[Semiparametric analysis of nonparametric proportional hazards models with mixed dependent censored data].

OBJECTIVE: To construct a nonparametric proportional hazards (PH) model for mixed informative interval-censored failure time data for predicting the risks in heart transplantation surgeries. METHODS: Based on the complexity of mixed informative interval-censored failure time data, we considered the interdependent relationship between failure time process and observation time process, constructed a nonparametric proportional hazards (PH) model to describe the nonlinear relationship between the risk factors and heart transplant surgery risks and proposed a two-step sieve estimation maximum likelihood algorithm. An estimation equation was established to estimate frailty variables using the observation process model. Ⅰ-spline and B-spline were used to approximate the unknown baseline hazard function and nonparametric function, respectively, to obtain the working likelihood function in the sieve space. The partial derivative of the model parameters was used to obtain the scoring equation. The maximum likelihood estimation of the parameters was obtained by solving the scoring equation, and a function curve of the impact of risk factors on the risk of heart transplantation surgery was drawn. RESULTS: Simulation experiment suggested that the estimated values obtained by the proposed method were consistent and asymptotically effective under various settings with good fitting effects. Analysis of heart transplant surgery data showed that the donor's age had a positive linear relationship with the surgical risk. The impact of the recipient's age at disease onset increased at first and then stabilized, but increased against at an older age. The donor-recipient age difference had a positive linear relationship with the surgical risk of heart transplantation. CONCLUSION: The nonparametric PH model established in this study can be used for predicting the risks in heart transplantation surgery and exploring the functional relationship between the surgery risks and the risk factors.

Comparison of outcomes between off-pump and on-pump coronary artery bypass graft surgery using collaborative targeted maximum likelihood estimation.

There are some discrepancies about the superiority of the off-pump coronary artery bypass grafting (CABG) surgery over the conventional cardiopulmonary bypass (on-pump). The aim of this study was estimating risk ratio of mortality in the off-pump coronary bypass compared with the on-pump using a causal model known as collaborative targeted maximum likelihood estimation (C-TMLE). The data of the Tehran Heart Cohort study from 2007 to 2020 was used. A collaborative targeted maximum likelihood estimation and targeted maximum likelihood estimation, and propensity score (PS) adjustment methods were used to estimate causal risk ratio adjusting for the minimum sufficient set of confounders, and the results were compared. Among 24,883 participants (73.6% male), 5566 patients died during an average of 8.2 years of follow-up. The risk ratio estimates (95% confidence intervals) by unadjusted log-binomial regression model, PS adjustment, TMLE, and C-TMLE methods were 0.86 (0.78-0.95), 0.88 (0.80-0.97), 0.88 (0.80-0.97), and 0.87(0.85-0.89), respectively. This study provides evidence for a protective effect of off-pump surgery on mortality risk for up to 8 years in diabetic and non-diabetic patients.

Leveraging new methods for comprehensive characterization of mitochondrial DNA in esophageal squamous cell carcinoma.

BACKGROUND: Mitochondria play essential roles in tumorigenesis; however, little is known about the contribution of mitochondrial DNA (mtDNA) to esophageal squamous cell carcinoma (ESCC). Whole-genome sequencing (WGS) is by far the most efficient technology to fully characterize the molecular features of mtDNA; however, due to the high redundancy and heterogeneity of mtDNA in regular WGS data, methods for mtDNA analysis are far from satisfactory. METHODS: Here, we developed a likelihood-based method dMTLV to identify low-heteroplasmic mtDNA variants. In addition, we described fNUMT, which can simultaneously detect non-reference nuclear sequences of mitochondrial origin (non-ref NUMTs) and their derived artifacts. Using these new methods, we explored the contribution of mtDNA to ESCC utilizing the multi-omics data of 663 paired tumor-normal samples. RESULTS: dMTLV outperformed the existing methods in sensitivity without sacrificing specificity. The verification using Nanopore long-read sequencing data showed that fNUMT has superior specificity and more accurate breakpoint identification than the current methods. Leveraging the new method, we identified a significant association between the ESCC overall survival and the ratio of mtDNA copy number of paired tumor-normal samples, which could be potentially explained by the differential expression of genes enriched in pathways related to metabolism, DNA damage repair, and cell cycle checkpoint. Additionally, we observed that the expression of CBWD1 was downregulated by the non-ref NUMTs inserted into its intron region, which might provide precursor conditions for the tumor cells to adapt to a hypoxic environment. Moreover, we identified a strong positive relationship between the number of mtDNA truncating mutations and the contribution of signatures linked to tumorigenesis and treatment response. CONCLUSIONS: Our new frameworks promote the characterization of mtDNA features, which enables the elucidation of the landscapes and roles of mtDNA in ESCC essential for extending the current understanding of ESCC etiology. dMTLV and fNUMT are freely available from https://github.com/sunnyzxh/dMTLV and https://github.com/sunnyzxh/fNUMT , respectively.

