Measurement of statistical evidence on an absolute scale following thermodynamic principles

Statistical analysis is used throughout biomedical research and elsewhere to assess strength of evidence. We have previously argued that typical outcome statistics (including p-values and maximum likelihood ratios) have poor measure-theoretic properties: they can erroneously indicate decreasing evidence as data supporting an hypothesis accumulate; and they are not amenable to calibration, necessary for meaningful comparison of evidence across different study designs, data types, and levels of analysis. We have also previously proposed that thermodynamic theory, which allowed for the first time derivation of an absolute measurement scale for temperature (T), could be used to derive an absolute scale for evidence (E). Here we present a novel thermodynamically-based framework in which measurement of E on an absolute scale, for which "one degree" always means the same thing, becomes possible for the first time. The new framework invites us to think about statistical analyses in terms of the flow of (evidential) information, placing this work in the context of a growing literature on connections among physics, information theory, and statistics.Comment: Final version of manuscript as published in Theory in Biosciences (2013

Statistical Evidence Measured on a Properly Calibrated Scale Across Nested and Non-nested Hypothesis Comparisons

Statistical modeling is often used to measure the strength of evidence for or against hypotheses on given data. We have previously proposed an information-dynamic framework in support of a properly calibrated measurement scale for statistical evidence, borrowing some mathematics from thermodynamics, and showing how an evidential analogue of the ideal gas equation of state could be used to measure evidence for a one-sided binomial hypothesis comparison (coin is fair versus coin is biased towards heads). Here we take three important steps forward in generalizing the framework beyond this simple example. We (1) extend the scope of application to other forms of hypothesis comparison in the binomial setting; (2) show that doing so requires only the original ideal gas equation plus one simple extension, which has the form of the Van der Waals equation; (3) begin to develop the principles required to resolve a key constant, which enables us to calibrate the measurement scale across applications, and which we find to be related to the familiar statistical concept of degrees of freedom. This paper thus moves our information-dynamic theory substantially closer to the goal of producing a practical, properly calibrated measure of statistical evidence for use in general applications

Coexistence of the Critical Slowing Down and Glassy Freezing in Relaxor Ferroelectrics

We have developed a dynamical model for the dielectric response in relaxor ferroelectrics which explicitly takes into account the coexistence of the critical slowing down and glassy freezing. The application of the model to the experiment in PMN allowed for the reconstruction of the nonequilibrium spin glass state order parameter and its comparison with the results of recent NMR experiment (Blinc et al., Phys. Rev. Lett. 83, No. 2 (1999)). It is shown that the degree of the local freezing is rather small even at temperatures where the field-cooled permittivity exceeds the frequency dependent permittivity by an order of magnitude. This observation indicates the significant role of the critical slowing down (accompanying the glass freezing) in the system dynamics. Also the theory predicts an important interrelationship between the frequency dependent permittivity and the zero-field-cooled permittivity, which proved to be consistent with the experiment in PMN (A. Levstik et. al., Phys. Rev. B 57, 11204 (1998))

Complex-Orbital Order in Fe_3O_4 and Mechanism of the Verwey Transition

Electronic state and the Verwey transition in magnetite (Fe_3O_4) are studied using a spinless three-band Hubbard model for 3d electrons on the B sites with the Hartree-Fock approximation and the exact diagonalisation method. Complex-orbital, e.g., 1/sqrt(2)[|zx> + i |yz>], ordered (COO) states having noncollinear orbital moments ~ 0.4 mu_B on the B sites are obtained with the cubic lattice structure of the high-temperature phase. The COO state is a novel form of magnetic ordering within the orbital degree of freedom. It arises from the formation of Hund's second rule states of spinless pseudo-d molecular orbitals in the Fe_4 tetrahedral units of the B sites and ferromagnetic alignment of their fictitious orbital moments. A COO state with longer periodicity is obtained with pseudo-orthorhombic Pmca and Pmc2_1 structures for the low-temperature phase. The state spontaneously lowers the crystal symmetry to the monoclinic and explains experimentally observed rhombohedral cell deformation and Jahn-Teller like distortion. From these findings, we consider that at the Verwey transition temperature, the COO state remaining to be short-range order impeded by dynamical lattice distortion in high temperature is developed into that with long-range order coupled with the monoclinic lattice distortion.Comment: 16 pages, 13 figures, 6 tables, accepted for publication in J. Phys. Soc. Jp

A genome-wide scan for common alleles affecting risk for autism

Although autism spectrum disorders (ASDs) have a substantial genetic basis, most of the known genetic risk has been traced to rare variants, principally copy number variants (CNVs). To identify common risk variation, the Autism Genome Project (AGP) Consortium genotyped 1558 rigorously defined ASD families for 1 million single-nucleotide polymorphisms (SNPs) and analyzed these SNP genotypes for association with ASD. In one of four primary association analyses, the association signal for marker rs4141463, located within MACROD2, crossed the genome-wide association significance threshold of P < 5 × 10−8. When a smaller replication sample was analyzed, the risk allele at rs4141463 was again over-transmitted; yet, consistent with the winner's curse, its effect size in the replication sample was much smaller; and, for the combined samples, the association signal barely fell below the P < 5 × 10−8 threshold. Exploratory analyses of phenotypic subtypes yielded no significant associations after correction for multiple testing. They did, however, yield strong signals within several genes, KIAA0564, PLD5, POU6F2, ST8SIA2 and TAF1C

Mapping autism risk loci using genetic linkage and chromosomal rearrangements.

