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Background Assays that are capable of detecting genome-wide chromatin interactions have produced massive amount of data and led to great understanding of the chromosomal three-dimensional (3D) structure. As technology becomes more sophisticated, higher-and-higher resolution data are being produced, going from the initial 1 Megabases (Mb) resolution to the current 10 Kilobases (Kb) or even 1 Kb resolution. The availability of genome-wide interaction data necessitates development of analytical methods to recover the underlying 3D spatial chromatin structure, but challenges abound. Most of the methods were proposed for analyzing data at low resolution (1 Mb). Their behaviors are thus unknown for higher resolution data. For such data, one of the key features is the high proportion of “0” contact counts among all available data, in other words, the excess of zeros. Results To address the issue of excess of zeros, in this paper, we propose a truncated Random effect EXpression (tREX) method that can handle data at various resolutions. We then assess the performance of tREX and a number of leading existing methods for recovering the underlying chromatin 3D structure. This was accomplished by creating in-silico data to mimic multiple levels of resolution and submit the methods to a “stress test”. Finally, we applied tREX and the comparison methods to a Hi-C dataset for which FISH measurements are available to evaluate estimation accuracy. Conclusion The proposed tREX method achieves consistently good performance in all 30 simulated settings considered. It is not only robust to resolution level and underlying parameters, but also insensitive to model misspecification. This conclusion is based on observations made in terms of 3D structure estimation accuracy and preservation of topologically associated domains. Application of the methods to the human lymphoblastoid cell line data on chromosomes 14 and 22 further substantiates the superior performance of tREX: the constructed 3D structure from tREX is consistent with the FISH measurements, and the corresponding distances predicted by tREX have higher correlation with the FISH measurements than any of the comparison methods. Software An open-source R-package is available at http://www.stat.osu.edu/~statgen/Software/tRex. Electronic supplementary material The online version of this article (doi:10.1186/s12859-016-0894-z) contains supplementary material, which is available to authorized users.

Background DNA methylation has been shown to play an important role in the silencing of tumor suppressor genes in various tumor types. In order to have a system-wide understanding of the methylation changes that occur in tumors, we have developed a differential methylation hybridization (DMH) protocol that can simultaneously assay the methylation status of all known CpG islands (CGIs) using microarray technologies. A large percentage of signals obtained from microarrays can be attributed to various measurable and unmeasurable confounding factors unrelated to the biological question at hand. In order to correct the bias due to noise, we first implemented a quantile regression model, with a quantile level equal to 75%, to identify hypermethylated CGIs in an earlier work. As a proof of concept, we applied this model to methylation microarray data generated from breast cancer cell lines. However, we were unsure whether 75% was the best quantile level for identifying hypermethylated CGIs. In this paper, we attempt to determine which quantile level should be used to identify hypermethylated CGIs and their associated genes. Results We introduce three statistical measurements to compare the performance of the proposed quantile regression model at different quantile levels (95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%), using known methylated genes and unmethylated housekeeping genes reported in breast cancer cell lines and ovarian cancer patients. Our results show that the quantile levels ranging from 80% to 90% are better at identifying known methylated and unmethylated genes. Conclusions In this paper, we propose to use a quantile regression model to identify hypermethylated CGIs by incorporating probe effects to account for noise due to unmeasurable factors. Our model can efficiently identify hypermethylated CGIs in both breast and ovarian cancer data.

Background DNA methylation plays an important role in the process of tumorigenesis. Identifying differentially methylated genes or CpG islands (CGIs) associated with genes between two tumor subtypes is thus an important biological question. The methylation status of all CGIs in the whole genome can be assayed with differential methylation hybridization (DMH) microarrays. However, patient samples or cell lines are heterogeneous, so their methylation pattern may be very different. In addition, neighboring probes at each CGI are correlated. How these factors affect the analysis of DMH data is unknown. Results We propose a new method for identifying differentially methylated (DM) genes by identifying the associated DM CGI(s). At each CGI, we implement four different mixed effect and generalized least square models to identify DM genes between two groups. We compare four models with a simple least square regression model to study the impact of incorporating random effects and correlations. Conclusions We demonstrate that the inclusion (or exclusion) of random effects and the choice of correlation structures can significantly affect the results of the data analysis. We also assess the false discovery rate of different models using CGIs associated with housekeeping genes.

Background Non-biological signal (or noise) has been the bane of microarray analysis. Hybridization effects related to probe-sequence composition and DNA dye-probe interactions have been observed in differential methylation hybridization (DMH) microarray experiments as well as other effects inherent to the DMH protocol. Results We suggest two models to correct for non-biologically relevant probe signal with an overarching focus on probe-sequence composition. The estimated effects are evaluated and the strengths of the models are considered in the context of DMH analyses. Conclusion The majority of estimated parameters were statistically significant in all considered models. Model selection for signal correction is based on interpretation of the estimated values and their biological significance.

Background In order to recapitulate tumor progression pathways using epigenetic data, we developed novel clustering and pathway reconstruction algorithms, collectively referred to as heritable clustering. This approach generates a progression model of altered DNA methylation from tumor tissues diagnosed at different developmental stages. The samples act as surrogates for natural progression in breast cancer and allow the algorithm to uncover distinct epigenotypes that describe the molecular events underlying this process. Furthermore, our likelihood-based clustering algorithm has great flexibility, allowing for incomplete epigenotype or clinical phenotype data and also permitting dependencies among variables. Results Using this heritable clustering approach, we analyzed methylation data obtained from 86 primary breast cancers to recapitulate pathways of breast tumor progression. Detailed annotation and interpretation are provided to the optimal pathway recapitulated. The result confirms the previous observation that aggressive tumors tend to exhibit higher levels of promoter hypermethylation. Conclusion Our results indicate that the proposed heritable clustering algorithms are a useful tool for stratifying both methylation and clinical variables of breast cancer. The application to the breast tumor data illustrates that this approach can select meaningful progression models which may aid the interpretation of pathways having biological and clinical significance. Furthermore, the framework allows for other types of biological data, such as microarray gene expression or array CGH data, to be integrated.