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Register a new userThe survival-incorporated median versus the median in the survivors or in the always-survivors: What are we measuring? And why?
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Added by
Qingyan Xiang
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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No Arabic abstract
Many clinical studies evaluate the benefit of treatment based on both survival and other ordinal/continuous clinical outcomes, such as neurocognitive scores or quality-of-life scores. In these studies, there are situations when the clinical outcomes are truncated by death, where subjects die before their clinical outcome is measured. Treating outcomes as missing or censored due to death can be misleading for treatment effect evaluation. We show that if we use the median in the survivors or in the always-survivors to summarize clinical outcomes, we may conclude a trade-off exists between the probability of survival and good clinical outcomes, even in settings where both the probability of survival and the probability of any good clinical outcome are better for one treatment. Therefore, we advocate not always treating death as a mechanism through which clinical outcomes are missing, but rather as part of the outcome measure. To account for the survival status, we describe the survival-incorporated median as an alternative summary measure for outcomes in the presence of death. The survival-incorporated median is the threshold such that 50% of the population is alive with an outcome above that threshold. We use conceptual examples to show that the survival-incorporated median provides a simple and useful summary measure to inform clinical practice.
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We present a cautionary study exploring the reliability of the H-delta line in the integrated spectra of galaxies for determining galaxy ages. Our database consists of the observed integrated spectra of ~120 early-type galaxies, of 7 metal-rich globular clusters in M31 and the Galactic globular cluster 47 Tuc, and of the open cluster M67. We have measured H-delta using index definitions designed to assess contamination from the CN molecule in and around H-delta by choosing combinations of bandpasses that both avoid and include a region of CN molecular lines redward of H-delta. We find systematic differences in the ages derived from H-delta measurements among the various definitions when extracting ages from H-delta in old stellar populations with enhanced CN bands due to non-solar abundance ratios. We propose that neighboring CN lines have a strong effect on pseudocontinuum and central bandpass levels. For stellar populations which have non-solar abundance ratios in C and/or N, population synthesis models that do not account for abundance ratio variations cannot reproduce accurately the CN 4216 AA band, which leads to a corresponding inaccuracy in reproducing the various H-delta indices. Hence, caution must be used when extracting galaxy ages from the H-delta line in old stellar populations with significant non-solar abundance ratios.
Statistical and computational methods are widely used in todays scientific studies. Using a female fertility potential in childhood cancer survivors as an example, we illustrate how these methods can be used to extract insight regarding biological processes from noisy observational data in order to inform decision making. We start by contextualizing the computational methods with the working example: the modelling of acute ovarian failure risk in female childhood cancer survivors to quantify the risk of permanent ovarian failure due to exposure to lifesaving but nonetheless toxic cancer treatments. This is followed by a description of the general framework of classification problems. We provide an overview of the modelling algorithms employed in our example, including one classic model (logistic regression) and two popular modern learning methods (random forest and support vector machines). Using the working example, we show the general steps of data preparation for modelling, variable selection steps for the classic model, and how model performance might be improved utilizing visualization tools. We end with a note on the importance of model evaluation.
In this paper we compare the performances of the chi-square and median likelihood analysis in the determination of cosmological constraints using type Ia supernovae data. We perform a statistical analysis using the 307 supernovae of the Union 2 compilation of the Supernova Cosmology Project and find that the chi-square statistical analysis yields tighter cosmological constraints than the median statistic if only supernovae data is taken into account. We also show that when additional measurements from the Cosmic Microwave Background and Baryonic Acoustic Oscillations are considered, the combined cosmological constraints are not strongly dependent on whether one applies the chi-square statistic or the median statistic to the supernovae data. This indicates that, when complementary information from other cosmological probes is taken into account, the performances of the chi-square and median statistics are very similar, demonstrating the robustness of the statistical analysis.
The Oja median is one of several extensions of the univariate median to the multivariate case. It has many nice properties, but is computationally demanding. In this paper, we first review the properties of the Oja median and compare it to other multivariate medians. Afterwards we discuss four algorithms to compute the Oja median, which are implemented in our R-package OjaNP. Besides these algorithms, the package contains also functions to compute Oja signs, Oja signed ranks, Oja ranks, and the related scatter concepts. To illustrate their use, the corresponding multivariate one- and $C$-sample location tests are implemented.
We show that symmetric spaces and thick affine buildings which are not of spherical type $A_1^r$ have no coarse median in the sense of Bowditch. As a consequence, they are not quasi-isometric to a CAT(0) cube complex, answering a question of Haglund. Another consequence is that any lattice in a simple higher rank group over a local field is not coarse median.
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