International audienceAutism spectrum disorders (ASDs) are common, heritable neurodevelopmental conditions. The genetic architecture of ASDs is complex, requiring large samples to overcome heterogeneity. Here we broaden coverage and sample size relative to other studies of ASDs by using Affymetrix 10K SNP arrays and 1,181 [corrected] families with at least two affected individuals, performing the largest linkage scan to date while also analyzing copy number variation in these families. Linkage and copy number variation analyses implicate chromosome 11p12-p13 and neurexins, respectively, among other candidate loci. Neurexins team with previously implicated neuroligins for glutamatergic synaptogenesis, highlighting glutamate-related genes as promising candidates for contributing to ASDs

Meta-analysis of GWAS of over 16,000 individuals with autism spectrum disorder highlights a novel locus at 10q24.32 and a significant overlap with schizophrenia.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked FilesOver the past decade genome-wide association studies (GWAS) have been applied to aid in the understanding of the biology of traits. The success of this approach is governed by the underlying effect sizes carried by the true risk variants and the corresponding statistical power to observe such effects given the study design and sample size under investigation. Previous ASD GWAS have identified genome-wide significant (GWS) risk loci; however, these studies were of only of low statistical power to identify GWS loci at the lower effect sizes (odds ratio (OR) <1.15).We conducted a large-scale coordinated international collaboration to combine independent genotyping data to improve the statistical power and aid in robust discovery of GWS loci. This study uses genome-wide genotyping data from a discovery sample (7387 ASD cases and 8567 controls) followed by meta-analysis of summary statistics from two replication sets (7783 ASD cases and 11359 controls; and 1369 ASD cases and 137308 controls).We observe a GWS locus at 10q24.32 that overlaps several genes including PITX3, which encodes a transcription factor identified as playing a role in neuronal differentiation and CUEDC2 previously reported to be associated with social skills in an independent population cohort. We also observe overlap with regions previously implicated in schizophrenia which was further supported by a strong genetic correlation between these disorders (Rg = 0.23; P = 9 × 10(-6)). We further combined these Psychiatric Genomics Consortium (PGC) ASD GWAS data with the recent PGC schizophrenia GWAS to identify additional regions which may be important in a common neurodevelopmental phenotype and identified 12 novel GWS loci. These include loci previously implicated in ASD such as FOXP1 at 3p13, ATP2B2 at 3p25.3, and a 'neurodevelopmental hub' on chromosome 8p11.23.This study is an important step in the ongoing endeavour to identify the loci which underpin the common variant signal in ASD. In addition to novel GWS loci, we have identified a significant genetic correlation with schizophrenia and association of ASD with several neurodevelopmental-related genes such as EXT1, ASTN2, MACROD2, and HDAC4.National Institutes of Mental Health (NIMH, USA) ACE Network Autism Genetic Resource Exchange (AGRE) is a program of Autism Speaks (USA) The Autism Genome Project (AGP) from Autism Speaks (USA) Canadian Institutes of Health Research (CIHR), Genome Canada Health Research Board (Ireland) Hilibrand Foundation (USA) Medical Research Council (UK) National Institutes of Health (USA) Ontario Genomics Institute University of Toronto McLaughlin Centre Simons Foundation Johns Hopkins Autism Consortium of Boston NLM Family foundation National Institute of Health grants National Health Medical Research Council Scottish Rite Spunk Fund, Inc. Rebecca and Solomon Baker Fund APEX Foundation National Alliance for Research in Schizophrenia and Affective Disorders (NARSAD) endowment fund of the Nancy Pritzker Laboratory (Stanford) Autism Society of America Janet M. Grace Pervasive Developmental Disorders Fund The Lundbeck Foundation universities and university hospitals of Aarhus and Copenhagen Stanley Foundation Centers for Disease Control and Prevention (CDC) Netherlands Scientific Organization Dutch Brain Foundation VU University Amsterdam Trinity Centre for High Performance Computing through Science Foundation Ireland Autism Genome Project (AGP) from Autism Speak

Polygenic transmission disequilibrium confirms that common and rare variation act additively to create risk for autism spectrum disorders

Autism spectrum disorder (ASD) risk is influenced by common polygenic and de novo variation. We aimed to clarify the influence of polygenic risk for ASD and to identify subgroups of ASD cases, including those with strongly acting de novo variants, in which polygenic risk is relevant. Using a novel approach called the polygenic transmission disequilibrium test and data from 6,454 families with a child with ASD, we show that polygenic risk for ASD, schizophrenia, and greater educational attainment is over-transmitted to children with ASD. These findings hold independent of proband IQ. We find that polygenic variation contributes additively to risk in ASD cases who carry a strongly acting de novo variant. Lastly, we show that elements of polygenic risk are independent and differ in their relationship with phenotype. These results confirm that the genetic influences on ASD are additive and suggest that they create risk through at least partially distinct etiologic pathways