Chromosome abnormalities in ovarian adenocarcinoma: III. Using breakpoint data to infer and test mathematical models for oncogenesis

Variable selection for disease progression models: methods for oncogenetic trees and application to cancer and HIV

Background

Disease progression models are important for understanding the critical steps during the development of diseases. The models are imbedded in a statistical framework to deal with random variations due to biology and the sampling process when observing only a finite population. Conditional probabilities are used to describe dependencies between events that characterise the critical steps in the disease process.

Many different model classes have been proposed in the literature, from simple path models to complex Bayesian networks. A popular and easy to understand but yet flexible model class are oncogenetic trees. These have been applied to describe the accumulation of genetic aberrations in cancer and HIV data. However, the number of potentially relevant aberrations is often by far larger than the maximal number of events that can be used for reliably estimating the progression models. Still, there are only a few approaches to variable selection, which have not yet been investigated in detail.

Results

We fill this gap and propose specifically for oncogenetic trees ten variable selection methods, some of these being completely new. We compare them in an extensive simulation study and on real data from cancer and HIV. It turns out that the preselection of events by clique identification algorithms performs best. Here, events are selected if they belong to the largest or the maximum weight subgraph in which all pairs of vertices are connected.

Conclusions

The variable selection method of identifying cliques finds both the important frequent events and those related to disease pathways.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1762-1) contains supplementary material, which is available to authorized users.

PhyloOncology: Understanding cancer through phylogenetic analysis

Despite decades of research and an enormity of resultant data, cancer remains a significant public health problem. New tools and fresh perspectives are needed to obtain fundamental insights, to develop better prognostic and predictive tools, and to identify improved therapeutic interventions. With increasingly common genome-scale data, one suite of algorithms and concepts with potential to shed light on cancer biology is phylogenetics, a scientific discipline used in diverse fields. From grouping subsets of cancer samples to tracing subclonal evolution during cancer progression and metastasis, the use of phylogenetics is a powerful systems biology approach. Well-developed phylogenetic applications provide fast, robust approaches to analyze high-dimensional, heterogeneous cancer data sets. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.

The mathematics of cancer: integrating quantitative models

Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

Identifying restrictions in the order of accumulation of mutations during tumor progression: effects of passengers, evolutionary models, and sampling

BACKGROUND

Cancer progression is caused by the sequential accumulation of mutations, but not all orders of accumulation are equally likely. When the fixation of some mutations depends on the presence of previous ones, identifying restrictions in the order of accumulation of mutations can lead to the discovery of therapeutic targets and diagnostic markers. The purpose of this study is to conduct a comprehensive comparison of the performance of all available methods to identify these restrictions from cross-sectional data. I used simulated data sets (where the true restrictions are known) but, in contrast to previous work, I embedded restrictions within evolutionary models of tumor progression that included passengers (mutations not responsible for the development of cancer, known to be very common). This allowed me to assess, for the first time, the effects of having to filter out passengers, of sampling schemes (when, how, and how many samples), and of deviations from order restrictions.

RESULTS

Poor choices of method, filtering, and sampling lead to large errors in all performance measures. Having to filter passengers lead to decreased performance, especially because true restrictions were missed. Overall, the best method for identifying order restrictions were Oncogenetic Trees, a fast and easy to use method that, although unable to recover dependencies of mutations on more than one mutation, showed good performance in most scenarios, superior to Conjunctive Bayesian Networks and Progression Networks. Single cell sampling provided no advantage, but sampling in the final stages of the disease vs. sampling at different stages had severe effects. Evolutionary model and deviations from order restrictions had major, and sometimes counterintuitive, interactions with other factors that affected performance.

CONCLUSIONS

This paper provides practical recommendations for using these methods with experimental data. It also identifies key areas of future methodological work and, in particular, it shows that it is both possible and necessary to embed assumptions about order restrictions and the nature of driver status within evolutionary models of cancer progression to evaluate the performance of inferential approaches.

Methods and challenges in timing chromosomal abnormalities within cancer samples

Motivation: Tumors acquire many chromosomal amplifications, and those acquired early in the lifespan of the tumor may be not only important for tumor growth but also can be used for diagnostic purposes. Many methods infer the order of the accumulation of abnormalities based on their occurrence in a large cohort of patients. Recently, Durinck et al. (2011) and Greenman et al. (2012) developed methods to order a single tumor’s chromosomal amplifications based on the patterns of mutations accumulated within those regions. This method offers an unprecedented opportunity to assess the etiology of a single tumor sample, but has not been widely evaluated.

Results: We show that the model for timing chromosomal amplifications is limited in scope, particularly for regions with high levels of amplification. We also show that the estimation of the order of events can be sensitive for events that occur early in the progression of the tumor and that the partial maximum likelihood method of Greenman et al. (2012) can give biased estimates, particularly for moderate read coverage or normal contamination. We propose a maximum-likelihood estimation procedure that fully accounts for sequencing variability and show that it outperforms the partial maximum-likelihood estimation method. We also propose a Bayesian estimation procedure that stabilizes the estimates in certain settings. We implement these methods on a small number of ovarian tumors, and the results suggest possible differences in how the tumors acquired amplifications.

Availability and implementation: We provide implementation of these methods in an R package cancerTiming, which is available from the Comprehensive R Archive Network (CRAN) at http://CRAN.R-project.org/.

Contact:epurdom@stat.Berkeley.edu

Supplementary information:Supplementary data are available at Bioinformatics online.

