Estimating correlation between multivariate longitudinal data in the presence of heterogeneity

Abstract Background Estimating correlation coefficients among outcomes is one of the most important analytical tasks in epidemiological and clinical research. Availability of multivariate longitudinal data presents a unique opportunity to assess joint evolution of outcomes over time. Bivariate linear mixed model (BLMM) provides a versatile tool with regard to assessing correlation. However, BLMMs often assume that all individuals are drawn from a single homogenous population where the individual trajectories are distributed smoothly around population average. Methods Using longitudinal mean deviation (MD) and visual acuity (VA) from the Ocular Hypertension Treatment Study (OHTS), we demonstrated strategies to better understand the correlation between multivariate longitudinal data in the presence of potential heterogeneity. Conditional correlation (i.e., marginal correlation given random effects) was calculated to describe how the association between longitudinal outcomes evolved over time within specific subpopulation. The impact of heterogeneity on correlation was also assessed by simulated data. Results There was a significant positive correlation in both random intercepts (ρ = 0.278, 95% CI: 0.121–0.420) and random slopes (ρ = 0.579, 95% CI: 0.349–0.810) between longitudinal MD and VA, and the strength of correlation constantly increased over time. However, conditional correlation and simulation studies revealed that the correlation was induced primarily by participants with rapid deteriorating MD who only accounted for a small fraction of total samples. Conclusion Conditional correlation given random effects provides a robust estimate to describe the correlation between multivariate longitudinal data in the presence of unobserved heterogeneity (NCT00000125)

Smooth double barriers in quantum mechanics

Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle energy, and their dependence on the barrier parameters are obtained for various cases. We also discuss the tunneling time, for which we obtain generalizations of the known results for rectangular barriers.Comment: 23 pages, 8 figures, a slightly reduced version to appear in American Journal of Physics, references correcte

Genetic Correlates of Brain Aging on MRI and Cognitive Test Measures: A Genome-Wide Association and Linkage Analysis in the Framingham Study

BACKGROUND: Brain magnetic resonance imaging (MRI) and cognitive tests can identify heritable endophenotypes associated with an increased risk of developing stroke, dementia and Alzheimer's disease (AD). We conducted a genome-wide association (GWA) and linkage analysis exploring the genetic basis of these endophenotypes in a community-based sample. METHODS: A total of 705 stroke- and dementia-free Framingham participants (age 62 +9 yrs, 50% male) who underwent volumetric brain MRI and cognitive testing (1999–2002) were genotyped. We used linear models adjusting for first degree relationships via generalized estimating equations (GEE) and family based association tests (FBAT) in additive models to relate qualifying single nucleotide polymorphisms (SNPs, 70,987 autosomal on Affymetrix 100K Human Gene Chip with minor allele frequency ≥ 0.10, genotypic call rate ≥ 0.80, and Hardy-Weinberg equilibrium p-value ≥ 0.001) to multivariable-adjusted residuals of 9 MRI measures including total cerebral brain (TCBV), lobar, ventricular and white matter hyperintensity (WMH) volumes, and 6 cognitive factors/tests assessing verbal and visuospatial memory, visual scanning and motor speed, reading, abstract reasoning and naming. We determined multipoint identity-by-descent utilizing 10,592 informative SNPs and 613 short tandem repeats and used variance component analyses to compute LOD scores. RESULTS: The strongest gene-phenotype association in FBAT analyses was between SORL1 (rs1131497; p = 3.2 × 10-6) and abstract reasoning, and in GEE analyses between CDH4 (rs1970546; p = 3.7 × 10-8) and TCBV. SORL1 plays a role in amyloid precursor protein processing and has been associated with the risk of AD. Among the 50 strongest associations (25 each by GEE and FBAT) were other biologically interesting genes. Polymorphisms within 28 of 163 candidate genes for stroke, AD and memory impairment were associated with the endophenotypes studied at p < 0.001. We confirmed our previously reported linkage of WMH on chromosome 4 and describe linkage of reading performance to a marker on chromosome 18 (GATA11A06), previously linked to dyslexia (LOD scores = 2.2 and 5.1). CONCLUSION: Our results suggest that genes associated with clinical neurological disease also have detectable effects on subclinical phenotypes. These hypothesis generating data illustrate the use of an unbiased approach to discover novel pathways that may be involved in brain aging, and could be used to replicate observations made in other studies.National Institutes of Health National Center for Research Resources Shared Instrumentation grant (ISI0RR163736-01A1); National Heart, Lung, and Blood Institute's Framingham Heart Study (N01-HC-25195); National Institute of Aging (5R01-AG08122, 5R01-AG16495); National Institute of Neurological Disorders and Stroke (5R01-NS17950