Shared single copy genes are generally reliable for inferring phylogenetic relationships among polyploid taxa.

Polyploidy, or whole-genome duplication, is expected to confound the inference of species trees with phylogenetic methods for two reasons. First, the presence of retained duplicated genes requires the reconciliation of the inferred gene trees to a proposed species tree. Second, even if the analyses are restricted to shared single copy genes, the occurrence of reciprocal gene loss, where the surviving genes in different species are paralogs from the polyploidy rather than orthologs, will mean that such genes will not have evolved under the corresponding species tree and may not produce gene trees that allow inference of that species tree. Here we analyze three different ancient polyploidy events, using synteny-based inferences of orthology and paralogy to infer gene trees from nearly 17,000 sets of homologous genes. We find that the simple use of single copy genes from polyploid organisms provides reasonably robust phylogenetic signals, despite the presence of reciprocal gene losses. Such gene trees are also most often in accord with the inferred species relationships inferred from maximum likelihood models of gene loss after polyploidy: a completely distinct phylogenetic signal present in these genomes. As seen in other studies, however, we find that methods for inferring phylogenetic confidence yield high support values even in cases where the underlying data suggest meaningful conflict in the phylogenetic signals.

Optimizing scan time and bayesian penalized likelihood reconstruction algorithm in copper-64 PET/CT imaging: a phantom study.

Objectives: The aim of this study was to evaluate Cu-64 PET phantom image quality using Bayesian Penalized Likelihood (BPL) and Ordered Subset Expectation Maximum with point-spread function modeling (OSEM-PSF) reconstruction algorithms. In the BPL, the regularization parameterßwas varied to identify the optimum value for image quality. In the OSEM-PSF, the effect of acquisition time was evaluated to assess the feasibility of shortened scan duration.Methods: A NEMA IEC PET body phantom was filled with known activities of water soluble Cu-64. The phantom was imaged on a PET/CT scanner and was reconstructed using BPL and OSEM-PSF algorithms. For the BPL reconstruction, variousßvalues (150, 250, 350, 450, and 550) were evaluated. For the OSEM-PSF algorithm, reconstructions were performed using list-mode data intervals ranging from 7.5 to 240 s. Image quality was assessed by evaluating the signal to noise ratio (SNR), contrast to noise ratio (CNR), and background variability (BV).Results: The SNR and CNR were higher in images reconstructed with BPL compared to OSEM-PSF. Both the SNR and CNR increased with increasingß, peaking atß= 550. The CNR for allß, sphere sizes and tumor-to-background ratios (TBRs) satisfied the Rose criterion for image detectability (CNR > 5). BPL reconstructed images withß= 550 demonstrated the highest improvement in image quality. For OSEM-PSF reconstructed images with list-mode data duration ≥ 120 s, the noise level and CNR were not significantly different from the baseline 240 s list-mode data duration.Conclusions: BPL reconstruction improved Cu-64 PET phantom image quality by increasing SNR and CNR relative to OSEM-PSF reconstruction. Additionally, this study demonstrated scan time can be reduced from 240 to 120 s when using OSEM-PSF reconstruction while maintaining similar image quality. This study provides baseline data that may guide future studies aimed to improve clinical Cu-64 imaging.

