6,161 research outputs found
Revisiting nested group testing procedures: new results, comparisons, and robustness
Group testing has its origin in the identification of syphilis in the US army
during World War II. Much of the theoretical framework of group testing was
developed starting in the late 1950s, with continued work into the 1990s.
Recently, with the advent of new laboratory and genetic technologies, there has
been an increasing interest in group testing designs for cost saving purposes.
In this paper, we compare different nested designs, including Dorfman, Sterrett
and an optimal nested procedure obtained through dynamic programming. To
elucidate these comparisons, we develop closed-form expressions for the optimal
Sterrett procedure and provide a concise review of the prior literature for
other commonly used procedures. We consider designs where the prevalence of
disease is known as well as investigate the robustness of these procedures when
it is incorrectly assumed. This article provides a technical presentation that
will be of interest to researchers as well as from a pedagogical perspective.
Supplementary material for this article is available online.Comment: Submitted for publication on May 3, 2016. Revised versio
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
Marginal analysis of longitudinal count data in long sequences: Methods and applications to a driving study
Most of the available methods for longitudinal data analysis are designed and
validated for the situation where the number of subjects is large and the
number of observations per subject is relatively small. Motivated by the
Naturalistic Teenage Driving Study (NTDS), which represents the exact opposite
situation, we examine standard and propose new methodology for marginal
analysis of longitudinal count data in a small number of very long sequences.
We consider standard methods based on generalized estimating equations, under
working independence or an appropriate correlation structure, and find them
unsatisfactory for dealing with time-dependent covariates when the counts are
low. For this situation, we explore a within-cluster resampling (WCR) approach
that involves repeated analyses of random subsamples with a final analysis that
synthesizes results across subsamples. This leads to a novel WCR method which
operates on separated blocks within subjects and which performs better than all
of the previously considered methods. The methods are applied to the NTDS data
and evaluated in simulation experiments mimicking the NTDS.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS507 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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.
Symmetric Rotating Wave Approximation for the Generalized Single-Mode Spin-Boson System
The single-mode spin-boson model exhibits behavior not included in the
rotating wave approximation (RWA) in the ultra and deep-strong coupling
regimes, where counter-rotating contributions become important. We introduce a
symmetric rotating wave approximation that treats rotating and counter-rotating
terms equally, preserves the invariances of the Hamiltonian with respect to its
parameters, and reproduces several qualitative features of the spin-boson
spectrum not present in the original rotating wave approximation both
off-resonance and at deep strong coupling. The symmetric rotating wave
approximation allows for the treatment of certain ultra and deep-strong
coupling regimes with similar accuracy and mathematical simplicity as does the
RWA in the weak coupling regime. Additionally, we symmetrize the generalized
form of the rotating wave approximation to obtain the same qualitative
correspondence with the addition of improved quantitative agreement with the
exact numerical results. The method is readily extended to higher accuracy if
needed. Finally, we introduce the two-photon parity operator for the two-photon
Rabi Hamiltonian and obtain its generalized symmetric rotating wave
approximation. The existence of this operator reveals a parity symmetry similar
to that in the Rabi Hamiltonian as well as another symmetry that is unique to
the two-photon case, providing insight into the mathematical structure of the
two-photon spectrum, significantly simplifying the numerics, and revealing some
interesting dynamical properties.Comment: 11 pages, 5 figure
Manual of Water Quality Models for Virginia Estuaries
It is not the purpose of this manual to make a nonmodeler able to develop a model by reading through it, since no manual of this nature can accomplish such a task. This manual is intended to increase the planner or manager\u27s options by acquainting him with various types of models and informing him of the availability of currently working models. This manual contains the following: 1. A scheme indicating the types of water quality models which could be constructed, i.e. an overview of choices in models. 2. A brief description of each type of models developed under the Cooperative State ~gencies program. 3. A list of empirical formulas or values for the rate constants used in the models. 4. A directory of water quality models which have been applied to Virginia estuaries
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