A Conjecture on Demographic Mortality at High Ages

Time-to-event regression is a frequent tool in biomedical research. In clinical trials this time is usually measured from the beginning of the study. The same approach is often adopted in the analysis of longitudinal observational studies. However, in recent years there has appeared literature making a case for the use of the date of birth as a starting point, and thus utilize age as the time-to-event. In this paper, we explore different types of age-scale models and compare them with time-on-study models in terms of the estimated regression coefficients they produce. We consider six proportional hazards regression models that differ in the choice of time scale and in the method of adjusting for the years before the study. By considering the estimating equations of these models as well as numerical simulations we conclude that correct adjustment for the age at entry is crucial in reducing bias of the estimated coefficients. The unadjusted age-scale model is inferior to any of the five other models considered, regardless of their choice of time scale. Additionally, if adjustment for age at entry is made, our analyses show very little to suggest that there exists any practically meaningful difference in the estimated regression coefficients depending on the choice of time scale. These findings are supported by four practical examples from the Framingham Heart Study.

Time Scale in Follow-up Studies

Statistics in MedicineVolume 28, Issue 8 p. 1315-1317 Letter to the Editor Comments on ‘Choice of time scale and its effect on significance of predictors in longitudinal studies’ by Michael J. Pencina, Martin G. Larson and Ralph B. D'Agostino, Statistics in Medicine 2007; 26:1343–1359 Mitchell H. Gail, Mitchell H. Gail Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, U.S.A.Search for more papers by this authorBarry Graubard, Barry Graubard Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, U.S.A.Search for more papers by this authorDavid F. Williamson, David F. Williamson Rollins School of Public Health, Emory University, Atlanta, GA, U.S.A.Search for more papers by this authorKatherine M. Flegal, Katherine M. Flegal National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD, U.S.A.Search for more papers by this author Mitchell H. Gail, Mitchell H. Gail Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, U.S.A.Search for more papers by this authorBarry Graubard, Barry Graubard Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, U.S.A.Search for more papers by this authorDavid F. Williamson, David F. Williamson Rollins School of Public Health, Emory University, Atlanta, GA, U.S.A.Search for more papers by this authorKatherine M. Flegal, Katherine M. Flegal National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD, U.S.A.Search for more papers by this author First published: 13 March 2009 https://doi.org/10.1002/sim.3473Citations: 19AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume28, Issue815 April 2009Pages 1315-1317 RelatedInformation

New magnetic anomaly identifications for the central part of the Cocos plate and the corresponding part of the Pacific plate indicate a pulse of extremely rapid seafloor spreading in the middle Miocene, about 11–18 Ma, possibly beginning as early as 25 Ma. The spacing of anomalies 5A–5D indicates a full spreading rate for the southern Cocos‐Pacific boundary of 180–210 mm/yr, depending on the choice of time scale. Relative to the maximum 0–3 Ma spreading rate of 152 mm/yr, this result significantly expands the upper limit of well documented rates.

Design of modern control laws motivates the creation of state-space models from aeroservoelastic models. Balanced truncation is often used to create reduced-order models. In the present work, a reduced-order model that employs a change in time scale in computing the balancing transformation is developed. The transformation matrix necessary to transform the original aeroservoelastic model is found from the aeroservoelastic model employing the recast time scale. Results from an aeroservoelastic wing and a supersonic transport model are shown, and it is demonstrated that, with an appropriate choice of time scale, the methodology results in greatly improved conditioning for the Lyapunov equations used to find the Gramians employed in the balancing transformation.

On a heat transport model for a turbulent plane jet

A critical specification lacking from much theory and research on organizations is that of time scale. Specification of the relevant time scale is as critical as the specification of the appropriate level or unit of analysis, a concept to which it is related. We define and explore five types of time scales and consider their implications for both the social constructionist and positivist approaches. Using examples from strategy and organizational theory, we show how the choice of time scale has important implications for the development of theory.

Light and heavy particles behave completely different in a turbulent flow field. In the present communication we discuss how one can discriminate between light and heavy particle behavior and how the important class of intermediate particles is identified. This latter class of particles exhibit challenging dynamics since they are affected both by inertia and Stokes drag, i.e. $$ {{d{\bf v}} / {dt}} = St^{ - 1} \left( {{\bf u} - {\bf v}} \right)$$ , where u and v are the Eulerian fluid and Lagrangian particle velocities. This Lagrangian equation is expressed in non-dimensional form where t and St denote time and particle relaxation time $$ \tau = 2/9\left( {\rho _p /\rho _f } \right)a^2 /v_f $$ normalized by an arbitrarily chosen time scale. This expression for τ is applicable for spherical particles with radius a smaller than the smallest length scales of the flow and provided that the particle Reynolds number is below unity. However, for the dimensionless particle relaxation time St, i.e. the socalled Stokes number, to play a distinguishing role in the particle dynamics, the choice of time scale becomes essential. With a properly selected time scale, the particle motion is dominated by Stokes drag if St<<1 and by inertia if St>>1.