[Genome-wide molecular screening for the identification of new targets in human hepatocellular carcinoma]

Molecular hepatocarcinogenesis represents a step-wise process which in most cases is associated with a well-defined chronic liver disease. By meta-analysis of classical comparative genomic hybridization (CGH) data an oncogenetic progression model could be generated (1q gain→ 8q gain → 4q loss → 16q loss → 13q loss). Array-based CGH allows the identification of etiology-dependent and independent genomic alterations. The Mouse Double Minute homologue 4 (MDM4) was shown to act as an oncogene of 1q32.1 gains in human hepatocellular carcinoma (HCC). Integration of genomic and epigenomic data facilitated the identification of tumor suppressor gene candidates in human HCC. For instance, Polo-like kinase 3 (PLK3) is frequently inactivated via promoter hypermethylation in combination with a loss of the second allele at 1p34.1. Both MDM4 overexpression and methylation-dependent inactivation of PLK3 represent potential targets for future therapeutic approaches.

BAC CGH-array identified specific small-scale genomic imbalances in diploid DMBA-induced rat mammary tumors

BACKGROUND

Development of breast cancer is a multistage process influenced by hormonal and environmental factors as well as by genetic background. The search for genes underlying this malignancy has recently been highly productive, but the etiology behind this complex disease is still not understood. In studies using animal cancer models, heterogeneity of the genetic background and environmental factors is reduced and thus analysis and identification of genetic aberrations in tumors may become easier. To identify chromosomal regions potentially involved in the initiation and progression of mammary cancer, in the present work we subjected a subset of experimental mammary tumors to cytogenetic and molecular genetic analysis.

METHODS

Mammary tumors were induced with DMBA (7,12-dimethylbenz[a]anthrazene) in female rats from the susceptible SPRD-Cu3 strain and from crosses and backcrosses between this strain and the resistant WKY strain. We first produced a general overview of chromosomal aberrations in the tumors using conventional kartyotyping (G-banding) and Comparative Genome Hybridization (CGH) analyses. Particular chromosomal changes were then analyzed in more details using an in-house developed BAC (bacterial artificial chromosome) CGH-array platform.

RESULTS

Tumors appeared to be diploid by conventional karyotyping, however several sub-microscopic chromosome gains or losses in the tumor material were identified by BAC CGH-array analysis. An oncogenetic tree analysis based on the BAC CGH-array data suggested gain of rat chromosome (RNO) band 12q11, loss of RNO5q32 or RNO6q21 as the earliest events in the development of these mammary tumors.

CONCLUSIONS

Some of the identified changes appear to be more specific for DMBA-induced mammary tumors and some are similar to those previously reported in ACI rat model for estradiol-induced mammary tumors. The later group of changes is more interesting, since they may represent anomalies that involve genes with a critical role in mammary tumor development. Genetic changes identified in this work are at very small scales and thus may provide a more feasible basis for the identification of the target gene(s). Identification of the genes underlying these chromosome changes can provide new insights to the mechanisms of mammary carcinogenesis.

Cumulative disease progression models for cross-sectional data: a review and comparison

A better understanding of disease progression is beneficial for early diagnosis and appropriate individual therapy. Many different approaches for statistical modelling of cumulative disease progression have been proposed in the literature, including simple path models up to complex restricted Bayesian networks. Important fields of application are diseases such as cancer and HIV. Tumour progression is measured by means of chromosome aberrations, whereas people infected with HIV develop drug resistances because of genetic changes of the HI-virus. These two very different diseases have typical courses of disease progression, which can be modelled partly by consecutive and partly by independent steps. This paper gives an overview of the different progression models and points out their advantages and drawbacks. Different models are compared via simulations to analyse how they work if some of their assumptions are violated. In a simulation study, we evaluate how models perform in terms of fitting induced multivariate probability distributions and topological relationships. We often find that the true model class used for generating data is outperformed by either a less or a more complex model class. The more flexible conjunctive Bayesian networks can be used to fit oncogenetic trees, whereas mixtures of oncogenetic trees with three tree components can be well fitted by mixture models with only two tree components.

A mathematical methodology for determining the temporal order of pathway alterations arising during gliomagenesis

Human cancer is caused by the accumulation of genetic alterations in cells. Of special importance are changes that occur early during malignant transformation because they may result in oncogene addiction and thus represent promising targets for therapeutic intervention. We have previously described a computational approach, called Retracing the Evolutionary Steps in Cancer (RESIC), to determine the temporal sequence of genetic alterations during tumorigenesis from cross-sectional genomic data of tumors at their fully transformed stage. Since alterations within a set of genes belonging to a particular signaling pathway may have similar or equivalent effects, we applied a pathway-based systems biology approach to the RESIC methodology. This method was used to determine whether alterations of specific pathways develop early or late during malignant transformation. When applied to primary glioblastoma (GBM) copy number data from The Cancer Genome Atlas (TCGA) project, RESIC identified a temporal order of pathway alterations consistent with the order of events in secondary GBMs. We then further subdivided the samples into the four main GBM subtypes and determined the relative contributions of each subtype to the overall results: we found that the overall ordering applied for the proneural subtype but differed for mesenchymal samples. The temporal sequence of events could not be identified for neural and classical subtypes, possibly due to a limited number of samples. Moreover, for samples of the proneural subtype, we detected two distinct temporal sequences of events: (i) RAS pathway activation was followed by TP53 inactivation and finally PI3K2 activation, and (ii) RAS activation preceded only AKT activation. This extension of the RESIC methodology provides an evolutionary mathematical approach to identify the temporal sequence of pathway changes driving tumorigenesis and may be useful in guiding the understanding of signaling rearrangements in cancer development.