A Research-Based Curriculum for Teaching the Photoelectric Effect

Physics faculty consider the photoelectric effect important, but many erroneously believe it is easy for students to understand. We have developed curriculum on this topic including an interactive computer simulation, interactive lectures with peer instruction, and conceptual and mathematical homework problems. Our curriculum addresses established student difficulties and is designed to achieve two learning goals, for students to be able to (1) correctly predict the results of photoelectric effect experiments, and (2) describe how these results lead to the photon model of light. We designed two exam questions to test these learning goals. Our instruction leads to better student mastery of the first goal than either traditional instruction or previous reformed instruction, with approximately 85% of students correctly predicting the results of changes to the experimental conditions. On the question designed to test the second goal, most students are able to correctly state both the observations made in the photoelectric effect experiment and the inferences that can be made from these observations, but are less successful in drawing a clear logical connection between the observations and inferences. This is likely a symptom of a more general lack of the reasoning skills to logically draw inferences from observations.Comment: submitted to American Journal of Physic

Association of metabolic dysregulation with volumetric brain magnetic resonance imaging and cognitive markers of subclinical brain aging in middle-aged adults: the Framingham Offspring Study.

ObjectiveDiabetic and prediabtic states, including insulin resistance, fasting hyperglycemia, and hyperinsulinemia, are associated with metabolic dysregulation. These components have been individually linked to increased risks of cognitive decline and Alzheimer's disease. We aimed to comprehensively relate all of the components of metabolic dysregulation to cognitive function and brain magnetic resonance imaging (MRI) in middle-aged adults.Research design and methodsFramingham Offspring participants who underwent volumetric MRI and detailed cognitive testing and were free of clinical stroke and dementia during examination 7 (1998-2001) constituted our study sample (n = 2,439; 1,311 women; age 61 ± 9 years). We related diabetes, homeostasis model assessment of insulin resistance (HOMA-IR), fasting insulin, and glycohemoglobin levels to cross-sectional MRI measures of total cerebral brain volume (TCBV) and hippocampal volume and to verbal and visuospatial memory and executive function. We serially adjusted for age, sex, and education alone (model A), additionally for other vascular risk factors (model B), and finally, with the inclusion of apolipoprotein E-ε4, plasma homocysteine, C-reactive protein, and interleukin-6 (model C).ResultsWe observed an inverse association between all indices of metabolic dysfunction and TCBV in all models (P &lt; 0.030). The observed difference in TCBV between participants with and without diabetes was equivalent to approximately 6 years of chronologic aging. Diabetes and elevated glycohemoglobin, HOMA-IR, and fasting insulin were related to poorer executive function scores (P &lt; 0.038), whereas only HOMA-IR and fasting insulin were inversely related to visuospatial memory (P &lt; 0.007).ConclusionsMetabolic dysregulation, especially insulin resistance, was associated with lower brain volumes and executive function in a large, relatively healthy, middle-aged, community-based cohort

Working with simple machines

A set of examples is provided that illustrate the use of work as applied to simple machines. The ramp, pulley, lever and hydraulic press are common experiences in the life of a student and their theoretical analysis therefore makes the abstract concept of work more real. The mechanical advantage of each of these systems is also discussed so that students can evaluate their usefulness as machines.Comment: 9 pages, 4 figure

Inverse association between cancer and Alzheimer’s disease: results from the Framingham Heart Study

Objectives: To relate cancer since entry into the Framingham Heart Study with the risk of incident Alzheimer’s disease and to estimate the risk of incident cancer among participants with and without Alzheimer’s disease. Design: Community based prospective cohort study; nested age and sex matched case-control study. Setting: Framingham Heart Study, USA. Participants: 1278 participants with and without a history of cancer who were aged 65 or more and free of dementia at baseline (1986-90). Main outcome measures Hazard ratios and 95% confidence intervals for the risks of Alzheimer’s disease and cancer. Results: Over a mean follow-up of 10 years, 221 cases of probable Alzheimer’s disease were diagnosed. Cancer survivors had a lower risk of probable Alzheimer’s disease (hazard ratio 0.67, 95% confidence interval 0.47 to 0.97), adjusted for age, sex, and smoking. The risk was lower among survivors of smoking related cancers (0.26, 0.08 to 0.82) than among survivors of non-smoking related cancers (0.82, 0.57 to 1.19). In contrast with their decreased risk of Alzheimer’s disease, survivors of smoking related cancer had a substantially increased risk of stroke (2.18, 1.29 to 3.68). In the nested case-control analysis, participants with probable Alzheimer’s disease had a lower risk of subsequent cancer (0.39, 0.26 to 0.58) than reference participants, as did participants with any Alzheimer’s disease (0.38) and any dementia (0.44). Conclusions: Cancer survivors had a lower risk of Alzheimer’s disease than those without cancer, and patients with Alzheimer’s disease had a lower risk of incident cancer. The risk of Alzheimer’s disease was lowest in survivors of smoking related cancers, and was not primarily explained by survival bias. This pattern for cancer is similar to that seen in Parkinson’s disease and suggests an inverse association between cancer and neurodegeneration

