Approximating multivariate posterior distribution functions from Monte Carlo samples for sequential Bayesian inference

An important feature of Bayesian statistics is the opportunity to do sequential inference: the posterior distribution obtained after seeing a dataset can be used as prior for a second inference. However, when Monte Carlo sampling methods are used for inference, we only have a set of samples from the posterior distribution. To do sequential inference, we then either have to evaluate the second posterior at only these locations and reweight the samples accordingly, or we can estimate a functional description of the posterior probability distribution from the samples and use that as prior for the second inference. Here, we investigated to what extent we can obtain an accurate joint posterior from two datasets if the inference is done sequentially rather than jointly, under the condition that each inference step is done using Monte Carlo sampling. To test this, we evaluated the accuracy of kernel density estimates, Gaussian mixtures, vine copulas and Gaussian processes in approximating posterior distributions, and then tested whether these approximations can be used in sequential inference. In low dimensionality, Gaussian processes are more accurate, whereas in higher dimensionality Gaussian mixtures or vine copulas perform better. In our test cases, posterior approximations are preferable over direct sample reweighting, although joint inference is still preferable over sequential inference. Since the performance is case-specific, we provide an R package mvdens with a unified interface for the density approximation methods

Heterofusion:Fusing genomics data of different measurement scales

In systems biology, it is becoming increasingly common to measure biochemical entities at different levels of the same biological system. Hence, data fusion problems are abundant in the life sciences. With the availability of a multitude of measuring techniques, one of the central problems is the heterogeneity of the data. In this paper, we discuss a specific form of heterogeneity, namely, that of measurements obtained at different measurement scales, such as binary, ordinal, interval, and ratio‐scaled variables. Three generic fusion approaches are presented of which two are new to the systems biology community. The methods are presented, put in context, and illustrated with a real‐life genomics example

Detection of Colorectal Cancer by Serum and Tissue Protein Profiling: A Prospective Study in a Population at Risk

Colorectal cancer (CRC) is the second most common cause of cancer-related death in Europe and its prognosis is largely dependent on stage at diagnosis. Currently, there are no suitable tumour markers for early detection of CRC. In a retrospective study we previously found discriminative CRC serum protein profiles with surface enhanced laser desorption ionisation—time of flight mass spectrometry (SELDI-TOF MS). We now aimed at prospective validation of these profiles. Additionally, we assessed their applicability for follow-up after surgery and investigated tissue protein profiles of patients with CRC and adenomatous polyps (AP). Serum and tissue samples were collected from patients without known malignancy with an indication for colonoscopy and patients with AP and CRC during colonoscopy. Serum samples of controls (CON; n = 359), patients with AP (n = 177) and CRC (n = 73), as well as tissue samples from AP (n = 52) and CRC (n = 47) were analysed as described previously. Peak intensities were compared by non-parametric testing. Discriminative power of differentially expressed proteins was assessed with support vector machines (SVM). We confirmed the decreased serum levels of apolipoprotein C-1 in CRC in the current population. No differences were observed between CON and AP. Apolipoprotein C-I levels did not change significantly within 1 month post-surgery, although a gradual return to normal levels was observed. Several proteins differed between AP and CRC tissue, among which a peak with similar mass as apolipoprotein C-1. This peak was increased in CRC compared to AP. Although we prospectively validated the serum decrease of apolipoprotein C-1 in CRC, serum protein profiles did not yield SVM classifiers with suitable sensitivity and specificity for classification of our patient groups

Genomic patterns resembling BRCA1- and BRCA2-mutated breast cancers predict benefit of intensified carboplatin-based chemotherapy

