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

A Study on Correlations Between the Initial Optical and Scintillation Properties and Their Radiation Damage for Lead Tungstate Crystals

This paper presents a study of correlations between the initial optical and scintillation properties and their radiation damage for mass produced lead tungstate crystals. A correlation was observed between crystal's initial light outputs and the values of its initial longitudinal transmittance at 360 nm. A strong correlation was found between the emission weighted radiation induced absorption coefficients and the relative losses of the longitudinal transmittance at 440 nm. Correlations were also observed between the relative losses of crystal's light output and the relative losses of its longitudinal transmittance at 440 nm, or the emission weighted radiation induced absorption coefficients. No correlations were observed between crystal's radiation hardness and its initial longitudinal transmittance or the slope of the initial longitudinal transmittance across the band edge

Phase locking of coupled lasers with many longitudinal modes

Detailed experimental and theoretical investigations on two coupled fiber lasers, each with many longitudinal modes, reveal that the behavior of the longitudinal modes depends on both the coupling strength as well as the detuning between them. For low to moderate coupling strength only longitudinal modes which are common for both lasers phase-lock while those that are not common gradually disappear. For larger coupling strengths, the longitudinal modes that are not common reappear and phase-lock. When the coupling strength approaches unity the coupled lasers behave as a single long cavity with correspondingly denser longitudinal modes. Finally, we show that the gradual increase in phase-locking as a function of the coupling strength results from competition between phase-locked and non phase-locked longitudinal modes.Comment: 3 pages, 4 figures, submitted to opt. let

Excited states of the quasi-one-dimensional hexagonal quantum antiferromagnets

We investigate the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compare our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreement after the higher-order contributions are included in our calculations.Comment: 7 pages, 5 figure