An approach for jointly modeling multivariate longitudinal measurements and discrete time-to-event data

In many medical studies, patients are followed longitudinally and interest is on assessing the relationship between longitudinal measurements and time to an event. Recently, various authors have proposed joint modeling approaches for longitudinal and time-to-event data for a single longitudinal variable. These joint modeling approaches become intractable with even a few longitudinal variables. In this paper we propose a regression calibration approach for jointly modeling multiple longitudinal measurements and discrete time-to-event data. Ideally, a two-stage modeling approach could be applied in which the multiple longitudinal measurements are modeled in the first stage and the longitudinal model is related to the time-to-event data in the second stage. Biased parameter estimation due to informative dropout makes this direct two-stage modeling approach problematic. We propose a regression calibration approach which appropriately accounts for informative dropout. We approximate the conditional distribution of the multiple longitudinal measurements given the event time by modeling all pairwise combinations of the longitudinal measurements using a bivariate linear mixed model which conditions on the event time. Complete data are then simulated based on estimates from these pairwise conditional models, and regression calibration is used to estimate the relationship between longitudinal data and time-to-event data using the complete data. We show that this approach performs well in estimating the relationship between multivariate longitudinal measurements and the time-to-event data and in estimating the parameters of the multiple longitudinal process subject to informative dropout. We illustrate this methodology with simulations and with an analysis of primary biliary cirrhosis (PBC) data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS339 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Future Gamma-Ray Imaging of Solar Eruptive Events

Solar eruptive events, the combination of large solar flares and coronal mass ejections (CMEs), accelerate ions to tens of Gev and electrons to hundreds of MeV. The energy in accelerated particles can be a significant fraction (up to tens of percent) of the released energy and is roughly equipartitioned between ions and electrons. Observations of the gamma-ray signatures produced by these particles interacting with the ambient solar atmosphere probes the distribution and composition of the accelerated population, as well as the atmospheric parameters and abundances of the atmosphere, ultimately revealing information about the underlying physics. Gamma-ray imaging provided by RHESSI showed that the interacting approx.20 MeV/nucleon ions are confined to flare magnetic loops rather than precipitating from a large CME-associated shock. Furthermore, RHESSI images show a surprising, significant spatial separation between the locations where accelerated ions and electrons are interacting, thus indicating a difference in acceleration or transport processes for the two types of particles. Future gamma-ray imaging observations, with higher sensitivity and greater angular resolution, can investigate more deeply the nature of ion acceleration. The technologies being proven on the Gamma-Ray Imager/Polarimeter for Solar flares (GRIPS), a NASA balloon instrument, are possible approaches for future instrumentation. We discuss the GRIPS instrument and the future of studying this aspect of solar eruptive events

Temporal Variability of Ion Acceleration and Abundances in Solar Flares

Solar flares accelerate both ions and electrons to high energies, and their X-ray and gamma-ray signatures not only probe the relationship between their respective acceleration, but also allow for the measurement of accelerated and ambient abundances. RHESSI observations have shown a striking close linear correlation of gamma-ray line fluence from accelerated ions greater than approximately 20 MeV and bremsstrahlung emission from relativistic accelerated electrons greater than 300 keV, when integrated over complete flares, suggesting a common acceleration mechanism. SMM/GRS observations, however, show a weaker correlation, and this discrepancy might be associated with previously observed electron-rich episodes within flares and/or temporal variability of gamma-ray line fluxes over the course of flares. We use the latest RHESSI gamma-ray analysis techniques to study the temporal behavior of the RHESSI flares, and determine what changes can be attributed to an evolving acceleration mechanism or to evolving abundances. We also discuss possible explanations for changing abundances

Solar Flares

Solar flares accelerate both ions and electrons to high energies, and their X-ray and gamma-ray signatures not only probe the relationship between their respective acceleration, but also allow for the measurement of accelerated and ambient abundances. RHESSI observations have shown a striking close linear correlation of gamma-ray line fluence from accelerated ions > approx.20 MeV and bremsstrahlung emission from relativistic accelerated electrons >300 keV, when integrated over complete flares, suggesting a common acceleration mechanism. SMM/GRS observations, however, show a weaker correlation, and this discrepancy might be associated with previously observed electron-rich episodes within flares and/or temporal variability of gamma-ray line fluxes over the course of flares. We use the latest RHESSI gamma-ray analysis techniques to study the temporal behavior of the RHESSI flares, and determine what changes can be attributed to an evolving acceleration mechanism or to evolving abundances

Temporal Variability of Ion Acceleration and Abundances in Solar Flares

solar flares accelerate both ions and electrons to high energies, and their x-ray and gamma-ray signatures not only probe the relationship between their respective acceleration, but also allow for the measurement of accelerated and ambient abundances. RHESSI observations have shown a striking close linear correlation of gamma-ray line fluence from accelerated ions > approx 20 MeV and bremsstrahlung emission from relativistic accelerated electrons >300 kev, when integrated over complete flares, suggesting a common acceleration mechanism. SMM/GRS observations, however, show a weaker correlation, and this discrepancy might be associated with previously observed electron-rich episodes within flares and/or temporal variability of gamma-ray line fluxes over the course of flares. We use the latest RHESSI gamma-ray analysis techniques to study the temporal behavior of the RHESSI flares, and determine what changes can be attributed to an evolving acceleration mechanism or to evolving abundances. We also discuss possible explanations for changing abundances

Preface

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On Estimating the Relationship between Longitudinal Measurements and Time-to-Event Data Using a Simple Two-Stage Procedure

Ye et al. (2008) proposed a joint model for longitudinal measurements and time-to-event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two-stage regression calibration approach which is simpler to implement than a joint mod-eling approach. In the first stage of their approach, the mixed model is fit without regard to the time-to-event data. In the second stage, the posterior expectation of an individual’s random effects from the mixed-model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach which can be applied for both discrete and continuous time-to-event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008). In agreement with the methodology proposed by Ye et al., an advantage of our proposed approach over joint mod-eling is that it can be implemented with standard statistical software and does not require complex estimation techniques.

Form measurements of micro-holes

The form measurement and gauge repeatability and reproducibility (R&R) of a micro-hole using a coordinate measurement machine (CMM) with a combination of optical and contact sensors were conducted in this study. The micro-holes, about 160 µm in diameter and 0.9 mm in depth, were fabricated using the electrical discharge machining process for diesel fuel injectors. The shape and size of micro-holes are important for the desired spray pattern, fuel economy and exhaust emission of diesel engines. In this study, the setup of the measurement machine and the procedure to determine the contact points are presented. Five form characteristics, the cylindricity, diameter, roundness, straightness and taper, of the micro-hole are analyzed from measurement points. The gauge R&R test is conducted to determine the micro-hole form measurement capability and to calculate the tolerance specifications for each characteristic that the CMM is capable of measuring. An example to quantify the change in the shape of the micro-holes before and after the abrasive flow machining is presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58130/2/mst7_11_045.pd

Batalin-Vilkovisky Integrals in Finite Dimensions

The Batalin-Vilkovisky method (BV) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangian system with symmetries. Localization (illustrated in terms of Duistermaat-Heckman localization) as well as anomalous symmetries are discussed in the framework of BV.Comment: 35 page