Investigating the potential of single-cell DNA methylation data to detect allele-specific methylation and imprinting.

Allele-specific methylation (ASM) is an epigenetic modification whereby one parental allele becomes methylated and the other unmethylated at a specific locus. ASM is most often driven by the presence of nearby heterozygous variants that influence methylation, but also occurs somatically in the context of genomic imprinting. In this study, we investigate ASM using publicly available single-cell reduced representation bisulfite sequencing (scRRBS) data on 608 B cells sampled from six healthy B cell samples and 1,230 cells from 11 chronic lymphocytic leukemia (CLL) samples. We developed a likelihood-based criterion to test whether a CpG exhibited ASM, based on the distributions of methylated and unmethylated reads both within and across cells. Applying our likelihood ratio test, 65,998 CpG sites exhibited ASM in healthy B cell samples according to a Bonferroni criterion (p < 8.4 × 10-9), and 32,862 CpG sites exhibited ASM in CLL samples (p < 8.5 × 10-9). We also called ASM at the sample level. To evaluate the accuracy of our method, we called heterozygous variants from the scRRBS data, which enabled variant-based calls of ASM within each cell. Comparing sample-level ASM calls to the variant-based measures of ASM, we observed a positive predictive value of 76%-100% across samples. We observed high concordance of ASM across samples and an overrepresentation of ASM in previously reported imprinted genes and genes with imprinting binding motifs. Our study demonstrates that single-cell bisulfite sequencing is a potentially powerful tool to investigate ASM, especially as studies expand to increase the number of samples and cells sequenced.

Robust best linear weighted estimator with missing covariates in survival analysis.

Missing data in covariates can result in biased estimates and loss of power to detect associations. We consider Cox regression in which some covariates are subject to missing. The inverse probability weighted approach is often applied to regression analysis with missing covariates. Inverse probability weighted estimators typically are less efficient than likelihood-based estimators, but in general are more robust against model misspecification. In this article, we propose a robust best linear weighted estimator for Cox regression with missing covariates. Our proposed estimator is the projection of the simple inverse probability weighted estimator onto the orthogonal complement of the score space based on a working regression model of the observed data. The efficiency gain is from the use of the association between the survival outcome variable and the available covariates, which is the working regression model. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via extensive simulation studies. The methods are applied to a colorectal cancer study to assess the association of the microsatellite instability status with colorectal cancer-specific mortality.

Molecular identification, phylogenetic analysis and histopathological study of pathogenic free-living amoebae isolated from discus fish (Symphysodon aequifasciatus) in Iran: 2020-2022.

Free-living amoebae (FLA) are capable of inhabiting diverse reservoirs independently, without relying on a host organism, hence their designation as "free-living". The majority of amoebae that infect freshwater or marine fish are amphizoic, or free-living forms that may colonize fish under particular circumstances. Symphysodon aequifasciatus, commonly referred to as the discus, is widely recognized as a popular ornamental fish species. The primary objective of the present study was to determine the presence of pathogenic free-living amoebae (FLA) in samples of discus fish. Fish exhibiting clinical signs, sourced from various fish farms, were transferred to the ornamental fish clinic. The skin, gills, and intestinal mucosa of the fish were collected and subjected to culturing on plates containing a 1% non-nutrient agar medium. The detection of FLA was conducted through morphological, histopathological and molecular methods. The construction of the phylogenetic tree for Acanthamoeba genotypes was achieved using the maximum likelihood approach. The molecular sequence analysis revealed that all cultures that tested positive for FLA were T4 genotype of Acanthamoeba and Acanthamoeba sp. The examination of gill samples using histopathological methods demonstrated the presence of lamellar epithelial hyperplasia, significant fusion of secondary lamellae, and infiltration of inflammatory cells. A multitude of cysts, varying in shape from circular to elliptical, were observed within the gills. The occurrence of interlamellar vesicles and amoeboid organisms could be observed within the epithelial tissue of the gills. In the current study, presence of the Acanthamoeba T4 genotype on the skin and gills of discus fish exhibiting signs of illness in freshwater ornamental fish farms was identified. This observation suggests the potential of a transmission of amoebic infection from ornamental fish to humans, thereby highlighting the need for further investigation into this infection among ornamental fish maintained as pets, as well as individuals who interact with them and their environment.