Cancer is a deadly disease that develops through the accumulation of genetic changes over time. Many biological models do not incorporate this temporal aspect of tumor formation and progression, in part due to the difficulty of determining the sequence of events through biological experimentation for most cancer types. We previously developed a computational algorithm with which we can quickly and cost-effectively determine the order in which mutations arise in the tumor even when large numbers of mutations are considered. In this paper, we extended our method to incorporate biological knowledge of the common pathways by which cancer progresses. We applied these techniques to primary glioblastoma, the most common form of brain cancer. We found that when all samples are taken into account, a temporal sequence of pathway events emerges; however, different subtypes of glioblastoma vary in their temporal sequence of events. This algorithm can also be easily applied to other cancer types as clinical data becomes available, showing the benefit of computational and mathematical tools in cancer research. Using temporal information, cancer biologists will be able to develop more accurate animal models of tumor formation and learn more about how mutations interact in time, thus leading to better treatments for cancer.

Oncogenetic tree modeling of human hepatocarcinogenesis

Classical comparative genomic hybridization (CGH) has been used to identify recurrent genomic alterations in human HCC. As hepatocarcinogenesis is considered as a stepwise process, we applied oncogenetic tree modeling on all available classical CGH data to determine occurrence of genetic alterations over time. Nine losses (1p, 4q, 6q, 8p, 9p, 13q, 16p, 16q and 17p) and ten gains (1q, 5p, 6p, 7p, 7q, 8q, 17q, 20p, 20q and Xq) of genomic information were used to build the oncogenetic tree model. Whereas gains of 1q and 8q together with losses of 8p formed a cluster that represents early etiology-independent alterations, the associations of gains at 6q and 17q as well as losses of 6p and 9p were observed during tumor progression. HBV-induced HCCs had significantly more chromosomal aberrations compared to HBV-negative tumors. Losses of 1p, 4q and 13q were associated with HBV-induced HCCs, whereas virus-negative HCCs showed an association of gains at 5p, 7, 20q and Xq. Using five aberrations that were significantly associated with tumor dedifferentiation a robust progression model of stepwise human hepatocarcinogensis (gain 1q → gain 8q → loss 4q → loss 16q → loss 13q) was developed. In silico analysis revealed that protumorigenic candidate genes have been identified for each recurrently altered hotspot. Thus, oncogenic candidate genes that are coded on chromosome arms 1q and 8q are promising targets for the prevention of malignant transformation and the development of biomarkers for the early diagnosis of human HCC that may significantly improve the treatment options and thus prognosis of HCC patients.

-8p12-23 and +20q are predictors of subtypes and metastatic pathways in colorectal cancer: construction of tree models using comparative genomic hybridization data

A substantial body of evidence suggests the genetic heterogeneous pattern and multiple pathways in colorectal cancer initiation and progression. In this study, we construct a branching tree and multiple distance-based tree models to elucidate these genetic patterns and pathways in colorectal cancer by using a data set comprised of 244 cases of comparative genomic hybridization. We identify the six most common gains of chromosomal regions of 7p (37.0%), 7q11-32 (34.8%), 8q (48.3%), 13q (49.1%), 20p (36.1%), and 20q (50.4%), and the nine most common losses of 1p13-36 (30.9%), 4p15 (24.3%), 4q33-34 (24.3%), 8p12-23 (50.9%), 15q13-14 (23.5%), 15q24-25 (24.3%), 17p (34.8%), 18p (36.5%), and 18q (61.7%) in colorectal cancer. We classify colorectal cancer into two distinct groups: one preceding with -8p12-23, and the other with +20q. The sample-based classification tree also demonstrates that colorectal cancer can be classified into multiple subtypes marked by -8p12-23 and +20q. By comparing chromosomal abnormalities between primary and metastatic colorectal cancer, we identify five potential metastatic pathways: (-18q, -18p), (-8p12-23, -4p15, -4q33-34), (+20q, +20p), (+20q, +7p, +7q11-32), and +8q. -8p12-23 and +20q are inferred to be the two marker events of colorectal cancer metastasis. The current oncogenetic tree models may contribute to our understanding towards molecular genetics in colorectal cancer. Particularly, the metastatic pathways we describe may provide pivotal clues for metastatic candidate genes, and thus impact on the prediction and intervention of metastatic colorectal cancer.

Construction of oncogenetic tree models reveals multiple pathways of oral cancer progression

Oral cancer develops and progresses by accumulation of genetic alterations. The interrelationship between these alterations and their sequence of occurrence in oral cancers has not been thoroughly understood. In the present study, we applied oncogenetic tree models to comparative genomic hybridization (CGH) data of 97 primary oral cancers to identify pathways of progression. CGH revealed the most frequent gains on chromosomes 8q (72.4%) and 9q (41.2%) and frequent losses on 3p (49.5%) and 8p (47.5%). Both mixture and distance-based tree models suggested multiple progression pathways and identified +8q as an early event. The mixture model suggested two independent pathways namely a major pathway with -8p and a less frequent pathway with +9q. The distance-based tree identified three progression pathways, one characterized by -8p, another by -3p and the third by alterations +11q and +7p. Differences were observed in cytogenetic pathways of node-positive and node-negative oral cancers. Node-positive cancers were characterized by more non-random aberrations (n = 11) and progressed via -8p or -3p. On the other hand, node-negative cancers involved fewer non-random alterations (n = 6) and progressed along -3p. In summary, the tree models for oral cancers provided novel information about the interactions between genetic alterations and predicted their probable order of occurrence.