Research Article| August 01, 2009 Mid-Cretaceous seafloor spreading pulse: Fact or fiction? M. Seton; M. Seton * 1EarthByte Group, School of Geosciences, Madsen Building F09, University of Sydney, Sydney, NSW 2006, Australia *E-mail: maria.seton@usyd.edu.au. Search for other works by this author on: GSW Google Scholar C. Gaina; C. Gaina 2Center for Geodynamics, Geological Survey of Norway, Leiv Eirikssons vei 39, N-7491 Trondheim, Norway Search for other works by this author on: GSW Google Scholar R.D. Müller; R.D. Müller 1EarthByte Group, School of Geosciences, Madsen Building F09, University of Sydney, Sydney, NSW 2006, Australia Search for other works by this author on: GSW Google Scholar C. Heine C. Heine 1EarthByte Group, School of Geosciences, Madsen Building F09, University of Sydney, Sydney, NSW 2006, Australia †Current address: StatoilHydro Global Exploration Technology, Drammensveien 264, N-0246 Oslo, Norway Search for other works by this author on: GSW Google Scholar Geology (2009) 37 (8): 687–690. https://doi.org/10.1130/G25624A.1 Article history received: 23 Oct 2008 rev-recd: 18 Mar 2009 accepted: 22 Mar 2009 first online: 03 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share MailTo Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation M. Seton, C. Gaina, R.D. Müller, C. Heine; Mid-Cretaceous seafloor spreading pulse: Fact or fiction?. Geology 2009;; 37 (8): 687–690. doi: https://doi.org/10.1130/G25624A.1 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract Two main hypotheses compete to explain the mid-Cretaceous global sea-level highstand: a massive pulse of oceanic crustal production that occurred during the Cretaceous Normal Superchron (CNS) and the "supercontinent breakup effect," which resulted in the creation of the mid-Atlantic and Indian ocean ridges at the expense of subducting old ocean floor in the Tethys and the Pacific. We have used global oceanic paleo-age grids, including now subducted ocean floor and two alternative time scales, to test these hypotheses. Our models show that a high average seafloor spreading rate of 92 mm/a in the Early Cretaceous that decreased to 60 mm/a during the Tertiary, with peaks of 86 mm/a and 70 mm/a at 105 Ma and 75 Ma ago, respectively, correspond to the two observed sea-level highstands in the Cretaceous. Calculations using GTS2004 produce lower seafloor spreading rates during the same period and diminish the mid-Cretaceous spreading pulse. Global ridge lengths increased in the earliest Cretaceous but stayed relatively constant through time. However, we find that the average age of the ocean basins through time is only weakly dependent on the choice of time scale. The expansive mid- and Late Cretaceous epicontinental seas, coupled with warm climates and oxygen-poor water masses, were ultimately driven by the younger average age of the Cretaceous seafloor and faster seafloor spreading rather than a vast increase in mid-ocean ridge length due to the breakup of Pangea or solely by higher seafloor spreading rates, as suggested previously. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

The paper presents aspects of model-free learning control initialization. Model-free learning has several advantages as general purpose approach or adaptive capability. However, practical implementation is not intuitive in each step. Choice of time scale in order to provide the necessary reactivity or level of granularity of states or control actions is not an easy problem. Before it learns environment it may disturb process control in an unacceptable way. This is the motivation to find rules for easer initialization and controller set-up.

