A BAYESIAN MARK INTERACTION MODEL FOR ANALYSIS OF TUMOR PATHOLOGY IMAGES

Abstract

With the advance of imaging technology, digital pathology imaging of tumor tissue slides is becoming a routine clinical procedure for cancer diagnosis. This process produces massive imaging data that capture histological details in high resolution. Recent developments in deep-learning methods have enabled us to identify and classify individual cells from digital pathology images at large scale. Reliable statistical approaches to model the spatial pattern of cells can provide new insight into tumor progression and shed light on the biological mechanisms of cancer. We consider the problem of modeling spatial correlations among three commonly seen cells observed in tumor pathology images. A novel geostatistical marking model with interpretable underlying parameters is proposed in a Bayesian framework. We use auxiliary variable MCMC algorithms to sample from the posterior distribution with an intractable normalizing constant. We demonstrate how this model-based analysis can lead to sharper inferences than ordinary exploratory analyses, by means of application to three benchmark datasets and a case study on the pathology images of 188 lung cancer patients. The case study shows that the spatial correlation between tumor and stromal cells predicts patient prognosis. This statistical methodology not only presents a new model for characterizing spatial correlations in a multitype spatial point pattern conditioning on the locations of the points, but also provides a new perspective for understanding the role of cell-cell interactions in cancer progression.

Keywords: Markov random field; Multitype point pattern; double Metropolis-Hastings; spatial correlation.

Fig. 1.

The plots of the rescaled marked points of [left]: amacrine with a unit standing for approximate 1000 μm, including 142 “light-off” cells (○) and 152 “light-on” cells (+); [middle]: betacells with a unit standing for approximate 1000 μm, including 70 “light-off” cells (○) and 65 “light-on” cells (+); [right]: lansing with a unit standing for approximate 282 m (≈ 924 ft), including 135 black oaks (○), 703 hickories (+), 514 maples (Δ), 105 miscellaneous trees (×), 346 red oaks (◻) and 448 white oaks (*).

Fig. 2.

The MIF functions estimated from [left]: amacrine; [middle]: betacells; [right]: lansing (only the MIFs between the same mark are shown here; see Figure S8 for the numerical results of interactions between different marks).

Fig. 3.

Lung cancer case study: Two examples of the rescaled marked point data from NLST dataset, where black, red and green points represent lymphocyte (○), stromal (+) and tumor (Δ) cells. For the data shown in the left, $\widehat{\lambda }=172.102$, ${\widehat{\pi }}_{\text{lym}}=0.022$, ${\widehat{\pi }}_{\text{str}}=0.173$, ${\widehat{\pi }}_{\text{tum}}=0.805$ and ${\widehat{\varphi }}_{\text{tum},\text{ str}}=0.012$ For the data shown in the right, $\widehat{\lambda }=169.268$, ${\widehat{\pi }}_{\text{lym}}=0.011$, ${\widehat{\pi }}_{\text{str}}=0.603$, ${\widehat{\pi }}_{\text{tum}}=0.386$ and ${\widehat{\varphi }}_{\text{tum},\text{str}}=0.162$.

Fig. 4.

Lung cancer case study: The Kaplan-Meier plot for the low and high-risk groups obtained by leave-one-out cross-validation (log rank test p-value < 0.0001).

Fig. 5.

Lung cancer case study: [left] The BIC plot of the model-based clustering on the patient-level parameters; [middle] The radar chart of the averaged patient-level parameters of the three groups (shown in different colors), where the outer ring and the center have the values of 0 and 1, respectively; [right] The Kaplan-Meier plot for the three groups with patient survival (log rank test p-value = 0.015).