We aim to improve the performance of the previously proposed signal decomposition matched filtering (SDMF) method [26] for the detection of copy-number variations (CNV) in the human genome. Through simulations, we show that the modified SDMF is robust even at high noise levels and outperforms the original SDMF method, which indirectly depends on CNV frequency. Simulations are also used to develop a systematic approach for selecting relevant parameter thresholds in order to optimize sensitivity, specificity and computational efficiency. We apply the modified method to array CGH data from normal samples in the cancer genome atlas (TCGA) and compare detected CNVs to those estimated using circular binary segmentation (CBS) [19], a hidden Markov model (HMM)-based approach [11] and a subset of CNVs in the Database of Genomic Variants. We show that a substantial number of previously identified CNVs are detected by the optimized SDMF, which also outperforms the other two methods.

Despite the relatively high accuracy of the naïve Bayes (NB) classifier, there may be several instances where it is not optimal, i.e. does not have the same classification performance as the Bayes classifier utilizing the joint distribution of the examined attributes. However, the Bayes classifier can be computationally intractable due to its required knowledge of the joint distribution. Therefore, we introduce a "pairwise naïve" Bayes (PNB) classifier that incorporates all pairwise relationships among the examined attributes, but does not require specification of the joint distribution. In this paper, we first describe the necessary and sufficient conditions under which the PNB classifier is optimal. We then discuss sufficient conditions for which the PNB classifier, and not NB, is optimal for normal attributes. Through simulation and actual studies, we evaluate the performance of our proposed classifier relative to the Bayes and NB classifiers, along with the HNB, AODE, LBR and TAN classifiers, using normal density and empirical estimation methods. Our applications show that the PNB classifier using normal density estimation yields the highest accuracy for data sets containing continuous attributes. We conclude that it offers a useful compromise between the Bayes and NB classifiers.

Bioinformatics (2011) 27(17) 2338–2345 The authors apologize for the following minor wording error at the bottom of p. 2344. The last sentence in the left column should read: However the computational cost of CBS was significantly higher (at least five times higher in simulations and eight times in real data), instead of ['O(5) in simulations and O(8) in real data].

MOTIVATION: Human genomic variability occurs at different scales, from single nucleotide polymorphisms (SNPs) to large DNA segments. Copy number variations (CNVs) represent a significant part of our genetic heterogeneity and have also been associated with many diseases and disorders. Short, localized CNVs, which may play an important role in human disease, may be undetectable in noisy genomic data. Therefore, robust methodologies are needed for their detection. Furthermore, for meaningful identification of pathological CNVs, estimation of normal allelic aberrations is necessary. RESULTS: We developed a signal processing-based methodology for sequence denoising followed by pattern matching, to increase SNR in genomic data and improve CNV detection. We applied this signal-decomposition-matched filtering (SDMF) methodology to 429 normal genomic sequences, and compared detected CNVs to those in the Database of Genomic Variants. SDMF successfully detected a significant number of previously identified CNVs with frequencies of occurrence ≥10%, as well as unreported short CNVs. Its performance was also compared to circular binary segmentation (CBS). through simulations. SDMF had a significantly lower false detection rate and was significantly faster than CBS, an important advantage for handling large datasets generated with high-resolution arrays. By focusing on improving SNR (instead of the robustness of the detection algorithm), SDMF is a very promising methodology for identifying CNVs at all genomic spatial scales. AVAILABILITY: The data are available at http://tcga-data.nci.nih.gov/tcga/ The software and list of analyzed sequence IDs are available at http://www.hsph.harvard.edu/~betensky/ A Matlab code for Empirical Mode Decomposition may be found at: http://www.clear.rice.edu/elec301/Projects02/empiricalMode/code.html CONTACT: [email protected].

Navarro and Ruiz (see ibid., vol.45, p.685-90, 1996) express the nonparametric maximum likelihood estimator (NPMLE) of the distribution of a failure-time random variable as a function of the NPMLE of generalized failure-rate functions. These generalized failure-rate functions are equal to the probability density functions of a doubly-truncated failure-time random variable at the endpoints of the truncating interval. Readers can infer from this paper that this simple estimator can be applied to a doubly-truncated sample of failure times. This commentary explains why that estimator does not apply to the general setting in which the observed failure times are doubly-truncated with subject-specific truncating intervals. A doubly-truncated sample of times to brain tumor progression illustrates the deviation of that estimator from the NPMLE for these data.