1,122 research outputs found
Shifting the Universe: Early Dark Energy and Standard Rulers
The presence of dark energy at high redshift influences both the cosmic sound
horizon and the distance to last scattering of the cosmic microwave background.
We demonstrate that through the degeneracy in their ratio, early dark energy
can lie hidden in the CMB temperature and polarization spectra, leading to an
unrecognized shift in the sound horizon. If the sound horizon is then used as a
standard ruler, as in baryon acoustic oscillations, then the derived
cosmological parameters can be nontrivially biased. Fitting for the absolute
ruler scale (just as supernovae must be fit for the absolute candle magnitude)
removes the bias but decreases the leverage of the BAO technique by a factor 2.Comment: 6 pages, 3 figure
Solvable K-essence Cosmologies and Modified Chaplygin Gas Unified Models of Dark Energy and Dark Matter
This paper is devoted to the investigation of modified Chaplygin gas model in
the context of solvable k-essence cosmologies. For this purpose, we construct
equations of state parameter of this model for some particular values of the
parameter . The graphical behavior of these equations are also discussed by
using power law form of potential. The relationship between k-essence and
modified Chaplygin gas model shows viable results in the dark energy scenario.
We conclude that the universe behaves as a cosmological constant, quintessence
phase or phantom phase depending upon .Comment: 14 pages, 6 figure
An Edgeworth expansion for finite population L-statistics
In this paper, we consider the one-term Edgeworth expansion for finite
population L-statistics. We provide an explicit formula for the Edgeworth
correction term and give sufficient conditions for the validity of the
expansion which are expressed in terms of the weight function that defines the
statistics and moment conditions.Comment: 14 pages. Minor revisions. Some explanatory comments and a numerical
example were added. Lith. Math. J. (to appear
Information measures and design issues in the study of mortality deceleration: findings for the gamma-Gompertz model
Mortality deceleration, or the slowing down of death rates at old ages, has been repeatedly investigated, but empirical studies of this phenomenon have produced mixed results. The scarcity of observations at the oldest ages complicates the statistical assessment of mortality deceleration, even in the parsimonious parametric framework of the gamma-Gompertz model considered here. The need for thorough verification of the ages at death can further limit the available data. As logistical constraints may only allow to validate survivors beyond a certain (high) age, samples may be restricted to a certain age range. If we can quantify the effects of the sample size and the age range on the assessment of mortality deceleration, we can make recommendations for study design. For that purpose, we propose applying the concept of the Fisher information and ideas from the theory of optimal design. We compute the Fisher information matrix in the gamma-Gompertz model, and derive information measures for comparing the performance of different study designs. We then discuss interpretations of these measures. The special case in which the frailty variance takes the value of zero and lies on the boundary of the parameter space is given particular attention. The changes in information related to varying sample sizes or age ranges are investigated for specific scenarios. The Fisher information also allows us to study the power of a likelihood ratio test to detect mortality deceleration depending on the study design. We illustrate these methods with a study of mortality among late nineteenth-century French-Canadian birth cohorts.Development and application of statistical models for medical scientific researc
A hybrid landmark Aalen-Johansen estimator for transition probabilities in partially non-Markov multi-state models
Multi-state models are increasingly being used to model complex
epidemiological and clinical outcomes over time. It is common to assume that
the models are Markov, but the assumption can often be unrealistic. The Markov
assumption is seldomly checked and violations can lead to biased estimation for
many parameters of interest. As argued by Datta and Satten (2001), the
Aalen-Johansen estimator of occupation probabilities is consistent also in the
non-Markov case. Putter and Spitoni (2018) exploit this fact to construct a
consistent estimator of state transition probabilities, the landmark
Aalen-Johansen estimator, which does not rely on the Markov assumption. A
disadvantage of landmarking is data reduction, leading to a loss of power. This
is problematic for less traveled transitions, and undesirable when such
transitions indeed exhibit Markov behaviour. Using a framework of partially
non-Markov multi-state models we suggest a hybrid landmark Aalen-Johansen
estimator for transition probabilities. The proposed estimator is a compromise
between regular Aalen-Johansen and landmark estimation, using transition
specific landmarking, and can drastically improve statistical power. The
methods are compared in a simulation study and in a real data application
modelling individual transitions between states of sick leave, disability,
education, work and unemployment. In the application, a birth cohort of 184951
Norwegian men are followed for 14 years from the year they turn 21, using data
from national registries
Dynamic predicting by landmarking as an alternative for multi-state modeling: an application to acute lymphoid leukemia data
This paper considers the problem of obtaining a dynamic prediction for 5-year failure free survival after bone marrow transplantation in ALL patients using data from the EBMT, the European Group for Blood and Marrow Transplantation. The paper compares the new landmark methodology as developed by the first author and the established multi-state modeling as described in a recent Tutorial in Biostatistics in Statistics in Medicine by the second author and colleagues. As expected the two approaches give similar results. The landmark methodology does not need complex modeling and leads to easy prediction rules. On the other hand, it does not give the insight in the biological processes as obtained for the multi-state model
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