Robust data integration from multiple external sources for generalized linear models with binary outcomes.

We aim to estimate parameters in a generalized linear model (GLM) for a binary outcome when, in addition to the raw data from the internal study, more than 1 external study provides summary information in the form of parameter estimates from fitting GLMs with varying subsets of the internal study covariates. We propose an adaptive penalization method that exploits the external summary information and gains efficiency for estimation, and that is both robust and computationally efficient. The robust property comes from exploiting the relationship between parameters of a GLM and parameters of a GLM with omitted covariates and from downweighting external summary information that is less compatible with the internal data through a penalization. The computational burden associated with searching for the optimal tuning parameter for the penalization is reduced by using adaptive weights and by using an information criterion when searching for the optimal tuning parameter. Simulation studies show that the proposed estimator is robust against various types of population distribution heterogeneity and also gains efficiency compared to direct maximum likelihood estimation. The method is applied to improve a logistic regression model that predicts high-grade prostate cancer making use of parameter estimates from 2 external models.

A parametric additive hazard model for time-to-event analysis.

BACKGROUND: In recent years, the use of non- and semi-parametric models which estimate hazard ratios for analysing time-to-event outcomes is continuously criticized in terms of interpretation, technical implementation, and flexibility. Hazard ratios in particular are critically discussed for their misleading interpretation as relative risks and their non-collapsibility. Additive hazard models do not have these drawbacks but are rarely used because they assume a non- or semi-parametric additive hazard which renders computation and interpretation complicated. METHODS: As a remedy, we propose a new parametric additive hazard model that allows results to be reported on the original time rather than on the hazard scale. Being an essentially parametric model, survival, hazard and probability density functions are directly available. Parameter estimation is straightforward by maximizing the log-likelihood function. RESULTS: Applying the model to different parametric distributions in a simulation study and in an exemplary application using data from a study investigating medical care to lung cancer patients, we show that the approach works well in practice. CONCLUSIONS: Our proposed parametric additive hazard model can serve as a powerful tool to analyze time-to-event outcomes due to its simple interpretation, flexibility and facilitated parameter estimation.

Likelihood-based feature representation learning combined with neighborhood information for predicting circRNA-miRNA associations.

Connections between circular RNAs (circRNAs) and microRNAs (miRNAs) assume a pivotal position in the onset, evolution, diagnosis and treatment of diseases and tumors. Selecting the most potential circRNA-related miRNAs and taking advantage of them as the biological markers or drug targets could be conducive to dealing with complex human diseases through preventive strategies, diagnostic procedures and therapeutic approaches. Compared to traditional biological experiments, leveraging computational models to integrate diverse biological data in order to infer potential associations proves to be a more efficient and cost-effective approach. This paper developed a model of Convolutional Autoencoder for CircRNA-MiRNA Associations (CA-CMA) prediction. Initially, this model merged the natural language characteristics of the circRNA and miRNA sequence with the features of circRNA-miRNA interactions. Subsequently, it utilized all circRNA-miRNA pairs to construct a molecular association network, which was then fine-tuned by labeled samples to optimize the network parameters. Finally, the prediction outcome is obtained by utilizing the deep neural networks classifier. This model innovatively combines the likelihood objective that preserves the neighborhood through optimization, to learn the continuous feature representation of words and preserve the spatial information of two-dimensional signals. During the process of 5-fold cross-validation, CA-CMA exhibited exceptional performance compared to numerous prior computational approaches, as evidenced by its mean area under the receiver operating characteristic curve of 0.9138 and a minimal SD of 0.0024. Furthermore, recent literature has confirmed the accuracy of 25 out of the top 30 circRNA-miRNA pairs identified with the highest CA-CMA scores during case studies. The results of these experiments highlight the robustness and versatility of our model.

