left||\mathbf{u}-\mathbf{v}\right||\right),$ where $\left||\mathbf{u}-\mathbf{v}\right||=r$ is a Euclidian norm and $\rho (r):\left[0,\infty \right)\to \left[0,\infty \right).$

A marked point process is a point process combined with some associated quantities (‘marks’) measured at each point. In our application marks are the CSI levels. Let us denote by $\Psi ={\cup }_i\{({\mathbf{u}}_i,m({\mathbf{u}}_i)),{\mathbf{u}}_i\in P\}$, a marked point process with a real-valued mark function $m({\mathbf{u}}_i)$ defined at each point ${\mathbf{u}}_i$. A single realization of $\Psi$ is called a marked point pattern (MPP). Conditional mean cMean(d) and conditional variance cVar(d) of a mark given that there is another point of the process a distance d away (Schlather et al., 2004) are defined as: $\mathit{cMean}(d)=E[m(\mathbf{u})|\mathbf{u},\mathbf{v}\in P,\left||\mathbf{u}-\mathbf{v}\right||=d]$  $\mathit{cVar}(d)=E[{\{m(\mathbf{u})-\mathit{cMean}(d)\}}^2|\mathbf{u},\mathbf{v}\in P,\left||\mathbf{u}-\mathbf{v}\right||=d]$ That is, cMean(d) and cVar(d) are functions of the distance d between points $\mathbf{u},\mathbf{v}\in P$. An independently marked point process has marks that are independent, identically distributed and independent of the locations. In case of independence between marks and points, cMean(d) and cVar(d) reduce to the familiar mean and variance of the marginal distribution of marks. Thus, cMean(d) and cVar(d) are direct extensions of the standard mean and variance of the mark distribution. They are non-constant functions of the inter-point distance d if there is a dependence between marks and their locations.

The following non-parametric estimators of cMean(d) and cVar(d) were proposed in Schlather (2001) and Schlather et al. (2004):

$$\widehat{\mathit{cMean}}\left(d\right)=N_d^{-1}\sum _{\left|\left||{\mathbf{u}}_k-{\mathbf{u}}_l\right||-d\right|\le \epsilon /2}m\left({\mathbf{u}}_k\right),$$

 

$$\widehat{\mathit{cVar}}\left(d\right)=N_d^{-1}\sum _{\left|\left||{\mathbf{u}}_k-{\mathbf{u}}_l\right||-d\right|\le \epsilon /2}{\left[m\left({\mathbf{u}}_k\right)-\widehat{\mathit{cMean}}\left(d\right)\right]}^2,$$

where $d\ge 0,$ is a distance between two points, $\epsilon >0$ is a fixed bin width and N_r is the number of pairs $\left({\mathbf{u}}_k,{\mathbf{u}}_l\right)$ such that $\left|\left||{\mathbf{u}}_k-{\mathbf{u}}_l\right||-r\right|\le \epsilon /2.$

For spatially inhomogeneous point patterns, Baddeley et al. (2000) developed non-parametric kernel density estimators of various point processes characteristics under the assumption of second-order intensity reweighted stationary processes. Since cancer cell point patterns within tumor sections are inherently inhomogeneous due to interspersed stromal cells and extracellular matrix, cMean(d) and cVar(d) are estimated using such non-parametric kernel density estimators under the assumption of second-order intensity reweighted stationary processes as implemented in R package spatstat (Baddeley and Turner, 2005).

In further developments, $\widehat{\mathit{cMean}}\left(d\right)$ and $\widehat{\mathit{cVar}}\left(d\right)$ denote the non-parametric kernel density estimates of cMean(d) and cVar(d), respectively. Since $\widehat{\mathit{cMean}}\left(d\right)$ or $\widehat{\mathit{cVar}}\left(d\right)$ are functions of the distance d between points in the pattern, we aggregate these functions into suitable indices that may be further investigated as predictors of the survival or other outcome. We propose to use the partial area under $\widehat{\mathit{cMean}}\left(d\right)$ or $\widehat{\mathit{cVar}}\left(d\right)$ in the subinterval $[0,d_{\text{max}}],\hspace{0.17em}0<d_{\text{max}}$ divided by d_max to standardize. Using the subinterval $[0,d_{\text{max}}]$ implies considering the dependence between marks and points only for the range $[0,d_{\text{max}}]$ of interpoint distances.

