Pure infiniteness, stability and C*-algebras of graphs and dynamical systems

Pure infiniteness (in sense of E.Kirchberg and M.R{\o}rdam) is considered for C*-algebras arising from singly generated dynamical systems. In particular, Cuntz-Krieger algebras and their generalizations, i.e., graph-algebras and O_A of an infinite matrix A, admit characterizations of pure infiniteness. As a consequence, these generalized Cuntz-Krieger algebras are traceless if and only if they are purely infinite. Also, a characterization of AF-algebras among these C*-algebras is given. In the case of graph-algebras of locally finite graphs, characterizations of stability are obtained.Comment: 31 page

The Liability Threshold Model for Censored Twin Data

Family studies provide an important tool for understanding etiology of diseases, with the key aim of discovering evidence of family aggregation and to determine if such aggregation can be attributed to genetic components. Heritability and concordance estimates are routinely calculated in twin studies of diseases, as a way of quantifying such genetic contribution. The endpoint in these studies are typically defined as occurrence of a disease versus death without the disease. However, a large fraction of the subjects may still be alive at the time of follow-up without having experienced the disease thus still being at risk. Ignoring this right-censoring can lead to severely biased estimates. We propose to extend the classical liability threshold model with inverse probability of censoring weighting of complete observations. This leads to a flexible way of modeling twin concordance and obtaining consistent estimates of heritability. We apply the method in simulations and to data from the population based Danish twin cohort where we describe the dependence in prostate cancer occurrence in twins

Lifespans of Twins : Does Zygosity Matter?

Studies with twins provide fundamental insights to lifespans of humans. We aim to clarify if monozygotic and dizygotic twin individuals differ in lifespan, that is, if zygosity matters. We investigate whether a possible difference in mortality after infancy between zygosities is stable in different age cohorts, and whether the difference remains when twins with unknown zygosity are taken into account. Further, we compare the distribution of long-livers, that is, the upper-tail of the lifespan distribution, between monozygotic and same-sex dizygotic twin individuals. The Danish Twin Registry provides a nationwide cohort of 109,303 twins born during 1870 to 1990 with valid vital status. Standard survival analysis is used to compare mortality in monozygotic and dizygotic twin individuals and twin individuals with unknown zygosity. The mortality of monozygotic and dizygotic twin individuals differs slightly after taking into consideration effects of birth- and age-cohorts, gender differences, and that twins are paired. However, no substantial nor systematic differences remain when taking twins with unknown zygosity into account. Further, the distribution of long-livers is very similar by zygosity, suggesting the same mortality process. The population-based and oldest twin cohort ever studied suggests that monozygotic and dizygotic twins have similar lifespans.Peer reviewe

Lifespans of Twins : Does Zygosity Matter?

Studies with twins provide fundamental insights to lifespans of humans. We aim to clarify if monozygotic and dizygotic twin individuals differ in lifespan, that is, if zygosity matters. We investigate whether a possible difference in mortality after infancy between zygosities is stable in different age cohorts, and whether the difference remains when twins with unknown zygosity are taken into account. Further, we compare the distribution of long-livers, that is, the upper-tail of the lifespan distribution, between monozygotic and same-sex dizygotic twin individuals. The Danish Twin Registry provides a nationwide cohort of 109,303 twins born during 1870 to 1990 with valid vital status. Standard survival analysis is used to compare mortality in monozygotic and dizygotic twin individuals and twin individuals with unknown zygosity. The mortality of monozygotic and dizygotic twin individuals differs slightly after taking into consideration effects of birth- and age-cohorts, gender differences, and that twins are paired. However, no substantial nor systematic differences remain when taking twins with unknown zygosity into account. Further, the distribution of long-livers is very similar by zygosity, suggesting the same mortality process. The population-based and oldest twin cohort ever studied suggests that monozygotic and dizygotic twins have similar lifespans.Peer reviewe

The heritability of BMI varies across the range of BMI-a heritability curve analysis in a twin cohort