Partly linear single-index cure models with a nonparametric incidence link function.

In cancer studies, it is commonplace that a fraction of patients participating in the study are cured, such that not all of them will experience a recurrence, or death due to cancer. Also, it is plausible that some covariates, such as the treatment assigned to the patients or demographic characteristics, could affect both the patients' survival rates and cure/incidence rates. A common approach to accommodate these features in survival analysis is to consider a mixture cure survival model with the incidence rate modeled by a logistic regression model and latency part modeled by the Cox proportional hazards model. These modeling assumptions, though typical, restrict the structure of covariate effects on both the incidence and latency components. As a plausible recourse to attain flexibility, we study a class of semiparametric mixture cure models in this article, which incorporates two single-index functions for modeling the two regression components. A hybrid nonparametric maximum likelihood estimation method is proposed, where the cumulative baseline hazard function for uncured subjects is estimated nonparametrically, and the two single-index functions are estimated via Bernstein polynomials. Parameter estimation is carried out via a curated expectation-maximization algorithm. We also conducted a large-scale simulation study to assess the finite-sample performance of the estimator. The proposed methodology is illustrated via application to two cancer datasets.

Adaptation of a mutual exclusivity framework to identify driver mutations within oncogenic pathways.

Distinguishing genomic alterations in cancer-associated genes that have functional impact on tumor growth and disease progression from the ones that are passengers and confer no fitness advantage have important clinical implications. Evidence-based methods for nominating drivers are limited by existing knowledge on the oncogenic effects and therapeutic benefits of specific variants from clinical trials or experimental settings. As clinical sequencing becomes a mainstay of patient care, applying computational methods to mine the rapidly growing clinical genomic data holds promise in uncovering functional candidates beyond the existing knowledge base and expanding the patient population that could potentially benefit from genetically targeted therapies. We propose a statistical and computational method (MAGPIE) that builds on a likelihood approach leveraging the mutual exclusivity pattern within an oncogenic pathway for identifying probabilistically both the specific genes within a pathway and the individual mutations within such genes that are truly the drivers. Alterations in a cancer-associated gene are assumed to be a mixture of driver and passenger mutations with the passenger rates modeled in relationship to tumor mutational burden. We use simulations to study the operating characteristics of the method and assess false-positive and false-negative rates in driver nomination. When applied to a large study of primary melanomas, the method accurately identifies the known driver genes within the RTK-RAS pathway and nominates several rare variants as prime candidates for functional validation. A comprehensive evaluation of MAGPIE against existing tools has also been conducted leveraging the Cancer Genome Atlas data.

Efficient estimation of Cox model with random change point.

In clinical studies, the risk of a disease may dramatically change when some biological indexes of the human body exceed some thresholds. Furthermore, the differences in individual characteristics of patients such as physical and psychological experience may lead to subject-specific thresholds or change points. Although a large literature has been established for regression analysis of failure time data with change points, most of the existing methods assume the same, fixed change point for all study subjects. In this paper, we consider the situation where there exists a subject-specific change point and two Cox type models are presented. The proposed models also offer a framework for subgroup analysis. For inference, a sieve maximum likelihood estimation procedure is proposed and the asymptotic properties of the resulting estimators are established. An extensive simulation study is conducted to assess the empirical performance of the proposed method and indicates that it works well in practical situations. Finally the proposed approach is applied to a set of breast cancer data.

Efficiency of the Breslow estimator in semiparametric transformation models.

Semiparametric transformation models for failure time data consist of a parametric regression component and an unspecified cumulative baseline hazard. The nonparametric maximum likelihood estimator (NPMLE) of the cumulative baseline hazard can be summarized in terms of weights introduced into a Breslow-type estimator (Weighted Breslow). At any given time point, the weights invoke an integral over the future of the cumulative baseline hazard, which presents theoretical and computational challenges. A simpler non-MLE Breslow-type estimator (Breslow) was derived earlier from a martingale estimating equation (MEE) setting observed and expected counts of failures equal, conditional on the past history. Despite much successful theoretical and computational development, the simpler Breslow estimator continues to be commonly used as a compromise between simplicity and perceived loss of full efficiency. In this paper we derive the relative efficiency of the Breslow estimator and consider the properties of the two estimators using simulations and real data on prostate cancer survival.