Thus, for the ith tissue MPP of the cancer cells centroids with CSI marks and corresponding $\mathit{cMea}{n}_i(d)$ and

$$\begin{array}{c}cVa{r}_i(d)\hspace{0.17em}\mathit{AUcMea}{n}_i\left(d_{\text{max}}\right)=d_{\text{max}}^{-1}{\int }_0^{d_{\text{max}}}\widehat{\mathit{cMea}{n}_i}\left(r\right)dr\\ A\mathit{UcVa}{r}_i\left(d_{\text{max}}\right)=d_{\text{max}}^{-1}{\int }_0^{d_{\text{max}}}\widehat{\mathit{cVa}{r}_i}\left(r\right)dr\end{array}$$

The R code implementing the computation of the proposed spatial indices is included in Supplementary Material.

Parameter d_max may be selected a priori or optimized for AUcMean and AUcVar using the standard training and validation or cross-validation strategy.

3 Materials and methods

3.1 Immunohistochemistry and image analysis

The proposed methodology was developed using immunohistochemistry image data on a large cohort of 1000+ breast cancer specimens. The tissue bank was collected into standard core-based tissue microarrays (TMAs) using 0.6 mm core diameter. The specimens were unselected consecutive cases with the inclusion criteria of available tumor tissue and clinical outcome data. Tumor specimens were reviewed by central pathologist and representative cancer tissue regions were selected for inclusion in tissue microarrays (TMAs). Immunohistochemistry using the Ki67 antibody is FDA-approved and is extensively used in clinical laboratories. The antibody for TWIST1 has been validated by Abcam and has been used in more than 100 reports. Stained slides were scanned at 20× magnification on the Scanscope laser scanner (Leica/Aperio) and fluorescent images were captured in three channels (Cy5-Alexa555-DAPI).

The Definiens Tissue Studio software platform was used to quantify protein markers from digitized immunohistochemistry image data. The digitized image data represent tri-color immunofluorescence-stained array sections detecting cell nuclei (DAPI channel), pan-cytokeratin stained carcinoma cells (Cy3 channel) and protein target of interest (Cy5-channel). The Tissue Studio platform has built-in routines for handling signal noise and image artifacts, and each image underwent visual inspection and quality control to eliminate problem spots. Once appropriate tissue regions have been selected, areas of cancer cells within each sample and cellular boundaries were identified through a cell segmentation algorithm that is supported by cytokeratin staining of carcinoma cells and DAPI staining of cell nuclei. This information was combined with operator-guided machine learning performed on a representative subset of different tumor tissues to generate an analysis solution that defines specific regions of interest (cancer cells). The analysis solution was then applied to the entire set of image data for each marker to convert the signal intensities at the pixel level into MSI of each marker across cancer cell region and cell signal intensity (CSI) within individual cancer cells at whole cell level or cell nucleus level. Spatial image information was recorded as x–y coordinates of the centroids of cells or nuclei. The tissue cores included into analysis, had to meet imaging quality control standards and include at least 50 cancer cells (actual range 50–3500 cells).

3.2 Development of spatial biomarkers

The primary outcome of interest is the progression free survival (PFS). For each $d_{\text{max}}=12,13,\dots ,100,\hspace{0.17em}\mathit{AUcMean}(d_{\text{max}})$ and $\mathit{AUcVar}(d_{\text{max}})$ were computed as described above separately for each tissue core image. The smallest considered d_max was equal to 12 because the median diameter of the cancer cells was $6\hspace{0.17em}\mu \mathrm{m}$. The value of $100\hspace{0.17em}\mu \mathrm{m}$ is an estimate of the size of the smallest clusters of cancer cells in the tissue. For a small number of patients (n = 39) with more than one tissue cores, $\mathit{AUcMean}(d_{\text{max}}),\hspace{0.17em}\mathit{AUcVar}(d_{\text{max}})$ and standard MSI were averaged for the multiple cores within the same patient. Respectively, all analyses of MSI, $\mathit{AUcMean}\left(d_{\text{max}}\right)$ and $\mathit{AUcVar}\left(d_{\text{max}}\right)$ as predictors of clinical outcome were based on independent samples without repeated measures per patient. All patients with known progression-free survival outcome and the CSI data available for the protein of interests were randomly assigned into a training cohort (with probability 0.35), validation cohort (with probability 0.15) and test cohort (with probability 0.5). Such relatively large test sets were selected to support multivariable analyses adjusting for effects of known clinico-pathological prognostic factors. Recursive partitioning with 10-fold cross-validation (R package rpart) was used to establish data-driven optimal cutoff for dichotomizing $\mathit{AUcMea}{n}_i\left(d_{\text{max}}\right)$ and $\mathit{AUcVa}{r}_i\left(d_{\text{max}}\right)$ for $d_{\text{max}}=12,13,\dots ,100$ in the training set. Then for each $d_{\text{max}}=12,13,\dots ,100$, the optimal cutoff was used to dichotomize the $\mathit{AUcMea}{n}_i\left(d_{\text{max}}\right)$ or $\mathit{AUcVa}{r}_i\left(d_{\text{max}}\right)$ and compute the corresponding hazard ratio (HR) in the validation set. The optimal value of d_max was selected corresponding to the largest effect size (largest HR or 1/HR) in the validation set. The final spatial biomarkers $\mathit{AUcMean}\left(d_{\text{max}}^M\right)$ and $\mathit{AUcVar}\left(d_{\text{max}}^V\right)$ with the corresponding cutoffs for dichotomizing were evaluated in the test set using the Kaplan–Meier survival curves and two-sided log-rank test.