Transcriptome analysis of serous ovarian cancers identifies differentially expressed chromosome 3 genes

Cytogenetic, molecular genetic and functional analyses have implicated chromosome 3 genes in epithelial ovarian cancers (EOC). To further characterize their contribution to EOC, the Affymetrix U133A GeneChip(R) was used to perform transcriptome analyses of chromosome 3 genes in primary cultures of normal ovarian surface epithelial (NOSE) cells (n = 14), malignant serous epithelial ovarian tumors (TOV) (n = 17), and four EOC cell lines (TOV-81D, TOV-112D, TOV-21G, and OV-90). A two-way comparative analysis of 735 known genes and expressed sequences identified 278 differentially expressed genes, where 43 genes were differentially expressed in at least 50% of the TOV samples. Three genes, RIS1 (at 3p21.31), GBE1 (at 3p12.2), and HEG1 (at 3q21.2), were similarly underexpressed in all TOV samples. Deregulation of the expression of these genes was not associated with loss of heterozygosity (LOH) of the genetic loci harboring them. LOH analysis of the RIS1, GBE1, and HEG1 loci was observed at frequencies of 14.3%, 13.7%, and 9.2%, respectively, in a series of 66 malignant TOV samples of the serous subtype. Reduced expression levels of RIS1, GBE1, and HEG1 were observed only in the tumorigenic EOC cell lines (TOV-21G, TOV-112D, and OV-90) and did not correlate with LOH. These results combined suggest that RIS1, GBE1, and HEG1, unlike classical tumor suppressor genes, are not likely to be primary targets of inactivation. This study provides a comprehensive analysis of chromosome 3 gene expression in NOSE and in EOC samples and identifies chromosome 3 gene candidates for further study.

Genomic Alterations in Ectopic and Eutopic Endometria of Women with Endometriosis

BACKGROUND/AIMS

Ectopic and eutopic endometria of women with endometriosis have been shown to contain genomic alterations. In this study, we sought to identify genomic alterations in both ectopic and eutopic endometria of 5 women with endometriosis and to examine whether the two tissues share any genomic alterations. We also attempted to classify tissue samples based on the alteration profiles.

METHODS

Laser capture microdissection was used to harvest epithelial cells. High-resolution comparative genomic hybridization microarrays were used to identify genomic alterations in eutopic and ectopic endometria from 5 women with endometriosis. The results were validated by real-time RT-PCR and loss of heterozygosity analysis.

RESULTS

All 5 patients had genomic alterations in their eutopic and ectopic endometria. The ectopic and eutopic endometria shared a sizable portion of genomic alterations. Cluster analysis of the genomic alteration profile correctly and consistently classified tissue samples from the 5 patients into two groups: peritoneal implants and ovarian cysts.

CONCLUSIONS

The correct classification of tissue samples into two groups suggests that these two subtypes of endometriosis may have distinct genomic alteration profiles and are thus distinct entities, as previously proposed. The shared alterations are likely the ones that harbor genes responsible for an increased propensity of endometrial debris to implant to the ectopic sites and for early events that lead to the establishment of lesions. Alternatively, these shared alterations may harbor genes that are dysregulated in both eutopic and ectopic endometria. The identified genomic alterations should help to zero in genes involved in the pathogenesis of endometriosis in future studies.

New probabilistic network models and algorithms for oncogenesis

Chromosomal aberrations in solid tumors appear in complex patterns. It is important to understand how these patterns develop, the dynamics of the process, the temporal or even causal order between aberrations, and the involved pathways. Here we present network models for chromosomal aberrations and algorithms for training models based on observed data. Our models are generative probabilistic models that can be used to study dynamical aspects of chromosomal evolution in cancer cells. They are well suited for a graphical representation that conveys the pathways found in a dataset. By allowing only pairwise dependencies and partition aberrations into modules, in which all aberrations are restricted to have the same dependencies, we reduce the number of parameters so that datasets sizes relevant to cancer applications can be handled. We apply our framework to a dataset of colorectal cancer tumor karyotypes. The obtained model explains the data significantly better than a model where independence between the aberrations is assumed. In fact, the obtained model performs very well with respect to several measures of goodness of fit and is, with respect to repetition of the training, more or less unique.

Transfer of chromosome 3 fragments suppresses tumorigenicity of an ovarian cancer cell line monoallelic for chromosome 3p

Multiple chromosome 3p tumor suppressor genes (TSG) have been proposed in the pathogenesis of ovarian cancer based on complex patterns of 3p loss. To attain functional evidence in support of TSGs and identify candidate regions, we applied a chromosome transfer method involving cell fusions of the tumorigenic OV90 human ovarian cancer cell line, monoallelic for 3p and an irradiated mouse cell line containing a human chromosome 3 in order to derive OV90 hybrids containing normal 3p fragments. The resulting hybrids showed complete or incomplete suppression of tumorigenicity in nude mouse xenograft assays, and varied in their ability to form colonies in soft agarose and three-dimensional spheroids in a manner consistent with alteration of their in vivo tumorigenic phenotypes. Expression microarray analysis identified a set of common differentially expressed genes, such as SPARC, DAB2 and VEGF, some of which have been shown implicated in ovarian cancer. Genotyping assays revealed that they harbored normal 3p fragments, some of which overlapped candidate TSG regions (3p25-p26, 3p24 and 3p14-pcen) identified previously in loss of heterozygosity analyses of ovarian cancers. However, only the 3p12-pcen region was acquired in common by all hybrids where expression microarray analysis identified differentially expressed genes. The correlation of 3p12-pcen transfer and tumor suppression with a concerted re-programming of the cellular transcriptome suggest that the putative TSG may have affected key underlying events in ovarian cancer.

