A Compensator Characterization of Planar Point Processes

Basic methods of explorative statistical analysis for stationary and isotropic planar point processes are briefly and informally reviewed. At the explorative level, planar point patterns may be characterized in terms of the intensity, the K-function and the pair correlation function. These second-order functions enable one to classify a given point process as completely random, clustering or repulsive. The repulsive behaviour may be quantified by an estimate of the hard-core distance. In the exploratory approach, the statistics are essentially free from model assumptions. Second-order spatial functions have been estimated to characterize genuine planar point processes in the macroscopic domain, for example in forestry, geography and epidemiology. For light microscopy and transmission electron microscopy, two situations are distinguished, which may be summarized as the genuine planar case and the stereological case. In the genuine planar case, a direct interpretation of the results of spatial statistics is feasible. Here, monolayers in cell culture, intramembranous particles on freeze fracture specimens and amacrine cells of the retina are mentioned as examples. In the stereological case, point patterns are generated by sections through 3D structures. Here the observed point patterns may arise as the centres of sectional profiles of particles, or as centres of sectional profiles of spatial fibre processes. In both situations, exploratory spatial point process statistics allow a quantitative characterization of sectional images for the purposes of group comparisons and classification. Moreover, for spatial fibre processes it has recently been shown that the observed pair correlation function of the centres of the fibre profiles is an estimate of the reduced pair correlation function of the fibre process in 3D. Hence for fibre processes a stereological interpretation of point process statistics obtained from sections is an additional option.

This paper provides a rigorous foundation for the second-order analysis of stationary point processes on general spaces. It illuminates the results of Bartlett on spatial point processes, and covers the point processes of stochastic geometry, including the line and hyperplane processes of Davidson and Krickeberg. The main tool is the decomposition of moment measures pioneered by Krickeberg and Vere-Jones. Finally some practical aspects of the analysis of point processes are discussed.

410O - Conditional Probability of Survival in Patients with Glioblastoma Multiforme in the Temozolomide Treatment Era

The disease outcome for patients with cancer is typically described in terms of estimated survival from diagnosis. Conditional probability offers more relevant information regarding survival for patients once they have survived for some time. We report conditional survival probabilities on the basis of 498 patients with glioblastoma multiforme receiving radiation and chemotherapy. For 1-year survivors, we evaluated variables that may inform subsequent survival. Motivated by the trend in data, we also evaluated the assumption of constant hazard. Patients enrolled onto seven phase II protocols between 1975 and 2007 were included. Conditional survival probabilities and 95% CIs were calculated. The Cox proportional hazards model was used to evaluate prognostic values of age, Karnofsky performance score (KPS), and prior progression 1-year post diagnosis. To assess the constant hazard assumption, we used a likelihood-ratio test to compare the Weibull and exponential distributions. The probabilities of surviving an additional year given survival to 1, 2, 3, and 4 years were 35%, 49%, 69%, and 93%, respectively. For patients who survived for 1 year, lower KPS and progression were significantly predictive of shorter survival (both P < .001), but age was not (hazard ratio, 1.22 for a 10-year increase; P = .25). The Weibull distribution fits the data significantly better than exponential (P = .02), suggesting nonconstant hazard. Conditional probabilities provide encouraging information regarding life expectancy to survivors of glioblastoma multiforme. Our data also showed that the constant hazard assumption may be violated in modern brain tumor trials. For single-arm trials, we advise using individual patient data from historical data sets for efficacy comparisons.

Conditional probability of survival in patients with biliary atresia after Kasai portoenterostomy: a Chinese population-based study