For some proteins, continuous versions of AUcMean and AUcVar may be of interest. In such cases, parameter d_max can be optimized as described above or using the standard cross-validation strategy. Since we were primarily interested in dichotomized biomarkers, d_max was not optimized for continuous AUcMean and AUcVar. Instead, the full range of $\mathit{AUcMean}(d_{\text{max}}),\hspace{0.17em}\mathit{AUcVar}(d_{\text{max}})$ for each $d_{\text{max}}=12,13,\dots ,100$ was evaluated as predictors of PFS to investigate the effect of d_max on association between PFS and $\mathit{AUcMean}(d_{\text{max}})$ or $\mathit{AUcVar}(d_{\text{max}})$. Recent publications on evaluation of new biomarkers suggest that well-established tests for coefficients in the regression model are the most appropriate for testing the prognostic utility of new biomarkers (e.g. Kerr et al., 2014; Vickers et al., 2011). Therefore, we used the standard hazard ratios in the Cox model for evaluating the continuous versions of AUcMean and AUcVar as well as MSI and marginal variance of CSI values if the proportional hazards assumption was appropriate. Otherwise, the values of the Supremum test statistics from the multiplicative hazard model (Martinussen and Scheike, 2002) were used.

3.3 Multivariable analysis of MSI and spatial biomarkers

Clinical outcome data were available for 1000+ patients. The post-surgery treatments were captured by indicator variables for chemotherapy, radiation therapy and hormone therapy. The data also included commonly employed clinical-pathological prognostic factors: age, race (white versus non-white), hormone receptor (HR) status, HER2 positivity, histologic grade, node status, tumor size (<2, 2–5, >5 cm), radiation therapy, chemotherapy and hormone therapy. The proportions of patients with missing values were small (0.6–3.7%) for all clinical-pathological covariates except for tumor size (11% missing) and hormone therapy status in hormone positive patients (33% missing). Therefore, for multivariable analysis, we used multiple imputations by chained equations (MICE) approach proposed by Van Buuren et al. (1999). Missing clinical covariates were imputed sequentially using R package MICE Van Buuren and Groothuis-Oudshoorn (2010). Forty (40) complete imputed datasets were created and used for further multivariable analysis. After fitting a statistical model to each imputed dataset, a pooling was used to combine the separate estimates and standard errors from each of the imputed datasets into an overall estimate with a standard error derived in Rubin (2004). The initial multivariable Cox proportional hazards model was constructed using the entire imputed datasets and included all clinical-pathological covariates but none of the biomarkers. A final parsimonious Cox model without biomarkers was obtained using backward elimination of non-significant variables, but HR status was retained regardless of significance. Then each new biomarker was added to this parsimonious Cox model, but the model was fitted only to the imputed datasets restricted to the test set. Covariates violating the proportional hazards assumption were evaluated using the supremum test of significance of the cumulative coefficient in the multiplicative hazard model (Martinussen and Scheike, 2002). The significant covariates violating the proportional hazards assumption were included as strata variables in the final Cox models.