Diagnostic plots for departures from proportional hazards in cohort study data

We report the influence of the strength of heat bath coupling on the demixing behavior in spinodal decomposing one component liquid-vapor systems. The smoothed particle hydrodynamics (SPH) method with a van der Waals equation of state is used for the simulation. A thermostat for SPH is introduced that is based on the Berendsen thermostat. It controls the strength of heat bath coupling and allows for quenches with exponential temperature decay at a certain thermalization time scale. The present method allows us to bridge several orders of magnitude in the thermalization time scale. The early stage is highly affected by the choice of time scale. A transition from exponential growth to a 1/2 ordinary power law scaling in the characteristic lengths is observed. At high initial temperatures the growth is logarithmic. The comparison with pure thermal simulations reveals latent heat to raise the mean system temperature. Large thermalization time scales and thermal conductivity are figured out to affect a stagnation of heating, which is explained with convective processes. Furthermore, large thermalization time scales are responsible for a stagnation of growth of domains, which is temporally embedded between early and late stage of phase separation. Therefore, it is considered as an intermediate stage. We present an aspect concerning this stage, namely that choosing larger thermalization time scales increases the duration. Moreover, it is observed that diffuse interfaces are formed during this stage, provided that the stage is apparent. We show that the differences in the evolution between pure thermal simulations and simulations with an instantaneously scaled mean temperature can be explained by the thermalization process, since a variation of the time scale allows for the bridging between these cases of limit.

Typical applications of marginal structural time-to-event (e.g., Cox) models have used time on study as the time scale. Here, the authors illustrate use of time on treatment as an alternative time scale. In addition, a method is provided for estimating Kaplan-Meier-type survival curves for marginal structural models. For illustration, the authors estimate the total effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome (AIDS) or death in 1,498 US men and women infected with human immunodeficiency virus and followed for 6,556 person-years between 1995 and 2002; 323 incident cases of clinical AIDS and 59 deaths occurred. Of the remaining 1,116 participants, 77% were still under observation at the end of follow-up. By using time on study, the hazard ratio for AIDS or death comparing always with never using highly active antiretroviral therapy from the marginal structural model was 0.52 (95% confidence interval: 0.35, 0.76). By using time on treatment, the analogous hazard ratio was 0.44 (95% confidence interval: 0.32, 0.60). In time-to-event analyses, the choice of time scale may have a meaningful impact on estimates of association and precision. In the present example, use of time on treatment yielded a hazard ratio further from the null and more precise than use of time on study as the time scale.

The growing body of longitudinal research on multimorbidity (≥ 2 chronic conditions) has identified that multimorbidity progression in mid and late life is associated with change in other health domains (e.g., mobility limitations) and can have far-reaching effects on person-centered outcomes such as health-related quality of life. Several increasingly accessible quantitative methods can be applied to the longitudinal study of multimorbidity and related health outcomes, but there has been relatively little work describing and synthesizing the merits and limitations of methods available for this purpose. We will discuss the application and limitations of popular longitudinal methods that can be applied to the study of change in multimorbidity and associated health outcomes. We will consider overarching issues in the longitudinal study of multimorbidity including operationalizing multimorbidity, data-related concerns such as measurement invariance, and choice of time scale (i.e., change in age or calendar time). We will then cover methods aligned to four specific research objectives: 1) examining individual change in multimorbidity, 2) identifying population sub-groups that follow similar trajectories of multimorbidity progression, 3) understanding when, how, and why individuals/groups shift to more advanced stages of multimorbidity, and 4) examining the co-progression of multimorbidity with key health domains over time. This work will help establish a common language for assessing longitudinal changes in multimorbidity, inform research that can fill gaps in our knowledge regarding multimorbidity progression and critical periods of change, and support the identification of groups that experience divergent rates and etiological pathways of disease progression.

To the Editor: Vistisen and Faerch [1] make an interesting point regarding the choice of time scale used to fit trajectory models. The authors assert that time since diagnosis would be the appropriate time scale when studying the aetiology of diabetes development or prognosis of diabetes, and we agree that this would be preferred. However, there are some practical issues for defining the appropriate time point of reference relative to diagnosis of disease in a population-based study, such as ours [2]. Examining trajectories up to the time of diagnosis would be ideal. However, it is hard to know the exact timing of diagnosis, since the collection of fasting blood and assays for cardiometabolic biomarkers were completed only in 2009 and therefore we have no data on comparable measures prior to 2009, which would be necessary to establish time of diagnosis. Data from the China Health and Nutrition Survey (CHNS) suggest that in this population the majority of diabetes is undiagnosed (over 50%) [3], and therefore it will be less likely to influence weight trajectories. All that being said, we acknowledge that our method, using time since enrolment could, as the authors suggest, introduce errors that may bias results. This is a testable hypothesis that could be addressed through a simulation study to see what types of inferences one could make using a variety of different approaches to handle time. Indeed, we would welcome the idea of such a future study and are currently investigating related issues using simulation studies. Additionally, future studies involving CHNS data—at which point we will have multiple measurements of fasting blood and assays for cardiometabolic biomarkers—will allow us to additionally investigate this question further.