Maximum likelihood estimation of renal transporter ontogeny profiles for pediatric PBPK modeling.

Optimal treatment of infants with many renally cleared drugs must account for maturational differences in renal transporter (RT) activity. Pediatric physiologically-based pharmacokinetic (PBPK) models may incorporate RT activity, but this requires ontogeny profiles for RT activity in children, especially neonates, to predict drug disposition. Therefore, RT expression measurements from human kidney postmortem cortical tissue samples were normalized to represent a fraction of mature RT activity. Using these data, maximum likelihood estimated the distributions of RT activity across the pediatric age spectrum, including preterm and term neonates. PBPK models of four RT substrates (acyclovir, ciprofloxacin, furosemide, and meropenem) were evaluated with and without ontogeny profiles using average fold error (AFE), absolute average fold error (AAFE), and proportion of observations within the 5-95% prediction interval. Novel maximum likelihood profiles estimated ontogeny distributions for the following RT: OAT1, OAT3, OCT2, P-gp, URAT1, BCRP, MATE1, MRP2, MRP4, and MATE-2 K. Profiles for OAT3, P-gp, and MATE1 improved infant furosemide and neonate meropenem PBPK model AFE from 0.08 to 0.70 and 0.53 to 1.34 and model AAFE from 12.08 to 1.44 and 2.09 to 1.36, respectively, and improved the percent of data within the 5-95% prediction interval from 48% to 98% for neonatal ciprofloxacin simulations, respectively. Even after accounting for other critical population-specific maturational differences, novel RT ontogeny profiles substantially improved neonatal PBPK model performance, providing validated estimates of maturational differences in RT activity for optimal dosing in children.

A Continuous Extension of Gene Set Enrichment Analysis Using the Likelihood Ratio Test Statistics Identifies Vascular Endothelial Growth Factor as a Candidate Pathway for Alzheimer's Disease via ITGA5.

BACKGROUND: Alzheimer's disease (AD) involves brain neuropathologies such as amyloid plaque and hyperphosphorylated tau tangles and is accompanied by cognitive decline. Identifying the biological mechanisms underlying disease onset and progression based on quantifiable phenotypes will help understand disease etiology and devise therapies. OBJECTIVE: Our objective was to identify molecular pathways associated with hallmark AD biomarkers and cognitive status, accounting for variables such as age, sex, education, and APOE genotype. METHODS: We introduce a pathway-based statistical approach, extending the gene set likelihood ratio test to continuous phenotypes. We first analyzed independently each of the three phenotypes (amyloid-ß, tau, cognition) using continuous gene set likelihood ratio tests to account for covariates, including age, sex, education, and APOE genotype. The analysis involved 634 subjects with data available for all three phenotypes, allowing for the identification of common pathways. RESULTS: We identified 14 pathways significantly associated with amyloid-ß; 5 associated with tau; and 174 associated with cognition, which showed a larger number of pathways compared to biomarkers. A single pathway, vascular endothelial growth factor receptor binding (VEGF-RB), exhibited associations with all three phenotypes. Mediation analysis showed that among the VEGF-RB family genes, ITGA5 mediates the relationship between cognitive scores and pathological biomarkers. CONCLUSIONS: We presented a new statistical approach linking continuous phenotypes, gene expression across pathways, and covariates like sex, age, and education. Our results reinforced VEGF RB2's role in AD cognition and demonstrated ITGA5's significant role in mediating the AD pathology-cognition connection.

Fixed and random effect selections in generalized linear mixed models.