4 Results

4.1 Ki67 biomarkers

For Ki67 protein levels, the spatial biomarkers AUcMean and AUcVar were computed for 1060 patients. In the validation phase, optimal $d_{\text{max}}=30\hspace{0.17em}\mu \mathrm{m}$ was selected for AUcMean and optimal $d_{\text{max}}=78\hspace{0.17em}\mu \mathrm{m}$ was selected for AUcVar. Further analyses results are reported for dichotomized $\mathit{AUcMean}(30\hspace{0.17em}\mu \mathrm{m})$ and $\mathit{AUcVar}(78\hspace{0.17em}\mu \mathrm{m})$ omitting the explicit d_max values to shorten the notation. Figure 3A shows high association between AUcMean and log-transformed MSI levels, and weaker association of AUcVar with either AUcMean or log-transformed MSI levels. All Ki67 markers (MSI, AUcMean and AUcVar) dichotomized for predicting PFS provided reproducible signals in the test set. As seen in Figure 3A, only 4.8% of 1060 patients did not have agreement between High AUcMean and High MSI or Low AUcMean and Low MSI. The disagreement was higher between dichotomized AUcVar and MSI (15.9%) or AUcVar and AUcMean (15%). Supplementary Table S1 shows the associations of all dichotomized Ki67 markers with known clinico-pathological prognostic factors.

Fig. 3.

Ki67 and TWIST1 biomarkers in the test set. (A) associations between MSI, AUcMean and AUcVar of Ki67; (B) Kaplan–Meier estimators of the progression-free survival (PFS) by composite spatial Ki67 marker defined as High AUcMean AND High AUcVar versus Low AUcMean OR Low AUcVar based on the fitted multivariable Cox model; (C) associations between MSI, AUcMean and AUcVar of TWIST1; (D) Kaplan–Meier estimators of the progression-free survival (PFS) by High versus Low AUcVar

When added to the parsimonious Cox model one at a time, each dichotomized Ki67 marker was a significant predictor of PFS (Supplementary Table S2). The hazard ratio associated with High level was similar for AUcVar (HR = 2.03, 95%CI: 1.13–3.66; P = 0.021) and AUcMean (HR = 2.12, 95%CI: 1.18–3.81; P = 0.014), and lower for MSI (HR = 1.79, 95%CI: 1.06–3.05; P = 0.034). Adding two or three Ki67 markers at the same time was not appropriate due to high collinearity, but we also considered all possible combinations of High/Low AUcMean and AUcVar and noticed that the risk of recurrence is distinctively higher for the patients with High AUcMean AND High AUcVar (Supplementary Fig. S1). Based on this, a composite spatial Ki67 marker was defined as High AUcMean AND High AUcVar versus Low AUcMean OR Low AUcVar. Supplementary Table S2 also presents the results from the Cox model including this composite spatial Ki67 marker. Patients with High AUcMean AND High AUcVar were at elevated risk of recurrence as compared to patients with Low AUcMean OR Low AUcVar (HR = 2.32, 95%CI: 1.34–4.02; P = 0.004). The Kaplan-Meier curves adjusted for the effects of other covariates in the Cox model (taken at the reference levels of other covariates) are shown in Figure 3B.

Further, we investigated the utility of continuous AUcMean or AUcVar as predictors of PFS depending on d_max. Supplementary Figures S2 and S3 show the histograms of AUcMean or AUcVar with $d_{\text{max}}=20,30,\dots ,100$. Notably, the distribution of AUcVar is highly skewed. Figure 4A and B shows the supremum test statistics (all significant at the level 0.05 without adjustment for multiple testing) from the multiplicative hazard model with time-dependent coefficients for Ki67 AUcMean or Ki67 AUcVar. The multiplicative hazard model was used because of the violations of the proportional hazards assumptions. Log-transformed Ki67 AUcMean and Ki67 AUcVar were used as predictors of PFS since log-transformation improved the model with Ki67 AUcVar and did not make a difference for Ki67 AUcMean. For any considered d_max in the range $12-100\hspace{0.17em}\mu \mathrm{m}$, Ki67 AUcMean and Ki67 AUcVar were significant predictors of PFS with Ki67 AUcMean being a stronger predictor than Ki67 AUcVar based on comparing the supremum test statistics. The predictive value of Ki67 AUcMean was negligibly dependent on d_max, while the supremum test statistics for Ki67 AUcVar slightly increased for d_max in the interval $12-50\hspace{0.17em}\mu \mathrm{m}$ and then was generally unchanged in the interval $50-100\hspace{0.17em}\mu \mathrm{m}$. Using the log-transformed MSI resulted in the value of supremum test statistics of $4.01(P=0.002)$, which is very similar to the supremum test statistics for Ki67 AUcMean (Fig. 4A). Similarly, using the log-transformed marginal variance of log CSI resulted in the value of supremum test statistics of $3.54(P=0.022)$, which is smaller than the supremum test statistics for Ki67 AUcVar for d_max in the range $50-100\hspace{0.17em}\mu \mathrm{m}$ (Fig. 4B). However, none of the continuous biomarkers remained a significant predictor in the multivariable model that adjusted for known clinico-pathological prognostic factors (data not shown).