Association of Metabolic Dysregulation With Volumetric Brain Magnetic Resonance Imaging and Cognitive Markers of Subclinical Brain Aging in Middle-Aged Adults

Objective: Diabetic and prediabtic states, including insulin resistance, fasting hyperglycemia, and hyperinsulinemia, are associated with metabolic dysregulation. These components have been individually linked to increased risks of cognitive decline and Alzheimer’s disease. We aimed to comprehensively relate all of the components of metabolic dysregulation to cognitive function and brain magnetic resonance imaging (MRI) in middle-aged adults. Research Design and Methods: Framingham Offspring participants who underwent volumetric MRI and detailed cognitive testing and were free of clinical stroke and dementia during examination 7 (1998–2001) constituted our study sample (n = 2,439; 1,311 women; age 61 ± 9 years). We related diabetes, homeostasis model assessment of insulin resistance (HOMA-IR), fasting insulin, and glycohemoglobin levels to cross-sectional MRI measures of total cerebral brain volume (TCBV) and hippocampal volume and to verbal and visuospatial memory and executive function. We serially adjusted for age, sex, and education alone (model A), additionally for other vascular risk factors (model B), and finally, with the inclusion of apolipoprotein E-ε4, plasma homocysteine, C-reactive protein, and interleukin-6 (model C). Results: We observed an inverse association between all indices of metabolic dysfunction and TCBV in all models (P < 0.030). The observed difference in TCBV between participants with and without diabetes was equivalent to approximately 6 years of chronologic aging. Diabetes and elevated glycohemoglobin, HOMA-IR, and fasting insulin were related to poorer executive function scores (P < 0.038), whereas only HOMA-IR and fasting insulin were inversely related to visuospatial memory (P < 0.007). Conclusions: Metabolic dysregulation, especially insulin resistance, was associated with lower brain volumes and executive function in a large, relatively healthy, middle-aged, community-based cohort

Identification of novel SHOX target genes in the developing limb using a transgenic mouse model

Deficiency of the human short stature homeobox-containing gene (SHOX) has been identified in several disorders characterized by reduced height and skeletal anomalies such as Turner syndrome, Léri-Weill dyschondrosteosis and Langer mesomelic dysplasia as well as isolated short stature. SHOX acts as a transcription factor during limb development and is expressed in chondrocytes of the growth plates. Although highly conserved in vertebrates, rodents lack a SHOX orthologue. This offers the unique opportunity to analyze the effects of human SHOX expression in transgenic mice. We have generated a mouse expressing the human SHOXa cDNA under the control of a murine Col2a1 promoter and enhancer (Tg(Col2a1-SHOX)). SHOX and marker gene expression as well as skeletal phenotypes were characterized in two transgenic lines. No significant skeletal anomalies were found in transgenic compared to wildtype mice. Quantitative and in situ hybridization analyses revealed that Tg(Col2a1-SHOX), however, affected extracellular matrix gene expression during early limb development, suggesting a role for SHOX in growth plate assembly and extracellular matrix composition during long bone development. For instance, we could show that the connective tissue growth factor gene Ctgf, a gene involved in chondrogenic and angiogenic differentiation, is transcriptionally regulated by SHOX in transgenic mice. This finding was confirmed in human NHDF and U2OS cells and chicken micromass culture, demonstrating the value of the SHOX-transgenic mouse for the characterization of SHOX-dependent genes and pathways in early limb development

Genetic determinants of cortical structure (thickness, surface area and volumes) among disease free adults in the CHARGE Consortium

Cortical thickness, surface area and volumes (MRI cortical measures) vary with age and cognitive function, and in neurological and psychiatric diseases. We examined heritability, genetic correlations and genome-wide associations of cortical measures across the whole cortex, and in 34 anatomically predefined regions. Our discovery sample comprised 22,824 individuals from 20 cohorts within the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) consortium and the United Kingdom Biobank. Significant associations were replicated in the Enhancing Neuroimaging Genetics through Meta-analysis (ENIGMA) consortium, and their biological implications explored using bioinformatic annotation and pathway analyses. We identified genetic heterogeneity between cortical measures and brain regions, and 160 genome-wide significant associations pointing to wnt/β-catenin, TGF-β and sonic hedgehog pathways. There was enrichment for genes involved in anthropometric traits, hindbrain development, vascular and neurodegenerative disease and psychiatric conditions. These data are a rich resource for studies of the biological mechanisms behind cortical development and aging