Generalized linear mixed models are commonly used to describe relationships between correlated responses and covariates in medical research. In this paper, we propose a simple and easily implementable regularized estimation approach to select both fixed and random effects in generalized linear mixed model. Specifically, we propose to construct and optimize the objective functions using the confidence distributions of model parameters, as opposed to using the observed data likelihood functions, to perform effect selections. Two estimation methods are developed. The first one is to use the joint confidence distribution of model parameters to perform simultaneous fixed and random effect selections. The second method is to use the marginal confidence distributions of model parameters to perform the selections of fixed and random effects separately. With a proper choice of regularization parameters in the adaptive LASSO framework, we show the consistency and oracle properties of the proposed regularized estimators. Simulation studies have been conducted to assess the performance of the proposed estimators and demonstrate computational efficiency. Our method has also been applied to two longitudinal cancer studies to identify demographic and clinical factors associated with patient health outcomes after cancer therapies.

Effect of color cross-correlated noise on the growth characteristics of tumor cells under immune surveillance.

Based on the Michaelis-Menten reaction model with catalytic effects, a more comprehensive one-dimensional stochastic Langevin equation with immune surveillance for a tumor cell growth system is obtained by considering the fluctuations in growth rate and mortality rate. To explore the impact of environmental fluctuations on the growth of tumor cells, the analytical solution of the steady-state probability distribution function of the system is derived using the Liouville equation and Novikov theory, and the influence of noise intensity and correlation intensity on the steady-state probability distributional function are discussed. The results show that the three extreme values of the steady-state probability distribution function exhibit a structure of two peaks and one valley. Variations of the noise intensity, cross-correlation intensity and correlation time can modulate the probability distribution of the number of tumor cells, which provides theoretical guidance for determining treatment plans in clinical treatment. Furthermore, the increase of noise intensity will inhibit the growth of tumor cells when the number of tumor cells is relatively small, while the increase in noise intensity will further promote the growth of tumor cells when the number of tumor cells is relatively large. The color cross-correlated strength and cross-correlated time between noise also have a certain impact on tumor cell proliferation. The results help people understand the growth kinetics of tumor cells, which can a provide theoretical basis for clinical research on tumor cell growth.

Multi-scale characterisation of homologous recombination deficiency in breast cancer.

BACKGROUND: Homologous recombination is a robust, broadly error-free mechanism of double-strand break repair, and deficiencies lead to PARP inhibitor sensitivity. Patients displaying homologous recombination deficiency can be identified using 'mutational signatures'. However, these patterns are difficult to reliably infer from exome sequencing. Additionally, as mutational signatures are a historical record of mutagenic processes, this limits their utility in describing the current status of a tumour. METHODS: We apply two methods for characterising homologous recombination deficiency in breast cancer to explore the features and heterogeneity associated with this phenotype. We develop a likelihood-based method which leverages small insertions and deletions for high-confidence classification of homologous recombination deficiency for exome-sequenced breast cancers. We then use multinomial elastic net regression modelling to develop a transcriptional signature of heterogeneous homologous recombination deficiency. This signature is then applied to single-cell RNA-sequenced breast cancer cohorts enabling analysis of homologous recombination deficiency heterogeneity and differential patterns of tumour microenvironment interactivity. RESULTS: We demonstrate that the inclusion of indel events, even at low levels, improves homologous recombination deficiency classification. Whilst BRCA-positive homologous recombination deficient samples display strong similarities to those harbouring BRCA1/2 defects, they appear to deviate in microenvironmental features such as hypoxic signalling. We then present a 228-gene transcriptional signature which simultaneously characterises homologous recombination deficiency and BRCA1/2-defect status, and is associated with PARP inhibitor response. Finally, we show that this signature is applicable to single-cell transcriptomics data and predict that these cells present a distinct milieu of interactions with their microenvironment compared to their homologous recombination proficient counterparts, typified by a decreased cancer cell response to TNFα signalling. CONCLUSIONS: We apply multi-scale approaches to characterise homologous recombination deficiency in breast cancer through the development of mutational and transcriptional signatures. We demonstrate how indels can improve homologous recombination deficiency classification in exome-sequenced breast cancers. Additionally, we demonstrate the heterogeneity of homologous recombination deficiency, especially in relation to BRCA1/2-defect status, and show that indications of this feature can be captured at a single-cell level, enabling further investigations into interactions between DNA repair deficient cells and their tumour microenvironment.