Fig. 4.

Continuous spatial biomarkers as predictors of PFS: (A) Ki67 AUcMean, (B) Ki67 AUcVar, (C) TWIST1 AUcMean, (D) TWIST1 AUcVar

In summary, combining the information in both dichotomized AUcMean and AUcVar provides a better prognostic marker as compared to using MSI or each spatial biomarker alone (continuous or dichotomized). Continuous or dichotomized AUcMean has higher predictive power as compared respectively to continuous or dichotomized AUcVar or MSI.

The $\mathit{AUcMean}(30\hspace{0.17em}\mu \mathrm{m})$ biomarker is based on the average CSI signals in micro-clusters with diameters equivalent to 5 cells. Thus, High AUcMean captures the presence of ‘hot microspots’ that may not be detectable by visual inspection. The $\mathit{AUcVar}(78\hspace{0.17em}\mu \mathrm{m})$ biomarker captures the heterogeneity of Ki67 levels in larger size clusters (∼13 cells in diameter), thus identifying areas of more active proliferation. The absence of ‘hot microspots’ or active proliferation areas defined the low risk group including $\sim 34\%$ of the cohort. In contrast, high levels of traditional Ki67 MSI are associated with high risk of recurrence.

4.2 TWIST1 biomarkers

For TWIST1 protein levels, the spatial biomarkers AUcMean and AUcVar were computed for 1008 patients. In the validation phase, optimal $d_{\text{max}}=80\hspace{0.17em}\mu \mathrm{m}$ was selected for dichotomized AUcVar, but no cutoff was identified for dichotomization of AUcMean. There was a cutoff identified for MSI in the training set but the signal was not reproducible in the test set. Figure 3C shows essentially no association between TWIST1 $\mathit{AUcVar}(80\hspace{0.17em}\mu \mathrm{m})$ and log-transformed MSI levels. In contrast to Ki67, only 33% of 1060 patients had an agreement between High TWIST1 AUcVar and High TWIST1 MSI or Low TWIST1 AUcVar and Low TWIST1 MSI (as dichotomized for predicting PFS). The majority of patients with disagreement between dichotomized TWIST1 AUcVar and MSI (56% of the entire cohort), had High TWIST1 MSI but Low TWIST1 AUcVar, while 11% had Low TWIST1 MSI but High TWIST1 AUcVar (Fig. 3C). Figure 3D illustrates the difference in PFS between High and Low TWIST1 AUcVar. The Supplementary Table S3 shows the associations of dichotomized TWIST1 AUcVar with known clinico-pathological prognostic factors. High TWIST1 AUcVar was significantly associated with Node Stage, but not with any other tumor characteristics. Further, the dichotomized TWIST1 AUcVar was evaluated in a multivariable Cox model fitted to the test set with 503 patients and 83 recurrence events. The results of the final Cox model are presented in Supplementary Table S4. High TWIST1 AUcVar was associated with higher risk of recurrence (HR = 1.89, 95% CI: 1.21–2.95, P = 0.007) after controlling for Node Stage and other significant clinico-pathological prognostic factors. Supplementary Figures S4 and S5 show the histograms of TWIST1 AUcMean and AUcVar with $d_{\text{max}}=20,30,\dots ,100$. The distribution of AUcVar is highly skewed, similar to Ki67. Figure 4C and D shows the hazard ratios corresponding to the unit increase with the unit equal to interquartile range of log-transformed AUcMean or AUcVar. The hazard ratios were significantly different from 1 for AUcMean with d_max in the range $51-100\hspace{0.17em}\mu \mathrm{m}$ (Fig. 4C) and for AUcVar with d_max in the range $12-100\hspace{0.17em}\mu \mathrm{m}$ (Fig. 4D). The predictive values of TWIST1 AUcMean and AUcVar were only weakly dependent on d_max (note narrow y-scales in Fig. 4C and D). The log-transformed MSI yielded a hazard ratio of 0.84 $(95\%CI:0.72-0.97;P=0.020)$, similar to the hazard ratios for AUcMean with d_max in the range $70-100\hspace{0.17em}\mu \mathrm{m}$ (Fig. 4C). The log-transformed marginal variance of log CSI was not predictive of PFS $(HR=1.12,95\%CI:0.97-1.30;P=0.117)$. None of the continuous biomarkers (marginal or conditional means or variances) remained a significant predictor in the multivariable model that adjusted for known clinico-pathological prognostic factors (data not shown). In addition, we considered a combined multivariable model including the best TWIST1 and Ki67 markers. Supplementary Table S5 reports the results of this Cox model. Both TWIST1 and Ki67 markers remained independently predictive of PFS with slightly reduced effect sizes.