Construction of evolutionary tree models for nasopharyngeal carcinoma using comparative genomic hybridization data

Nasopharyngeal carcinoma (NPC) is a malignancy associated with remarkable racial and geographic factors. The development and progression of NPC may involve the accumulation of multiple genetic alterations over a long time. For understanding the putative order of genetic alteration in NPC tumorigenesis, we used evolutionary tree models (branching and distance-based tree models) to analyze comparative genomic hybridization (CGH) data of previously published NPC cases (n = 103). Consistent loss of 3p for both tree models was an important early event in NPC progression. Chromosome 12 gain was another important early event, and may represent a subclass different from 3p- derived subclasses of NPC. The tree models also suggested that at least two subclasses of 3p- derived NPC, one marked by 1q+, 9p-, and 13q- and the other marked by 14q-, 16q-, 9q-, and 1p-.

Linksets of tumor chromosome breakpoints related to survival in ovarian adenocarcinoma

Biological processes are often accompanied by occurrences of multiple events, such as activation of certain cell types, change in prevalence of cell subpopulations (such as T cells), changes in concentration of proteins or peptides, or breaks in chromosomes. Some co-occurrences of these events are by chance, but others may have meaningful relations to the underlying biological process. The methodology of linksets is designed to detect the presence of potentially meaningful co-occurrences. Due to the complex ways in which linksets can determine the observed occurrences of multiple events, some moderately powerful computational methods are necessary for statistical estimation. Here, linkset models are fitted to data on chromosome breakpoints in ovarian adenocarcinomas, in order to answer the question motivating the project that collected them--whether there are nonrandom co-occurrences of breakpoints in particular chromosome regions, and whether these might be of prognostic significance. The results identify breakpoints in 1p1 as associated with early mortality when they occur in linksets of breakpoints in 1p3 and any one of 11q1, 11q2, or 6q2. Conversely, breakpoints in 6p2, 1q3, and 7p1 occur in linksets associated with late mortality. This is, to our knowledge, the first demonstration of a new method for analyzing patterns of event occurrence in biological data.

Patterns of gene expression that characterize long-term survival in advanced stage serous ovarian cancers

PURPOSE

A better understanding of the underlying biology of invasive serous ovarian cancer is critical for the development of early detection strategies and new therapeutics. The objective of this study was to define gene expression patterns associated with favorable survival.

EXPERIMENTAL DESIGN

RNA from 65 serous ovarian cancers was analyzed using Affymetrix U133A microarrays. This included 54 stage III/IV cases (30 short-term survivors who lived <3 years and 24 long-term survivors who lived >7 years) and 11 stage I/II cases. Genes were screened on the basis of their level of and variability in expression, leaving 7,821 for use in developing a predictive model for survival. A composite predictive model was developed that combines Bayesian classification tree and multivariate discriminant models. Leave-one-out cross-validation was used to select and evaluate models.

RESULTS

Patterns of genes were identified that distinguish short-term and long-term ovarian cancer survivors. The expression model developed for advanced stage disease classified all 11 early-stage ovarian cancers as long-term survivors. The MAL gene, which has been shown to confer resistance to cancer therapy, was most highly overexpressed in short-term survivors (3-fold compared with long-term survivors, and 29-fold compared with early-stage cases). These results suggest that gene expression patterns underlie differences in outcome, and an examination of the genes that provide this discrimination reveals that many are implicated in processes that define the malignant phenotype.

CONCLUSIONS

Differences in survival of advanced ovarian cancers are reflected by distinct patterns of gene expression. This biological distinction is further emphasized by the finding that early-stage cancers share expression patterns with the advanced stage long-term survivors, suggesting a shared favorable biology.

Learning Multiple Evolutionary Pathways from Cross-Sectional Data

We introduce a mixture model of trees to describe evolutionary processes that are characterized by the ordered accumulation of permanent genetic changes. The basic building block of the model is a directed weighted tree that generates a probability distribution on the set of all patterns of genetic events. We present an EM-like algorithm for learning a mixture model of K trees and show how to determine K with a maximum likelihood approach. As a case study, we consider the accumulation of mutations in the HIV-1 reverse transcriptase that are associated with drug resistance. The fitted model is statistically validated as a density estimator, and the stability of the model topology is analyzed. We obtain a generative probabilistic model for the development of drug resistance in HIV that agrees with biological knowledge. Further applications and extensions of the model are discussed.