Point process analyses are widely used in ecology and geography to understand the impact and relevance of spatial distribution of points in a complex system. To date, only few studies have explored point process analyses in the context of tumor heterogeneity. Malignancies often show variable patterns of cellular distribution, and the relationship of these topographic variables with underlying biological processes and clinical outcomes is not well understood. Here, we performed spatial point process analyses in diffuse large B-cell lymphoma (DLBCL), leveraging advances in multiplexed immunohistochemistry and cellular phenotyping, with downstream multi-omic and clinicopathological analyses. We have demonstrated that survival in DLBCL is strongly associated with the fraction of malignant cells showing co-expression of the oncogenes MYC and BCL2 in the absence of BCL6 (M+2+6-). These cells display non-random spatial organization within tumor infiltrates, deviating from a poisson distribution. We therefore modeled the spatial organization of M+2+6- cells within DLBCL, using x-y coordinate information from multiplexed fluorescent immunohistochemistry (mfIHC) in four independent cohorts (N=449 patients). We derived spatial point patterns, upon which Geyers point process models were applied. We observed that patients could be divided into two groups based on these: one group showed “clustered” spatial organization, while the other displayed a “dispersed” M+2+6- cell distribution. Cases with predominantly “dispersed” M+2+6- cells showed shorter overall survival in all analyzed cohorts (P &amp;lt; 0.05 in 4/4 cohorts). We performed multi-omic analyses to identify potential biological explanations for this association between topography and clinical outcome. Using digital spatial profiling of the transcriptome from CD20, CD3 and CD68 compartments in 47 DLBCL samples, we observed that lymphomas with an M+2+6- ‘dispersed’ phenotype had an immunologically cold microenvironment enriched in Tregs and exhausted CD4+ and CD8+ T cells. Through an integration with single-cell transcriptomic analyses (N=22 samples) we observed that malignant B-cells from cases with M+2+6- ‘dispersed’ phenotype expressed genes implicated in cell migration and adhesion, but also in potentially targetable immune checkpoints such as LAG3. In summary, by integrating multiplexed immunophenotyping and point process analysis with molecular profiling in the setting of DLBCL, we show that a dispersed pattern of distribution of the M+2+6- subclonal fraction uniquely confers poor prognosis, and associates with a potentially reversible immune cold microenvironment composition. This represents the first demonstration that the spatial distribution of malignant cell subpopulations in lymphoma can embody biological and clinical significance. Citation Format: Shruti Shridar, Michal Marek Hoppe, Patrick Jaynes, Gayatri Kumar, Siddham Jasoria, Ziwei Meng, Vaibhav Rajan, Kasthuri Kannan, Claudio Tripodo, Anand Devaprasath Jeyasekharan. The spatial organization of cells expressing MYC and BCL2 affects immune microenvironment composition and prognosis in DLBCL [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 3648.

BackgroundLeft ventricular assist devices (LVADs) improve outcomes in patients with end‐stage heart failure and are increasingly implanted for destination therapy. We describe dynamic estimates of event‐free survival with conditional survival probabilities in a destination therapy LVAD population.Methods and ResultsWe studied 8245 adult patients in INTERMACS (Interagency Registry for Mechanically Assisted Circulatory Support) implanted with a continuous‐flow destination therapy LVAD. The composite primary end point was death, device exchange or removal, or heart transplantation. Conditional survival probabilities were calculated and stratified by implantation characteristics and nonfatal adverse events experienced within the first year after implant. Probabilities of surviving an additional 1 to 3 years were numerically higher after longer prior event‐free survival. INTERMACS profile 1, extracorporeal membrane oxygenation support, prior or concomitant surgery, and dialysis within 48 hours of implantation were associated with significantly lower event‐free survival in the first year but did not impact event‐free survival beyond then. For patients who experienced a nonfatal adverse event within the first year, subsequent 1‐year conditional survival was lower than in the absence of that event for stroke (65% [95% CI, 57%–73%] versus 75% [95% CI, 73%–77%]; P<0.001), device‐related infection (64% [95% CI 57%–71%] versus 76% [95% CI, 74%–78%]; P<0.001), and pump thrombosis or malfunction (64% [95% CI, 57%–70%] versus 76% [95% CI, 74%–78%]; P<0.001).ConclusionsConditional survival in patients with destination therapy LVADs improves over time, even for patients with unfavorable implantation characteristics. However, LVAD‐related complications including stroke, device‐related infection, and pump thrombosis or malfunction have an enduring negative influence on dynamic estimates of long‐term prognosis.

With standard treatment for glioblastoma (GBM) consisting of surgery followed by radiotherapy (RT) with concurrent and adjuvant temozolomide (TMZ), median survival is ~14.6 months. This is not as informative to patients who have survived for some time. Conditional probability of survival may offer more relevant survival estimates. Outcomes/conditional probability of survival and post-progression survival (PPS) estimates were retrospectively reviewed in the TMZ treatment era of 882 consecutive patients with a diagnosis of GBM from January 2004 to August 2010. Median age of entire cohort was 62 years including 62 % males. Baseline performance status (PS) was 0-1 in 67, 23 % had frontal lobe tumors, 58 % received concurrent RT/TMZ ± adjuvant TMZ. Survival (OS) was similar for those with frontal lobe tumors versus other locations (P = 0.25). OS for patients receiving standard RT/TMZ ± TMZ was 14.2 months. Age, PS, extent of surgery, therapy post-surgery had significant effects on OS. OS for entire cohort at 1, 2, 3, 4, 5 years was 43.4, 17.9, 10.4, 8.4, 7.2 % respectively. Conditional probability of survival of an additional year given survival to 1, 2, 3, 4, 5 years was 41.4, 58, 80.7, 85.7, 81.5 % respectively. Conditional probability of survival for those patients receiving concurrent RT/TMZ ± adjuvant TMZ was similar. Patients who progress >18 months after their initial treatment for GBM had significantly greater 2 and 5 year PPS as well as OS. Conditional probabilities of survival may provide more meaningful life expectancy predictions for survivors of GBM than conventional survival outcomes.