In summary, only dichotomized AUcVar that quantifies tumor heterogeneity in TWIST1 protein levels, but not AUcMean or mean or variance of marginal TWIST1 distribution had a prognostic value.

5 Simulation study

We simulated different types of marked point patterns (MPPs) corresponding to patterns of tumor protein heterogeneity commonly found in cancer tissues. In the unit square window ($[0,1]\times [0,1]$), three types cancer cell point patterns were simulated, including (i) homogeneous distribution of cells; (ii) large clusters of cells; (iii) small clusters of cells. The following combinations of low and high CSI signal patterns were considered.

Type A: ‘Only Low CSI’ including (i) homogeneous scenario AH (uniform Poisson process with intensity 100); (ii) large clusters scenario AL (Matern clustered point process with intensity of the Poisson process of cluster centers λ = 4, radius parameter of the clusters r = 0.4 and mean number of points per cluster N_cl = 20); and (iii) small clusters scenario AS (Matern clustered point process with intensity of the Poisson process of cluster centers λ = 20, radius parameter of the clusters r = 0.4 and mean number of points per cluster N_cl = 4). The log-transformed marks (CSI levels) had normal distribution with mean 3.0 and standard deviation 0.5 ($N(2.0,{0.5}^2)$). Representative MPPs is shown in Figure 5A (type AH), H (type AL), O (type AS).

Fig. 5.

Representative simulated marked point patterns (MPPs) of typical spatial distributions of cancer cells and protein expression levels, including type A with low CSIs (A, H, O), type B with 10% of high CSIs (B, I, P), type B with 20% of high CSIs (C, J, Q), type C with 10% of high CSIs (D, K, R), type C with 20% of high CSIs (E, L, S), type D with 10% of high CSIs (F, M, T), type D with 20% of high CSIs (G, N, U)

Type B: ‘Salt-and-pepper mixture of Low and High CSI’ MPPs were simulated as mixtures of independent marked point processes of high CSI levels and low CSI levels. The marked point process of low CSI had log-transformed marks with marginal distribution [$N(2.0,{0.5}^2$) and marked point process of high CSI had log-transformed marks with marginal distribution $N(5.0,{0.2}^2)$]. Spatially, high CSI levels distributed as uniform Poisson process with intensity 10 or 20, as indicated in the name of the scenario. Low CSI levels were spatially distributed as in type A scenarios, but with intensity 90 and 80 so that combined intensity of the mixture pattern (the average number of points per unit area) was always 100. Type B scenarios included (i) homogeneous scenarios BH10 and BH20 (Fig. 5B and C); (ii) large clusters scenarios BL10 and BL20 (Fig. 5I and J); and small clusters scenarios BS10 and BS20 (Fig. 5P and Q). These patterns of heterogeneity represent typical patterns of high CSI levels. MPP in Figure 1E is similar to BL20 and BS20 in Figure 5J and Q.

