Bayesian network data imputation with application to survival tree analysis

Retrospective clinical datasets are often characterized by a relatively small sample size and many missing data. In this case, a common way for handling the missingness consists in discarding from the analysis patients with missing covariates, further reducing the sample size. Alternatively, if the mechanism that generated the missing allows, incomplete data can be imputed on the basis of the observed data, avoiding the reduction of the sample size and allowing methods to deal with complete data later on. Moreover, methodologies for data imputation might depend on the particular purpose and might achieve better results by considering specific characteristics of the domain. The problem of missing data treatment is studied in the context of survival tree analysis for the estimation of a prognostic patient stratification. Survival tree methods usually address this problem by using surrogate splits, that is, splitting rules that use other variables yielding similar results to the original ones. Instead, our methodology consists in modeling the dependencies among the clinical variables with a Bayesian network, which is then used to perform data imputation, thus allowing the survival tree to be applied on the completed dataset. The Bayesian network is directly learned from the incomplete data using a structural expectation–maximization (EM) procedure in which the maximization step is performed with an exact anytime method, so that the only source of approximation is due to the EM formulation itself. On both simulated and real data, our proposed methodology usually outperformed several existing methods for data imputation and the imputation so obtained improved the stratification estimated by the survival tree (especially with respect to using surrogate splits).

A Tree Augmented Classifier Based on Extreme Imprecise Dirichlet Model

In this paper we present TANC, i.e., a tree-augmented naive credal classifier based on imprecise probabilities; it models prior near-ignorance via the Extreme Imprecise Dirichlet Model (EDM) (Cano et al., 2007) and deals conservatively with missing data in the training set, without assuming them to be missing-at-random. The EDM is an approximation of the global Imprecise Dirichlet Model (IDM), which considerably simplifies the computation of upper and lower probabilities; yet, having been only recently introduced, the quality of the provided approximation needs still to be verified. As first contribution, we extensively compare the output of the naive credal classifier (one of the few cases in which the global IDM can be exactly implemented) when learned with the EDM and the global IDM; the output of the classifier appears to be identical in the vast majority of cases, thus supporting the adoption of the EDM in real classification problems. Then, by experiments we show that TANC is more reliable than the precise TAN (learned with uniform prior), and also that it provides better performance compared to a previous (Zaffalon, 2003) TAN model based on imprecise probabilities. TANC treats missing data by considering all possible completions of the training set, but avoiding an exponential increase of the computational times; eventually, we present some preliminary results with missing data.

NP-hardness of MAP in Ternary Tree Bayesian Networks

This paper strengthens the NP-hardness result for the (partial) maximum a posteriori (MAP) problem in Bayesian networks with topology of trees (every variable has at most one parent) and variable cardinality at most three. MAP is the problem of querying the most probable state configuration of some (not necessarily all) of the network variables given evidence. It is demonstrated that the problem remains hard even in such simplistic networks.

Accessory minerals and potentially toxic elements in Tanzanian vermiculites with respect to agricultural applications

The study assessed accessory minerals and metals in Tanzanian vermiculites with respect to their potential suitability for agricultural applications. Mineral and chemical analyses were involved. Pot experiments were also conducted to assess plant uptake of metals from soil with vermiculites. Fibrous sepiolite and amphiboles were minerals of health concern found in some samples. The sepiolite fibers had aspect ratios similar to those of asbestos minerals, which cause respiratory disorders and lung cancer when inhaled and thus pose a potential health risk to animals and humans. The amphibole fibers were thicker than 10 μm and are unlikely to be inhaled. Chromium (Cr) and nickel (Ni) concentrations in some samples were greater than the limits permitted in agricultural soils, but the elements are not highly plant available and do not inhibit the uptake of essential macronutrients. Heating vermiculites at 400-600° C enhanced extractability of Cr and Ni and should preferably be avoided. © Taylor & Francis Group, LLC.

Genetic mapping of the rice ionome in leaves and grain:Identification of QTLs for 17 elements including arsenic, cadmium, iron and selenium

Research into the composition of cereal grains is motivated by increased interest in food quality. Here multi-element analysis is conducted on leaves and grain of the Bala x Azucena rice mapping population grown in the field. Quantitative trait loci (QTLs) for the concentration of 17 elements were detected, revealing 36 QTLs for leaves and 41 for grains. Epistasis was detected for most elements. There was very little correlation between leaf and grain element concentrations. For selenium, lead, phosphorus and magnesium QTLs were detected in the same location for both tissues. In general, there were no major QTL clusters, suggesting separate regulation of each element. QTLs for grain iron, zinc, molybdenum and selenium are potential targets for marker assisted selection to improve seed nutritional quality. An epistatic interaction for grain arsenic also looks promising to decrease the concentration of this carcinogenic element. © Springer Science+Business Media B.V. 2009.