Machine Learning Classification of Spatial Patterns of Malignant Cells Reveals Implications in Prognosis and Tumor Microenvironment Composition in Lymphoma

This paper presents methods for the detection and assessment of non-infectious uveitis, a leading cause of vision loss in working age adults. In the first part, we propose a classification model that can accurately predict the presence of uveitis and differentiate between different stages of the disease using optical coherence tomography (OCT) images. We utilize the Grad-CAM visualization technique to elucidate the decision-making process of the classifier and gain deeper insights into the results obtained. In the second part, we apply and compare three methods for the detection of detached particles in the retina that are indicative of uveitis. The first is a fully supervised detection method, the second is a marked point process (MPP) technique, and the third is a weakly supervised segmentation that produces per-pixel masks as output. The segmentation model is used as a backbone for a fully automated pipeline that can segment small particles of uveitis in two-dimensional (2-D) slices of the retina, reconstruct the volume, and produce centroids as points distribution in space. The number of particles in retinas is used to grade the disease, and point process analysis on centroids in three-dimensional (3-D) shows clustering patterns in the distribution of the particles on the retina.

Conditional Survival of Patients with Diffuse Large B-Cell Lymphoma.

Methods for the statistical analysis of stationary spatial point process data are now well established, methods for nonstationary processes less so. One of many sources of nonstationary point process data is a case-control study in environmental epidemiology. In that context, the data consist of a realization of each of two spatial point processes representing the locations, within a specified geographical region, of individual cases of a disease and of controls drawn at random from the population at risk. In this article, we extend work by Baddeley, Møller, and Waagepetersen (2000, Statistica Neerlandica54, 329-350) concerning estimation of the second-order properties of a nonstationary spatial point process. First, we show how case-control data can be used to overcome the problems encountered when using the same data to estimate both a spatially varying intensity and second-order properties. Second, we propose a semiparametric method for adjusting the estimate of intensity so as to take account of explanatory variables attached to the cases and controls. Our primary focus is estimation, but we also propose a new test for spatial clustering that we show to be competitive with existing tests. We describe an application to an ecological study in which juvenile and surviving adult trees assume the roles of controls and cases.

Placement of deep brain stimulating electrodes in the subthalamic nucleus (STN) to treat Parkinson's disease (PD) also allows the recording of single neuron spiking activity. Analyses of these unique data offer an important opportunity to better understand the pathophysiology of PD. Despite the point process nature of PD neural spiking activity, point process methods are rarely used to analyze these recordings. We develop a point process representation of PD neural spiking activity using a generalized linear model to describe long- and short-term temporal dependencies in the spiking activity of 28 STN neurons from seven PD patients and 35 neurons from one healthy primate (surrogate control) recorded, while the subjects executed a directed-hand movement task. We used the point process model to characterize each neuron's bursting, oscillatory, and directional tuning properties during key periods in the task trial. Relative to the control neurons, the PD neurons showed increased bursting, increased 10-30 Hz oscillations, and increased fluctuations in directional tuning. These features, which traditional methods failed to capture accurately, were efficiently summarized in a single model in the point process analysis of each neuron. The point process framework suggests a useful approach for developing quantitative neural correlates that may be related directly to the movement and behavioral disorders characteristic of PD.

Purpose The purpose of this paper is to review the Fuzzy Markov development for assessing the structural integrity of buried transportation bridges. In doing so, the appropriateness of Fuzzy Markov will be assessed, leading to the subsequent model. Design/methodology/approach This research will utilize the Fuzzy Markov techniques as the conceptual framework. Such methodology is further supported via the utilization and evaluation of 30 buried transportation bridges using the developed Fuzzy Markov model. Findings Subsequently, through a developed Fuzzy Markov model, this research found that as the basis of structural resilience, specific matrices for age-dependent transition probability can be compiled using conditional survival probabilities in the various structural states; as the basis of structural integrity, specific environmental and economic schemes can also be established based on inspection intervals, intervention systems and failure phases; exact inspection and maintenance intervals can be scheduled to further prolong an asset’s life; and clear and early warning signs can also be formulated for immediate intervention when the structural integrity of the asset are indeed compromised. Originality/value The gap within the literature currently surrounds the limitation of computational analysis for some buried structures such as bridges. Specifically, to streamline such evaluation and regimes, a Fuzzy Markov is developed and reviewed.

Conditional Survival Probabilities Following Stereotactic Body Radiation Therapy for Early-Stage Non-small Cell Lung Cancer