Type C: ‘Small clusters of High CSI’ MPPs were simulated as mixtures of independent marked point processes of high CSI levels and low CSI levels with the marginal distributions exactly the same as for Type B. High CSI levels were spatially distributed as Matern clustered point process with intensity of the Poisson process of cluster centers λ = 5 and either r = 0.15 and N_cl = 4 (for scenarios CH20, CL20 and CS20 shown in Fig. 5E, L and S) or r = 0.08 and N_cl = 2 (for scenarios CH10, CL10 and CS10 shown in Fig. 5D, K and R). Low CSI levels were spatially distributed as in type B scenarios, including (i) homogeneous scenarios CH10 and CH20 (Fig. 5D and E); (ii) large clusters scenarios CL10 and CL20 (Fig. 5K and L); and small clusters scenarios CS10 and CS20 (Fig. 5R and S). These patterns of heterogeneity are also typical for high CSI levels. MPPs in Figure 1F and in Figure 2D are similar to CL10 and CS10 in Figure 5K and R but with smaller difference between high and low CSI.

Type D: ‘Micro-clusters of High CSI’ MPPs were simulated as mixtures of independent marked point processes of high CSI levels and low CSI levels with the marginal distributions exactly the same as for Type B and C. High CSI levels were spatially distributed as Matern clustered point process with intensity of the Poisson process of cluster centers λ = 5 and either r = 0.06 and N_cl = 4 (for scenarios DH20, DL20 and DS20 shown in Fig. 5G, N and U) or r = 0.04 and N_cl = 2 (for scenarios DH10, DL10 and DS10 shown in Fig. 5F, M and T). Low CSI levels were spatially distributed as in type A and B scenarios, including (i) homogeneous scenarios CH10 and CH20 (Fig. 5D and E); (ii) large clusters scenarios CL10 and CL20 (Fig. 5K and L); and small clusters scenarios CS10 and CS20 (Fig. 5R and S). MPP in Figure 1G is similar to DL10 and DS10 in Figure 5N and U.

For each simulation scenario, 100 MPPs were simulated and their $\widehat{\mathit{cMean}}\left(d\right)$ and $\widehat{\mathit{cVar}}\left(d\right)$ were computed using the R package spatstat (Baddeley and Turner, 2005). Then the AUcMean and AUcVar were tabulated for $d_{\text{max}}=0.05,0.1,\dots ,1.0$. The resulting indices for the first 50 simulated patterns for each scenario are shown in Supplementary Figures S6–S9. For scenarios without high CSI levels (AH, AL, AS) and scenarios with homogeneously distributed high and all CSI levels (BH10, BH20), the levels of AUcMean and AUcVar were independent of d_max. With large clusters of cancer cells and homogeneously distributed high CSI levels (BL10, BL20), AUcMean and AUcVar were minimally sensitive to d_max at the lower values. However, with small clusters of cancer cells and homogeneously distributed high CSI levels (BS10, BS20), AUcMean and AUcVar increased up to $\sim d_{\mathit{max}}=0.4$ and then stabilized on the same level (Supplementary Figs S6 and S7). Similar dependence on d_max was observed for AUcMean in all type C and D scenarios with small clusters of cancer cells (CS10, CS20, DS10, DS20, Supplementary Fig. S8) and for AUcVar in scenarios CS10 and CS20 (Supplementary Fig. S9). Meanwhile, for the rest of the type C and D scenarios, AUcMean initially decreased for small d_max and then stabilized on the same level (Supplementary Fig. S8). The changes were small for scenarios with 10% of high CSI levels and larger for scenarios with 20% of high CSI levels. Also in type C and D scenarios, AUcVar showed higher magnitude and variability of dependence on d_max (Supplementary Fig. S9) with majority of scenarios yielding quite different values of AUcVar for $d_{\text{max}}\le 0.2$ and $d_{\text{max}}\ge 0.5$. Figure 6 shows the boxplots of $\mathit{AUcVar}(0.1)$ and marginal MSI distributions for all simulated MPPs patterns. Supplementary Figures S10 and S11 present also boxplots of the marginal variances, AUcMean and AUcVar for $d_{\text{max}}=0.2,0.5,1.0$.

Fig. 6.

Marginal mean distributions (A, C, E) and AUcVar distributions (B, D, F) by typical pattern of high CSI levels: homogeneous (A, B), large clusters (C, D), small clusters (E, F)

In summary, mean and variance of the marginal mark distributions are clearly different for different proportions of high CSI levels (none versus 10% versus 20%) and insensitive to the differences between spatial distributions of high CSI levels (type B versus C versus D). In contrast, AUcMean and AUcVar distinguish between different types of high CSI heterogeneity for suitably chosen d_max. These metrics increase as the size of the high CSI clusters decrease (type B corresponds to a cluster as big as MPP) even when the marginal distribution of CSI levels is the same (Fig. 6). However, this distinction between different types of CSI heterogeneity diminishes and disappears when d_max becomes substantially larger than the size of the high CSI clusters ($d_{\text{max}}\ge 0.5$ in our simulations). Importantly, these properties of the spatial and marginal metrics are consistent in different overall point patterns (homogeneous, large or small clusters of points).

