Volume 12, Issue 2

Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data sets from the model. In this paper we show that under the assumption of the existence of a uniform additive model error term, ABC algorithms give exact results when sufficient summaries are used. This interpretation allows the approximation made in many previous application papers to be understood, and should guide the choice of metric and tolerance in future work. ABC algorithms can be generalized by replacing the 0–1 cut-off with an acceptance probability that varies with the distance of the simulated data from the observed data. The acceptance density gives the distribution of the error term, enabling the uniform error usually used to be replaced by a general distribution. This generalization can also be applied to approximate Markov chain Monte Carlo algorithms. In light of this work, ABC algorithms can be seen as calibration techniques for implicit stochastic models, inferring parameter values in light of the computer model, data, prior beliefs about the parameter values, and any measurement or model errors.

The process of occurrence of genomic aberrations over time in the genetic material of cancer cells reflects the progression of the cancer. Modern technologies like aCGH (array Comparative Genomic Hybridization) and MPS (Massive Parallel Sequencing) provide high-resolution measurements of DNA copy number aberrations, that reveal the full scale of genomic aberrations. A continuous time Markov chain model is proposed to describe the accumulation of aberrations over time. Time however is a latent variable (with the number of aberrations as a proxy). Integrating out time, yields the distribution of the observed DNA copy number data. The model parameters are estimated from high-dimensional DNA copy number data by means of penalized maximum pseudo- and likelihood and method of moments procedures. Having fitted the model, posterior time estimates of the advancement of each sample’s cancer are obtained and the most likely locations of a sample’s aberrations are predicted. The three estimation methods are compared in a simulation study. The paper closes with an application of the proposed methodology on cancer data.

How deep is deep enough? While RNA-sequencing represents a well-established technology, the required sequencing depth for detecting all expressed genes is not known. If we leave the entire biological overhead and meta-information behind we are dealing with a classical sampling process. Such sampling processes are well known from population genetics and thoroughly investigated. Here we use the Pitman Sampling Formula to model the sampling process of RNA-sequencing. By doing so we characterize the sampling by means of two parameters which grasp the conglomerate of different sequencing technologies, protocols and their associated biases. We differ between two levels of sampling: number of reads per gene and respectively, number of reads starting at each position of a specific gene. The latter approach allows us to evaluate the theoretical expectation of uniform coverage and the performance of sequencing protocols in that respect. Most importantly, given a pilot sequencing experiment we provide an estimate for the size of the underlying sampling universe and, based on these findings, evaluate an estimator for the number of newly detected genes when sequencing an additional sample of arbitrary size.

Identification of genome-wide epigenetic changes, the stable changes in gene function without a change in DNA sequence, under various conditions plays an important role in biomedical research. High-throughput epigenetic experiments are useful tools to measure genome-wide epigenetic changes, but the measured intensity levels from these high-resolution genome-wide epigenetic profiling data are often spatially correlated with high noise levels. In addition, it is challenging to detect genome-wide epigenetic changes across multiple conditions, so efficient statistical methodology development is needed for this purpose. In this study, we consider ANOVA models with spatially varying coefficients, combined with a hierarchical Bayesian approach, to explicitly model spatial correlation caused by location-dependent biological effects (i.e., epigenetic changes) and borrow strength among neighboring probes to compare epigenetic changes across multiple conditions. Through simulation studies and applications in drug addiction and depression datasets, we find that our approach compares favorably with competing methods; it is more efficient in estimation and more effective in detecting epigenetic changes. In addition, it can provide biologically meaningful results.