Introduction: BRCA-mutated breast cancer cells lack the DNA-repair mechanism homologous recombination that is required for error-free DNA double-strand break (DSB) repair. Homologous recombination deficiency (HRD) may cause hypersensitivity to DNA DSB-inducing agents, such as bifunctional alkylating agents and platinum salts. HRD can be caused by BRCA mutations, and by other mechanisms. To identify HRD, studies have focused on triple-negative (TN) breast cancers as these resemble BRCA1-mutated breast cancer closely and might also share this hypersensitivity. However, ways to identify HRD in non-BRCA-mutated, estrogen receptor (ER)-positive breast cancers have remained elusive. The current study provides evidence that genomic patterns resembling BRCA1- or BRCA2- mutated breast cancers can identify breast cancer patients with TN as well as ER-positive, HER2-negative tumors that are sensitive to intensified, DSB-inducing chemotherapy. Methods: Array comparative genomic hybridization (aCGH) was used to classify breast cancers. Patients with tumors with similar aCGH patterns as BRCA1- and/or BRCA2-mutated breast cancers were defined as having a BRCA-like(CGH) status, others as non-BCRA-like(CGH). Stage-III patients (n = 249) had participated in a randomized controlled trial of adjuvant high-dose (HD) cyclophosphamide-thiotepa-carboplatin (CTC) versus 5-fluorouracil-epirubicin-cyclophosphamide (FE90C) chemotherapy. Results: Among patients with BRCA-like(CGH) tumors (81/249, 32%), a significant benefit of HD-CTC compared to FE90C was observed regarding overall survival (adjusted hazard ratio 0.19, 95% CI: 0.08 to 0.48) that was not seen for patients with non-BRCA-like(CGH) tumors (adjusted hazard ratio 0.90, 95% CI: 0.53 to 1.54) (P = 0.004). Half of all BRCA-like(CGH) tumors were ER-positive. Conclusions: Distinct aCGH patterns differentiated between HER2-negative patients with a markedly improved outcome after adjuvant treatment with an intensified DNA-DSB-inducing regimen (BRCA-like(CGH) patients) and those without benefit (non-BRCA-like(CGH) patients)

A critical evaluation of network and pathway based classifiers for outcome prediction in breast cancer

Recently, several classifiers that combine primary tumor data, like gene expression data, and secondary data sources, such as protein-protein interaction networks, have been proposed for predicting outcome in breast cancer. In these approaches, new composite features are typically constructed by aggregating the expression levels of several genes. The secondary data sources are employed to guide this aggregation. Although many studies claim that these approaches improve classification performance over single gene classifiers, the gain in performance is difficult to assess. This stems mainly from the fact that different breast cancer data sets and validation procedures are employed to assess the performance. Here we address these issues by employing a large cohort of six breast cancer data sets as benchmark set and by performing an unbiased evaluation of the classification accuracies of the different approaches. Contrary to previous claims, we find that composite feature classifiers do not outperform simple single gene classifiers. We investigate the effect of (1) the number of selected features; (2) the specific gene set from which features are selected; (3) the size of the training set and (4) the heterogeneity of the data set on the performance of composite feature and single gene classifiers. Strikingly, we find that randomization of secondary data sources, which destroys all biological information in these sources, does not result in a deterioration in performance of composite feature classifiers. Finally, we show that when a proper correction for gene set size is performed, the stability of single gene sets is similar to the stability of composite feature sets. Based on these results there is currently no reason to prefer prognostic classifiers based on composite features over single gene classifiers for predicting outcome in breast cancer

The Tumor Immune Landscape and Architecture of Tertiary Lymphoid Structures in Urothelial Cancer

Candidate immune biomarkers have been proposed for predicting response to immunotherapy in urothelial cancer (UC). Yet, these biomarkers are imperfect and lack predictive power. A comprehensive overview of the tumor immune contexture, including Tertiary Lymphoid structures (TLS), is needed to better understand the immunotherapy response in UC. We analyzed tumor sections by quantitative multiplex immunofluorescence to characterize immune cell subsets in various tumor compartments in tumors without pretreatment and tumors exposed to preoperative anti-PD1/CTLA-4 checkpoint inhibitors (NABUCCO trial). Pronounced immune cell presence was found in UC invasive margins compared to tumor and stroma regions. CD8+PD1+ T-cells were present in UC, particularly following immunotherapy. The cellular composition of TLS was assessed by multiplex immunofluorescence (CD3, CD8, FoxP3, CD68, CD20, PanCK, DAPI) to explore specific TLS clusters based on varying immune subset densities. Using a k-means clustering algorithm, we found five distinct cellular composition clusters. Tumors unresponsive to anti-PD-1/CTLA-4 immunotherapy showed enrichment of a FoxP3+ T-cell-low TLS cluster after treatment. Additionally, cluster 5 (macrophage low) TLS were significantly higher after pre-operative immunotherapy, compared to untreated tumors. We also compared the immune cell composition and maturation stages between superficial (submucosal) and deeper TLS, revealing that superficial TLS had more pronounced T-helper cells and enrichment of early TLS than TLS located in deeper tissue. Furthermore, superficial TLS displayed a lower fraction of secondary follicle like TLS than deeper TLS. Taken together, our results provide a detailed quantitative overview of the tumor immune landscape in UC, which can provide a basis for further studies