Thus, the proposed spatial indices AUcMean and AUcVar provide numeric metrics that can distinguish between different common types of intra-tumoral heterogeneity of CSI levels. Meanwhile, mean and variance of the marginal distribution of CSI levels are sensitive to the differences in proportions and magnitude of high CSI levels but not to the differences in spatial distribution of high CSI levels.

6 Discussion

We developed a methodology that provides objective means to quantify intratumoral heterogeneity of proteins or other analyte levels in IHC images at single cell resolution. Our studies demonstrate that AUcVar metric of CSI expression heterogeneity may provide prognostic information either when the standard MSI levels can serve as outcome predictors (Ki67 case) or when MSI levels are uninformative as predictors of clinical outcome (TWIST1 case). The proposed spatial indices AUcMean and AUcVar are continuous metrics, but it is possible to use them as continuous biomarkers or dichotomize. In this work, we simultaneously optimized dichotomization and selection of d_max for support of AUcMean and AUcVar. An alternative way of selecting d_max may be based on tissue morphology (the size of the islands of cancer cells) or the size of the clusters that are expected to matter from the biological point of view.

Our real data analysis showed very low sensitivity of continuous AUcMean and AUcVar to the choice of d_max. However, the prognostic values of dichotomized AUcMean and AUcVar were improved by optimizing d_max. Based on simulation results, the AUcMean and AUcVar are robust when d_max is large enough in scenarios where high CSI signals do not tend to cluster. Visual examination of the ICH images or sample MPPs may be used to determine whether high CSI signals do tend to cluster. In the absence of observed clustering, it is recommended to choose large d_max for robust results. However, when clusters of high CSI signals are prevalent, then AUcMean and AUcVar may be sensitive to the choice of d_max. Our simulations indicate that choosing d_max equal to the smallest size of the clusters of interest yields higher AUcMean and AUcVar values for patterns with smaller clusters of high CSI signals as compared to AUcMean and AUcVar values for patterns with larger clusters of high CSI signals. The size of the clusters of high CSI signals can be evaluated in exploratory analysis of marked point patterns of cancer cells. It is expected that the size of the high CSI clusters would vary between different proteins and across different cancer types. Moreover, the size of the high CSI clusters may also vary substantially from patient to patient due to inter-tumor heterogeneity. Therefore, when sufficient amount of data is available, it is always beneficial to perform optimization of d_max using a standard training/validation or cross-validation approach.

For TWIST1, our results using continuous AUcMean versus dichotomized AUcVar may appear contradicting. The univariate effects of MSI or AUcMean with HR<1 disagree with multiple reports that high TWIST1 in breast cancer is associated with poor prognosis (Qiao et al., 2017). The results indicating higher risk for patients with high TWIST1 AUcVar (which is only possible when there is a subpopulation of cells with high TWIST1 expression) are more consistent with published results. The observed univariate effects of MSI or AUcMean are most likely due to confounding between high MSI or AUcMean and low AUcVar levels in 56% of the patients (Fig. 3C).

One limitation of the proposed approach is that it requires single cell segmentation. However, segmentation is necessary to tell apart cancer and stroma cells, and advances in histology cell segmentation software continue to improve cell segmentation accuracy. Another potential limitation for analysis of TMA cores and biopsies is a necessity to have large enough number of cancer cells available for estimating AUcMean and AUcVar. But this is not a limitation for using the proposed approach to analyze the data from the whole tissue slides that include tens of thousands cancer cells.

For the present work, we applied the proposed methods to QIF-IHC levels of proteins in breast cancer, but our approach is directly applicable to other analytes, including ribonucleic acids and post-translational protein modifications, as well as to any histology-based quantification method that allows capturing continuous analyte levels in individual cells, including chromogen, fluorescence or mass spectrometry-based analyses. Moreover, our methodology is applicable to quantification of spatial cell-to-cell heterogeneity in analytes not only within the cancer cell population but also across populations of non-malignant stromal cells of the tumors (e.g. fibroblasts, endothelial cells and immune cells), as well as to any solid cancer types, healthy tissues and benign disease.