In omics studies aimed at the early detection and diagnosis of cancer, bioinformatics tools play a significant role when analyzing high dimensional, complex datasets, as well as when identifying a small set of biomarkers. However, in many cases, there are ambiguities in the robustness and the consistency of the discovered biomarker sets, since the feature selection methods often lead to irreproducible results. To address this, both the stability and the classification power of several chemometrics-based feature selection algorithms were evaluated using the Monte Carlo sampling technique, aiming at finding the most suitable feature selection methods for early cancer detection and biomarker discovery. To this end, two data sets were analyzed, which comprised of MALDI-TOF-MS and LC/TOF-MS spectra measured on serum samples in order to diagnose ovarian cancer. Using these datasets, the stability and the classification power of multiple feature subsets found by different feature selection methods were quantified by varying either the number of selected features, or the number of samples in the training set, with special emphasis placed on the property of stability. The results show that high consistency does not necessarily guarantee high predictive power. In addition, differences in the stability, as well as agreement in feature lists between several feature selection methods, depend on several factors, such as the number of available samples, feature sizes, quality of the information in the dataset, etc. Among the tested methods, only the variable importance in projection (VIP)-based method shows complementary properties, providing both highly consistent and accurate subsets of features. In addition, successive projection analysis (SPA) was excellent with regards to maintaining high stability over a wide range of experimental conditions. The stability of several feature selection methods is highly variable, stressing the importance of making the proper choice among feature selection methods. Therefore, rather than evaluating the selected features using only classification accuracy, stability measurements should be examined as well to improve the reliability of biomarker discovery.

DNA methylation is a well-recognized epigenetic mechanism that has been the subject of a growing body of literature typically focused on the identification and study of profiles of DNA methylation and their association with human diseases and exposures. In recent years, a number of unsupervised clustering algorithms, both parametric and non-parametric, have been proposed for clustering large-scale DNA methylation data. However, most of these approaches do not incorporate known biological relationships of measured features, and in some cases, rely on unrealistic assumptions regarding the nature of DNA methylation. Here, we propose a modified version of a recursively partitioned mixture model (RPMM) that integrates information related to the proximity of CpG loci within the genome to inform correlation structures from which subsequent clustering analysis is based. Using simulations and four methylation data sets, we demonstrate that integrating biologically informative correlation structures within RPMM resulted in improved goodness-of-fit, clustering consistency, and the ability to detect biologically meaningful clusters compared to methods which ignore such correlation. Integrating biologically-informed correlation structures to enhance modeling techniques is motivated by the rapid increase in resolution of DNA methylation microarrays and the increasing understanding of the biology of this epigenetic mechanism.

Knowledge of genes influencing longitudinal patterns may offer information about predicting disease progression. We developed a systematic procedure for testing association between SNP genotypes and longitudinal phenotypes. We evaluated false positive rates and statistical power to localize genes for disease progression. We used genome-wide SNP data from the Framingham Heart Study. With longitudinal data from two real studies unrelated to Framingham, we estimated three trajectory curves from each study. We performed simulations by randomly selecting 500 individuals. In each simulation replicate, we assigned each individual to one of the three trajectory groups based on the underlying hypothesis (null or alternative), and generated corresponding longitudinal data. Individual Bayesian posterior probabilities (BPPs) for belonging to a specific trajectory curve were estimated. These BPPs were treated as a quantitative trait and tested (using the Wald test) for genome-wide association. Empirical false positive rates and power were calculated. Our method maintained the expected false positive rate for all simulation models. Also, our method achieved high empirical power for most simulations. Our work presents a method for disease progression gene mapping. This method is potentially clinically significant as it may allow doctors to predict disease progression based on genotype and determine treatment accordingly.

We evaluated statistical approaches to facilitate and improve multi-stage designs for clinical proteomic studies which plan to transit from laboratory discovery to clinical utility. To find the design with the greatest expected number of true discoveries under constraints on cost and false discovery, the operating characteristics of the multi-stage study were optimized as a function of sample sizes and nominal type-I error rates at each stage. A nested simulated annealing algorithm was used to find the best solution in the bounded spaces constructed by multiple design parameters. This approach is demonstrated to be feasible and lead to efficient designs. The use of biological grouping information in the study design was also investigated using synthetic datasets based on a cardiac proteomic study, and an actual dataset from a clinical immunology proteomic study. When different protein patterns presented, performance improved when the grouping was informative, with little loss in performance when the grouping was uninformative.