Oncogenetic tree models based on cytogenetic data: new insights into the development of epithelial tumors of the thymus

Epithelial tumors of the thymus are rare neoplasms typically arising in the anterior mediastinum. There is an ongoing discussion whether thymomas of different histological subtypes form a biological continuum or represent distinct biological entities. To further investigate this question, we performed a statistical analysis of CGH data of 65 previously published cases. Losses of 3p, 6p, 6q, 13q, 16q, and 17p, as well as gains on 1q, were found in at least 10% of the cases. Comparing the data from B2, B3, and C thymomas, we noted an increasing complexity of karyotypes that may be well explained by a sequential order of these types. The frequencies of losses on 16q and 17p show a significant trend with respect to the sequence from B2 to B3 and C thymomas, indicating that these aberrations may be important events in the transition between these tumor types. To identify pathways of genetic development and progression of thymomas, we used oncogenetic tree models representing the dependencies between recurrent chromosomal aberrations. This analysis suggests that gains on the long arm of chromosome 1 occur early in tumor development and are correlated with losses on 6p and 6q. There is a weak correlation with losses on 16q and 17p, which appear to be late events. An independent pathway leads to losses on 3p and 13q, which are closely correlated. Our results indicate that the development of thymomas seems to be in some part a multistep mechanism. Oncogenetic tree models are a helpful means to determine developmental pathways of tumors arising from the same progenitor cell, as shown here for thymomas.

Estimating cancer survival and clinical outcome based on genetic tumor progression scores

MOTIVATION

In cancer research, prediction of time to death or relapse is important for a meaningful tumor classification and selecting appropriate therapies. Survival prognosis is typically based on clinical and histological parameters. There is increasing interest in identifying genetic markers that better capture the status of a tumor in order to improve on existing predictions. The accumulation of genetic alterations during tumor progression can be used for the assessment of the genetic status of the tumor. For modeling dependences between the genetic events, evolutionary tree models have been applied.

RESULTS

Mixture models of oncogenetic trees provide a probabilistic framework for the estimation of typical pathogenetic routes. From these models we derive a genetic progression score (GPS) that estimates the genetic status of a tumor. GPS is calculated for glioblastoma patients from loss of heterozygosity measurements and for prostate cancer patients from comparative genomic hybridization measurements. Cox proportional hazard models are then fitted to observed survival times of glioblastoma patients and to times until PSA relapse following radical prostatectomy of prostate cancer patients. It turns out that the genetically defined GPS is predictive even after adjustment for classical clinical markers and thus can be considered a medically relevant prognostic factor.

AVAILABILITY

Mtreemix, a software package for estimating tree mixture models, is freely available for non-commercial users at http://mtreemix.bioinf.mpi-sb.mpg.de. The raw cancer datasets and R code for the analysis with Cox models are available upon request from the corresponding author.

Comparative genomic hybridization analysis of astrocytomas: prognostic and diagnostic implications

Astrocytoma is comprised of a group of common intracranial neoplasms that are classified into four grades based on the World Health Organization histological criteria and patient survival. To date, histological grade, patient age, and clinical performance, as reflected in the Karnofsky score, are the most reliable prognostic predictors. Recently, there has been a significant effort to identify additional prognostic markers using objective molecular genetic techniques. We believe that the identification of such markers will characterize new chromosomal loci important in astrocytoma progression and aid clinical diagnosis and prognosis. To this end, our laboratory used comparative genomic hybridization to identify DNA sequence copy number changes in 102 astrocytomas. Novel losses of 19p loci were detected in low-grade pilocytic astrocytomas and losses of loci on 9p, 10, and 22 along with gains on 7, 19, and 20 were detected in a significant proportion of high-grade astrocytomas. The Cox proportional hazards statistical modeling showed that the presence of +7q and -10q comparative genomic hybridization alterations significantly increased a patient's risk of dying, independent of histological grade. This investigation demonstrates the efficacy of comparative genomic hybridization for identifying tumor suppressor and oncogene loci in different astrocytic grades. The cumulative effect of these loci is an important consideration in their diagnostic and prognostic implications.

Statistical behavior of complex cancer karyotypes

Epithelial tumors commonly show complex and variable karyotypes that obscure the identification of general patterns of the karyotypic evolution. To overcome some of these problems, we previously systematically analyzed the accumulated cytogenetic data from individual tumor types by using various statistical means. In the present study, we compare previous results obtained for nine tumor types and perform several meta-analyses of data obtained from a number of epithelial tumors, including head and neck, kidney, bladder, breast, colorectal, ovarian, and lung cancer, as well as from malignant melanoma and Wilms tumor, with the specific aim of discovering common patterns of karyotypic evolution. We show that these tumors frequently develop through a hypo- or a hyperdiploid pathway and progress by an increasing number of alternative imbalances through at least two karyotypic phases, Phases I and II, and possibly through a third, Phase III. During Phase I, the karyotypes exhibited a power law distribution of both the number of changes per tumor and the frequency distribution at which bands were involved in breaks. At the transition from Phase I to Phase II/III, the observed power law distributions were lost, indicating a transition from an ordered and highly structured process to a disordered and chaotic pattern. The change in karyotypic orderliness at the transition from Phase I to Phase II/III was also shown by a drastic difference in karyotypic entropy.