Background The heritability of traits such as body mass index (BMI), a measure of obesity, is generally estimated using family and twin studies, and increasingly by molecular genetic approaches. These studies generally assume that genetic effects are uniform across all trait values, yet there is emerging evidence that this may not always be the case. Method/Subjects This paper analyzes twin data using a recently developed measure of heritability called the heritability curve. Under the assumption that trait values in twin pairs are governed by a flexible Gaussian mixture distribution, heritability curves may vary across trait values. The data consist of repeated measures of BMI on 1506 monozygotic (MZ) and 2843 like-sexed dizygotic (DZ) adult twin pairs, gathered from multiple surveys in older Finnish Twin Cohorts. Results The heritability curve and BMI value-specific MZ and DZ pairwise correlations were estimated, and these varied across the range of BMI. MZ correlations were highest at BMI values from 21 to 24, with a stronger decrease for women than for men at higher values. Models with additive and dominance effects fit best at low and high BMI values, while models with additive genetic and common environmental effects fit best in the normal range of BMI. Conclusions We demonstrate that twin and molecular genetic studies need to consider how genetic effects vary across trait values. Such variation may reconcile findings of traits with high heritability and major differences in mean values between countries or over time.Peer reviewe

Cancer in twin pairs discordant for smoking : The Nordic Twin Study of Cancer

The discordant twin pair study design is powerful to control for familial confounding. We employed this approach to investigate the associations of smoking with several cancers. The NorTwinCan study combines data from the Danish, Finnish, Norwegian and Swedish twin and cancer registries. Follow-up started when smoking status was determined and ended at cancer diagnosis confirmed by information in the cancer registry, death or end of follow-up. We classified the participants as never (n = 59 093), former (n = 21 168) or current (n = 47 314) smokers. We pooled data from twin pairs where one co-twin was diagnosed with any of the following tobacco-related cancers: esophagus, kidney, larynx, liver, oral cavity, pancreas, pharynx or urinary bladder, while their co-twin had none of those. Lung cancer was included in further analysis. We used Cox regression allowing for pair-specific baseline functions to estimate hazard ratios (HRs) with 95% confidence intervals (CIs). For tobacco-related cancer sites, we recorded 7379 cases during median 27 years of follow-up. The analyses based on individual twins showed that former (HR 1.31, 95% CI: 1.17-1.48) and current (HR 2.14 [1.95-2.34]) smokers are at increased risk to develop one of cancers listed above, compared to never smokers. Among 109 monozygotic twin pairs discordant for cancer and smoking, the HR was 1.85 (95% CI: 1.15-2.98) among current smokers and 1.69 (1.00-2.87) among former smokers when compared to their never smoking co-twin. Thus, associations of smoking with several cancers were replicated for discordant identical twin pairs. Analyses based on genetically informative data provide evidence consistent with smoking causing multiple cancers.Peer reviewe

The Nordic Twin Study on Cancer - NorTwinCan

Nordic twin studies have played a critical role in understanding cancer etiology and elucidating the nature of familial effects on site-specific cancers. The NorTwinCan consortium is a collaborative effort that capitalizes on unique research advantages made possible through the Nordic system of registries. It was constructed by linking the population-based twin registries of Denmark, Finland, Norway and Sweden to their country-specific national cancer and cause-of-death registries. These linkages enable the twins to be followed many decades for cancer incidence and mortality. To date, two major linkages have been conducted: NorTwinCan I in 2011-2012 and NorTwinCan II in 2018. Overall, there are 315,413 eligible twins, 57,236 incident cancer cases and 58 years of follow-up, on average. In the initial phases of our work, NorTwinCan established the world's most comprehensive twin database for studying cancer, developed novel analytical approaches tailored to address specific research considerations within the context of the Nordic data and leveraged these models and data in research publications that provide the most accurate estimates of heritability and familial risk of cancers reported in the literature to date. Our findings indicate an excess familial risk for nearly all cancers and demonstrate that the incidence of cancer among twins mirrors the rate in the general population. They also revealed that twin concordance for cancer most often manifests across, rather than within, cancer sites, and we are currently focusing on the analysis of these cross-cancer associations.Peer reviewe

Theory and Practice in Quantitative Genetics

With the rapid advances in molecular biology, the near completion of the human genome, the development of appropriate statistical genetic methods and the availability of the necessary computing power, the identification of quantitative trait loci has now become a realistic prospect for quantitative geneticists. We briefly describe the theoretical biometrical foundations underlying quantitative genetics. These theoretical underpinnings are translated into mathematical equations that allow the assessment of the contribution of observed (using DNA samples) and unobserved (using known genetic relationships) genetic variation to population variance in quantitative traits. Several statistical models for quantitative genetic analyses are described, such as models for the classical twin design, multivariate and longitudinal genetic analyses, extended twin analyses, and linkage and association analyses. For each, we show how the theoretical biometrical model can be translated into algebraic equations that may be used to generate scripts for statistical genetic software packages, such as Mx, Lisrel, SOLAR, or MERLIN. For using the former program a web-library (available from http://www.psy.vu.nl/mxbib) has been developed of freely available scripts that can be used to conduct all genetic analyses described in this paper