A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently developed Iterative Conditional Fitting (ICF) algorithm with the Expectation Maximization (EM) algorithm. It provides positive definite estimates for any sample size, and does not rely on any structural assumption on the PPZ. It can be easily adapted to many versions of EM.Comment: Accepted for publication in Statistics and Computin

Fractal geometry of spin-glass models

Stability and diversity are two key properties that living entities share with spin glasses, where they are manifested through the breaking of the phase space into many valleys or local minima connected by saddle points. The topology of the phase space can be conveniently condensed into a tree structure, akin to the biological phylogenetic trees, whose tips are the local minima and internal nodes are the lowest-energy saddles connecting those minima. For the infinite-range Ising spin glass with p-spin interactions, we show that the average size-frequency distribution of saddles obeys a power law $\sim w^{-D}$, where w=w(s) is the number of minima that can be connected through saddle s, and D is the fractal dimension of the phase space

Non-compartment model to compartment model pharmacokinetics transformation meta-analysis – a multivariate nonlinear mixed model

Background To fulfill the model based drug development, the very first step is usually a model establishment from published literatures. Pharmacokinetics model is the central piece of model based drug development. This paper proposed an important approach to transform published non-compartment model pharmacokinetics (PK) parameters into compartment model PK parameters. This meta-analysis was performed with a multivariate nonlinear mixed model. A conditional first-order linearization approach was developed for statistical estimation and inference. Results Using MDZ as an example, we showed that this approach successfully transformed 6 non-compartment model PK parameters from 10 publications into 5 compartment model PK parameters. In simulation studies, we showed that this multivariate nonlinear mixed model had little relative bias (<1%) in estimating compartment model PK parameters if all non-compartment PK parameters were reported in every study. If there missing non-compartment PK parameters existed in some published literatures, the relative bias of compartment model PK parameter was still small (<3%). The 95% coverage probabilities of these PK parameter estimates were above 85%. Conclusions This non-compartment model PK parameter transformation into compartment model meta-analysis approach possesses valid statistical inference. It can be routinely used for model based drug development

Reassessing Design and Analysis of two-Colour Microarray Experiments Using Mixed Effects Models

Gene expression microarray studies have led to interesting experimental design and statistical analysis challenges. The comparison of expression profiles across populations is one of the most common objectives of microarray experiments. In this manuscript we review some issues regarding design and statistical analysis for two-colour microarray platforms using mixed linear models, with special attention directed towards the different hierarchical levels of replication and the consequent effect on the use of appropriate error terms for comparing experimental groups. We examine the traditional analysis of variance (ANOVA) models proposed for microarray data and their extensions to hierarchically replicated experiments. In addition, we discuss a mixed model methodology for power and efficiency calculations of different microarray experimental designs

A stitch in time: Efficient computation of genomic DNA melting bubbles

Background: It is of biological interest to make genome-wide predictions of the locations of DNA melting bubbles using statistical mechanics models. Computationally, this poses the challenge that a generic search through all combinations of bubble starts and ends is quadratic. Results: An efficient algorithm is described, which shows that the time complexity of the task is O(NlogN) rather than quadratic. The algorithm exploits that bubble lengths may be limited, but without a prior assumption of a maximal bubble length. No approximations, such as windowing, have been introduced to reduce the time complexity. More than just finding the bubbles, the algorithm produces a stitch profile, which is a probabilistic graphical model of bubbles and helical regions. The algorithm applies a probability peak finding method based on a hierarchical analysis of the energy barriers in the Poland-Scheraga model. Conclusions: Exact and fast computation of genomic stitch profiles is thus feasible. Sequences of several megabases have been computed, only limited by computer memory. Possible applications are the genome-wide comparisons of bubbles with promotors, TSS, viral integration sites, and other melting-related regions.Comment: 16 pages, 10 figure

The DLV System for Knowledge Representation and Reasoning

This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to $\Delta^P_3$-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof. Furthermore, we illustrate the general architecture of the DLV system which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.Comment: 56 pages, 9 figures, 6 table

An Integrated Approach for the Analysis of Biological Pathways using Mixed Models

Gene class, ontology, or pathway testing analysis has become increasingly popular in microarray data analysis. Such approaches allow the integration of gene annotation databases, such as Gene Ontology and KEGG Pathway, to formally test for subtle but coordinated changes at a system level. Higher power in gene class testing is gained by combining weak signals from a number of individual genes in each pathway. We propose an alternative approach for gene-class testing based on mixed models, a class of statistical models that

The Reproducibility of Lists of Differentially Expressed Genes in Microarray Studies

Reproducibility is a fundamental requirement in scientific experiments and clinical contexts. Recent publications raise concerns about the reliability of microarray technology because of the apparent lack of agreement between lists of differentially expressed genes (DEGs). In this study we demonstrate that (1) such discordance may stem from ranking and selecting DEGs solely by statistical significance (P) derived from widely used simple t-tests; (2) when fold change (FC) is used as the ranking criterion, the lists become much more reproducible, especially when fewer genes are selected; and (3) the instability of short DEG lists based on P cutoffs is an expected mathematical consequence of the high variability of the t-values. We recommend the use of FC ranking plus a non-stringent P cutoff as a baseline practice in order to generate more reproducible DEG lists. The FC criterion enhances reproducibility while the P criterion balances sensitivity and specificity