Intratumor chromosomal heterogeneity in advanced carcinomas of the uterine cervix

Intratumor heterogeneity in chromosomal aberrations is believed to represent a major challenge in the treatment of cancer. The aim of our work was to assess the chromosomal heterogeneity of advanced cervical carcinomas and to distinguish aberrations that had occurred at a late stage of the disease from early events. A total of 55 biopsies, sampled from 2-4 different sites within 20 tumors, were analyzed by use of comparative genomic hybridization. Heterogeneous aberrations were identified as those present in at least 1 of the biopsies and which were not seen, nor seen as a tendency, in the others of the same tumor. The homogeneous aberrations were those seen in all biopsies of the tumor. The most frequent homogeneous aberrations were gain of 3q (65%), 20q (65%) and 5p (50%), indicating that these are early events in the development of the disease. Chromosomal heterogeneity was observed in 11 tumors. The most frequent heterogeneous aberrations were loss of 4p14-q25 (60% of 10 cases with this aberration), and gain of 2p22-pter (50% of 6 cases), 11qcen-q13 (33% of 9 cases) and 8q (27% of 11 cases), suggesting that these events promote progression at a later stage. Many of the heterogeneous regions contained genes known to influence the prognosis of cervical cancer, such as 7p (EGFR), 8q (c-MYC), 11qcen-q13 (CCND1) and 17q (ERBB2). Three evolution sequences for the subpopulations in the heterogeneous tumors were identified: a serial, a parallel and a mixed sequence. In 2 tumors with a serial sequence, it was indicated that the aberrations +8 and -X had occurred after the other heterogeneous aberrations and hence were the aberrations most recently formed. Our results suggest pronounced chromosomal instability in advanced cervical carcinomas. Moreover, aggressive and treatment-resistant subpopulations may emerge at a late stage and possibly contribute to a poor prognosis of the advanced stages.

Statistical analyses of karyotypic complexity in head and neck squamous cell carcinoma

More than 250 head and neck squamous cell carcinomas (HNSCCs) with clonal chromosomal abnormalities have been reported. Even though the pattern of aberrations is nonrandom, no specific primary or secondary karyotypic abnormalities have been identified. One explanation for the still-rudimentary understanding of the cytogenetic evolution in HNSCC could be the pronounced karyotypic complexity seen in these tumors. In an attempt to overcome this difficulty, we have applied several statistical methods such as hierarchical cluster analysis, multidimensional scaling, and k-means clustering, which allow the identification and interpretation of karyotypic pathways, as well as establishing a temporal order of chromosomal imbalances on 241 published and 70 previously unpublished HNSCC karyotypes. From the analysis of the distribution of the number of imbalances per tumor we suggest that the carcinomas evolve through three phases representing different stages of chromosomal instability. Two major cytogenetic pathways, one dominated by gains and another by losses, were identified by means of principal component analysis. These were initiated by +7 and by any of the aberrations 1p-, 3p-, or 7q-, respectively.

Cytogenetics and molecular genetics of ovarian cancer

Genetic alterations identified in human ovarian tumors by conventional banding, fluorescence in situ hybridization, comparative genomic hybridization, chromosome microdissection, loss of heterozygosity, chromosome microcell-mediated chromosome transfer, and microarray gene expression analysis are summarized and correlated. The significance of these findings with respect to pathologic classification and clinical application are discussed.

Estimating an oncogenetic tree when false negatives and positives are present

Human solid tumors are believed to be caused by a sequence of genetic abnormalities arising in the tumor cells. The understanding of these sequences is extremely important for improving cancer treatment. Models for the occurrence of the abnormalities include linear structure and a recently proposed tree-based structure. In this paper we extend the pure oncogenetic tree model by introducing false positive and false negative observations. We state conditions sufficient for the reconstruction of the generating tree. As an example we analyze a comparative genomic hybridization data set and show that addition of the error model significantly improves the ability of the model to describe the data.

Multicolor spectral karyotyping of serous ovarian adenocarcinoma

We applied multicolor spectral karyotyping (SKY) to decipher the chromosomal complexity of a panel of seven cell lines and four primary tumors derived from patients with high-grade serous adenocarcinoma of the ovary. By this method we identified a total of 188 unbalanced translocations, nine reciprocal translocations [t(2;15)(q13;q23), t(7;17) (q32;q21), t(8;22)(p11;q11), t(8;22) (q24;q13), t(10;19) (q24;q13.2), t(11;19) (q13;p11), t(12;21)(q13;q22),t(18;20) (q?11;q?11), t(18;22)(q?11;q?13)], 6 isochromosomes [i(1q), i(7q), i(8q), i(9p), i(17q), i(21q)], and 23 deletions. By detailed mapping of rearrangement breakpoints, it was possible to identify several recurring breakpoint clusters at chromosomal bands 1p36, 2p11, 2p23, 3p21, 3q21, 4p11, 6q11, 8p11, 9q34, 10p11, 11p11, 11q13, 12p13, 12q13, 17q21, 18p11, 18q11, 20q11, and 21q22. Recurrent interstitial deletion of chromosomal bands 8p11, 11p11, and 12q13 and a recurrent unbalanced translocation--der(6)t(6;8)(q11;q11)-were also identified. In addition, a homogeneously staining region localized in one cell line to 11q13 was found using SKY to be derived from genetic material originating from chromosome 12. Subsequent comparative genomic hybridization (CGH) studies on this tumor revealed the amplification of DNA sequences derived from the short arm of chromosome 12 at the 12p11.2 region. These studies demonstrate the power of SKY, CGH, and G-banding to resolve the full spectrum of chromosomal rearrangements in serous ovarian adenocarcinoma.