Major and trace elements in milk and Halloumi cheese as markers for authentication of goat feeding regimes and geographical origin

Sixty samples of milk, Halloumi cheese and local grazing plants (i.e. shrubs) were collected over a year from dairy farms located on three different locations of Cyprus. Major and trace elements were quantified using inductively coupled plasma-atomic emission spectroscopy (ICP-AES). Milk and Halloumi cheese produced in different geographical locations presented significant differences in the concentration of some of the elements analysed. Principal component analysis showed grouping of samples according to the region of production for both milk and cheese samples. These findings show that the assay of elements can provide useful fingerprints for the characterisation of dairy products.

Trace elements as predictors of preeclampsia in type 1 diabetic pregnancy

Preeclampsia (PE) affects approximately 5% of all pregnancies, but is increased several-fold in women with pre-gestational type 1 diabetes mellitus (T1DM). Increased oxidative stress and altered maternal plasma trace elements that modulate the antioxidant system have been implicated in PE. In non-diabetic women, increased plasma copper and iron and decreased manganese, selenium, and zinc have been associated with PE in cross-sectional studies. In a longitudinal study, we hypothesized that plasma levels of trace elements differ between T1DM women with vs. without subsequent PE. Samples were collected during the first (gestation 12.2 ± 1.9 weeks, [mean ± SD]), second (21.6 ± 1.5 weeks), and third (31.5 ± 1.7 weeks) trimesters of pregnancy, all before the onset of PE. We compared 23 T1DM women who subsequently developed PE with 24 T1DM women who remained normotensive; and we included 19 non-diabetic (non-DM) normotensive pregnant women as reference controls. Trace elements were measured using inductively coupled plasma mass spectroscopy. In T1DM women with subsequent PE vs normotensive, only plasma zinc was significantly higher at the first trimester, while copper:zinc and copper:high-density lipoprotein cholesterol ratios were higher throughout gestation (all P < .05). These findings persisted after adjustment for covariates. Higher copper:zinc ratios may contribute to oxidative stress in T1DM women who develop PE. Ratios of pro- to anti-oxidant factors may predict risk for PE in diabetic pregnancies more effectively than individual trace element levels.

Global identification of androgen response elements

Chromatin immunoprecipitation (ChIP) is an invaluable tool in the study of transcriptional regulation. ChIP methods require both a priori knowledge of the transcriptional regulators which are important for a given biological system and high-quality specific antibodies for these targets. The androgen receptor (AR) is known to play essential roles in male sexual development, in prostate cancer and in the function of many other AR-expressing cell types (e.g. neurons and myocytes). As a ligand-activated transcription factor the AR also represents an endogenous, inducible system to study transcriptional biology. Therefore, ChIP studies of the AR can make use of treatment contrast experiments to define its transcriptional targets. To date several studies have mapped AR binding sites using ChIP in combination with genome tiling microarrays (ChIP-chip) or direct sequencing (ChIP-seq), mainly in prostate cancer cell lines and with varying degrees of genomic coverage. These studies have provided new insights into the DNA sequences to which the AR can bind, identified AR cooperating transcription factors, mapped thousands of potential AR regulated genes and provided insights into the biological processes regulated by the AR. However, further ChIP studies will be required to fully characterise the dynamics of the AR-regulated transcriptional programme, to map the occupancy of different AR transcriptional complexes which result in different transcriptional output and to delineate the transcriptional networks downstream of the AR.

Improving composite damage modelling through automatic placement of cohesive elements

Numerous experimental studies of damage in composite laminates have shown that intralaminar (in-plane) matrix cracks lead to interlaminar delamination (out-of-plane) at ply interfaces. The smearing of in-plane cracks over a volume, as a consequence of the use of continuum damage mechanics, does not always effectively capture the full extent of the interaction between the two failure mechanisms. A more accurate representation is obtained by adopting a discrete crack approach via the use of cohesive elements, for both in-plane and out-of-plane damage. The difficulty with cohesive elements is that their location must be determined a priori in order to generate the model; while ideally the position of the crack migration, and more generally the propagation path, should be obtained as part of the problem’s solution. With the aim of enhancing current modelling capabilities with truly predictive capabilities, a concept of automatic insertion of interface elements is utilized. The consideration of a simple traction criterion in relation to material strength, evaluated at each node of the model (or of the regions of the model where it is estimated cracks might form), allows for the determination of initial crack location and subsequent propagation by the insertion of cohesive elements during the course of the analysis. Several experimental results are modelled using the commercial package ABAQUS/Standard with an automatic insertion subroutine developed in this work, and the results are presented to demonstrate the capabilities of this technique.