Replica analysis of overfitting in regression models for time-to-event data

Overfitting, which happens when the number of parameters in a model is too large compared to the number of data points available for determining these parameters, is a serious and growing problem in survival analysis. While modern medicine presents us with data of unprecedented dimensionality, these data cannot yet be used effectively for clinical outcome prediction. Standard error measures in maximum likelihood regression, such as p-values and z-scores, are blind to overfitting, and even for Cox's proportional hazards model (the main tool of medical statisticians), one finds in literature only rules of thumb on the number of samples required to avoid overfitting. In this paper we present a mathematical theory of overfitting in regression models for time-to-event data, which aims to increase our quantitative understanding of the problem and provide practical tools with which to correct regression outcomes for the impact of overfitting. It is based on the replica method, a statistical mechanical technique for the analysis of heterogeneous many-variable systems that has been used successfully for several decades in physics, biology, and computer science, but not yet in medical statistics. We develop the theory initially for arbitrary regression models for time-to-event data, and verify its predictions in detail for the popular Cox model.Comment: 37 pages, 9 figure

Adenomatoid hyperplasia of palatal minor salivary glands

Adenomatoid hyperplasia of palatal minor mucous glands is rare but significant because the clinical appearance mimics malignant disease. The typical history of a painless, indolent palatal swelling, together with the histological picture of benign glandular hyperplasia and hypertrophy, are illustrated in this report

Reduced mechanical efficiency in left-ventricular trabeculae of the spontaneously hypertensive rat.

Long-term systemic arterial hypertension, and its associated compensatory response of left-ventricular hypertrophy, is fatal. This disease leads to cardiac failure and culminates in death. The spontaneously hypertensive rat (SHR) is an excellent animal model for studying this pathology, suffering from ventricular failure beginning at about 18 months of age. In this study, we isolated left-ventricular trabeculae from SHR-F hearts and contrasted their mechanoenergetic performance with those from nonfailing SHR (SHR-NF) and normotensive Wistar rats. Our results show that, whereas the performance of the SHR-F differed little from that of the SHR-NF, both SHR groups performed less stress-length work than that of Wistar trabeculae. Their lower work output arose from reduced ability to produce sufficient force and shortening. Neither their heat production nor their enthalpy output (the sum of work and heat), particularly the energy cost of Ca(2+) cycling, differed from that of the Wistar controls. Consequently, mechanical efficiency (the ratio of work to change of enthalpy) of both SHR groups was lower than that of the Wistar trabeculae. Our data suggest that in hypertension-induced left-ventricular hypertrophy, the mechanical performance of the tissue is compromised such that myocardial efficiency is reduced

Conformal Parametrisation of Loxodromes by Triples of Circles

We provide a parametrisation of a loxodrome by three specially arranged cycles. The parametrisation is covariant under fractional linear transformations of the complex plane and naturally encodes conformal properties of loxodromes. Selected geometrical examples illustrate the usage of parametrisation. Our work extends the set of objects in Lie sphere geometry---circle, lines and points---to the natural maximal conformally-invariant family, which also includes loxodromes.Comment: 14 pages. 9 PDF in four figures, AMS-LaTe

Ecological globalisation, serial depletion and the medieval trade of walrus rostra

The impacts of early ecological globalisation may have had profound economic and environmental consequences for human settlements and animal populations. Here, we review the extent of such historical impacts by investigating the medieval trade of walrus (Odobenus rosmarus rosmarus) ivory. We use an interdisciplinary approach including chaîne opératoire, ancient DNA (aDNA), stable isotope and zooarchaeological analysis of walrus rostra (skull sections) to identify their biological source and subsequent trade through Indigenous and urban networks. This approach complements and improves the spatial resolution of earlier aDNA observations, and we conclude that almost all medieval European finds of walrus rostra likely derived from Greenland. We further find that shifting urban nodes redistributed the traded ivory and that the latest medieval rostra finds were from smaller, often female, walruses of a distinctive DNA clade, which is especially prevalent in northern Greenland. Our results suggest that more and smaller animals were targeted at increasingly untenable distances, which reflects a classic pattern of resource depletion. We consider how the trade of walrus and elephant ivory intersected, and evaluate the extent to which emergent globalisation and the “resource curse” contributed to the abandonment of Norse Greenland

Synthesis-View: visualization and interpretation of SNP association results for multi-cohort, multi-phenotype data and meta-analysis

<p>Abstract</p> <p>Background</p> <p>Initial genome-wide association study (GWAS) discoveries are being further explored through the use of large cohorts across multiple and diverse populations involving meta-analyses within large consortia and networks. Many of the additional studies characterize less than 100 single nucleotide polymorphisms (SNPs), often include multiple and correlated phenotypic measurements, and can include data from multiple-sites, multiple-studies, as well as multiple race/ethnicities. New approaches for visualizing resultant data are necessary in order to fully interpret results and obtain a broad view of the trends between DNA variation and phenotypes, as well as provide information on specific SNP and phenotype relationships.</p> <p>Results</p> <p>The Synthesis-View software tool was designed to visually synthesize the results of the aforementioned types of studies. Presented herein are multiple examples of the ways Synthesis-View can be used to report results from association studies of DNA variation and phenotypes, including the visual integration of p-values or other metrics of significance, allele frequencies, sample sizes, effect size, and direction of effect.</p> <p>Conclusions</p> <p>To truly allow a user to visually integrate multiple pieces of information typical of a genetic association study, innovative views are needed to integrate multiple pieces of information. As a result, we have created "Synthesis-View" software for the visualization of genotype-phenotype association data in multiple cohorts. Synthesis-View is freely available for non-commercial research institutions, for full details see <url>https://chgr.mc.vanderbilt.edu/synthesisview</url>.</p

Increasing human motor skill acquisition by driving theta-gamma coupling

Skill learning is a fundamental adaptive process, but the mechanisms remain poorly understood. Some learning paradigms, particularly in the memory domain, are closely associated with gamma activity that is amplitude-modulated by the phase of underlying theta activity, but whether such nested activity patterns also underpin skill learning is unknown. Here we addressed this question by using transcranial alternating current stimulation (tACS) over sensorimotor cortex to modulate theta-gamma activity during motor skill acquisition, as an exemplar of a non-hippocampal-dependent task. We demonstrated, and then replicated, a significant improvement in skill acquisition with theta-gamma tACS, which outlasted the stimulation by an hour. Our results suggest that theta-gamma activity may be a common mechanism for learning across the brain and provides a putative novel intervention for optimising functional improvements in response to training or therapy