Graph models of oncogenesis with an application to melanoma

We describe several analytical techniques for use in developing genetic models of oncogenesis including: methods for the selection of important genetic events, construction of graph models (including distance-based trees, branching trees, contingency trees and directed acyclic graph models) from these events and methods for interpretation of the resulting models. The models can be used to make predictions about: which genetic events tend to occur early, which events tend to occur together and the likely order of events. Unlike simple path models of oncogenesis, our models allow dependencies to exist between specific genetic changes and allow for multiple, divergent paths in tumor progression. A variety of genetic events can be used with the graph models including chromosome breaks, losses or gains of large DNA regions, small mutations and changes in methylation. As an application of the techniques, we use a recently published cytogenetic analysis of 206 melanoma cases [Nelson et al. (2000), Cancer Genet. Cytogenet.122, 101-109] to derive graph models for chromosome breaks in melanoma. Among our predictions are: (1) breaks in 6q1 and 1q1 are early events, with 6q1 preferentially occurring first and increasing the probability of a break in 1q1 and (2) breaks in the two sets [1p1, 1p2, 9q1] and [1q1, 7p2, 9p2] tend to occur together. This study illustrates that the application of graph models to genetic data from tumor sets provide new information on the interrelationships among genetic changes during tumor progression.

Distance-based reconstruction of tree models for oncogenesis

Comparative genomic hybridization (CGH) is a laboratory method to measure gains and losses in the copy number of chromosomal regions in tumor cells. It is hypothesized that certain DNA gains and losses are related to cancer progression and that the patterns of these changes are relevant to the clinical consequences of the cancer. It is therefore of interest to develop models which predict the occurrence of these events, as well as techniques for learning such models from CGH data. We continue our study of the mathematical foundations for inferring a model of tumor progression from a CGH data set that we started in Desper et al. (1999). In that paper, we proposed a class of probabilistic tree models and showed that an algorithm based on maximum-weight branching in a graph correctly infers the topology of the tree, under plausible assumptions. In this paper, we extend that work in the direction of the so-called distance-based trees, in which events are leaves of the tree, in the style of models common in phylogenetics. Then we show how to reconstruct the distance-based trees using tree-fitting algorithms developed by researchers in phylogenetics. The main advantages of the distance-based models are that 1) they represent information about co-occurrences of all pairs of events, instead of just some pairs, 2) they allow quantitative predictions about which events occur early in tumor progression, and 3) they bring into play the extensive methodology and software developed in the context of phylogenetics. We illustrate the distance-based tree method and how it complements the branching tree method, with a CGH data set for renal cancer.

Multivariate analyses of genomic imbalances in solid tumors reveal distinct and converging pathways of karyotypic evolution

A total of 3,016 malignant solid tumors (kidney, colorectal, breast, head and neck, ovarian, and lung carcinomas, neuroglial tumors, malignant melanoma, and testicular germ cell tumors) were selected for statistical analyses regarding karyotypic evolution. Genomic imbalances, i.e., net gains and losses, present in more than 5% of each tumor type were identified. Individual tumors were then classified with respect to absence or presence of these imbalances. To analyze for possible patterns of correlated imbalances, principal component analyses (PCA) were performed. Furthermore, algorithms were developed to analyze the temporal order of the imbalances, as well as the possible selection for early or late appearance in the karyotypic evolution. By analyzing the temporal order of imbalances common to many tumor types, a general order for nine of these emerged, namely, +7, -3p, -6q, -1p, -8p, -17p, -9p, -18, and -22. The distributions of the number of imbalances per case revealed a geometrical distribution, ranging from one to nine imbalances per tumor, in the majority of the tumor types. In tumor types in which cases with a high number of imbalances per case were frequent, notably head and neck, ovarian, and lung carcinomas, the overall distributions were bimodal, indicating the presence of two modes of chromosome evolution. By combining data from the PCA with the temporal analyses, it was possible to identify karyotypic pathways. It was found that the majority of the tumor types displayed more than one cytogenetic route, but, as the karyotypic evolution continued, these converged to a common pathway.

Analysis of secondary chromosomal alterations in 165 cases of follicular lymphoma with t(14;18)

Follicular lymphoma is characterized by the t(14;18) in up to 85% of cases. Almost all cases display evidence of secondary chromosomal alterations at initial diagnosis. The influence of recurrent secondary changes on disease progression has not been fully determined. The purpose of this study was to define the full spectrum of recurrent karyotypic events present at diagnosis in a large cohort of cases and to evaluate the sequence of cytogenetic evolution in relation to morphologic progression. A total of 165 cases of follicular lymphoma with t(14;18) were ascertained for which complete clinical information, histopathology, immunophenotype, and karyotype were available. One hundred sixty cases showed secondary alterations with an average of 7.9 additional changes per case. Recurrent alterations seen at the 10% or greater level included +X, +1q21-q44, +7, +12q, +18q, del(1)(p36), del(6q), del(10)(q22-q24), the development of polyploidy and sidelines, and the presence of extra marker chromosomes and chromosomal additions. Changes that correlated with morphologic progression included del(1)(p36), del(6q), del(10)(q22-q24), +7, the total number of abnormalities, the number of markers and additions, and the presence of polyploidy. The most frequent second event arising after the t(14;18) was duplication of the der(18)t(14;18). This study demonstrates that the number and type of secondary chromosomal alterations in follicular lymphoma is highly variable between cases, but that a relatively small number of changes are seen repeatedly in different combinations. A consistent pattern of cytogenetic evolution could not be identified. Potentially significant gene duplications or amplifications may be disguised within marker chromosomes and additions. Additional cytogenetic investigation is required to decipher the karyotypic complexity associated with the progression of follicular lymphoma.