Dataset Information

A REFERENCE-INVARIANT HEALTH DISPARITY INDEX BASED ON RENYI DIVERGENCE.

ABSTRACT: One of four overarching goals of Healthy People 2020 (HP2020) is to achieve health equity, eliminate disparities, and improve the health of all groups. In health disparity indices (HDIs) such as the mean log deviation (MLD) and Theil index (TI), disparities are relative to the population average, whereas in the index of disparity (IDisp) the reference is the group with the least adverse health outcome. Although the latter may be preferable, identification of a reference group can be affected by statistical reliability. To address this issue, we propose a new HDI, the Rényi index (RI), which is reference-invariant. When standardized, the RI extends the Atkinson index, where a disparity aversion parameter can incorporate societal values associated with health equity. In addition, both the MLD and TI are limiting cases of the RI. Also, a symmetrized Rényi index (SRI) can be constructed, resulting in a symmetric measure in the two distributions whose relative entropy is being evaluated. We discuss alternative symmetric and reference-invariant HDIs derived from the generalized entropy (GE) class and the Bregman divergence, and argue that the SRI is more robust than its GE-based counterpart to small changes in the distribution of the adverse health outcome. We evaluate the design-based standard errors and bootstrapped sampling distributions for the SRI, and illustrate the proposed methodology using data from the National Health and Nutrition Examination Survey (NHANES) on the 2001-04 prevalence of moderate or severe periodontitis among adults aged 45-74, which tracks Oral Health objective OH-5 in HP2020. Such data, which uses a binary individual-level outcome variable, are typical of HP2020 data.

SUBMITTER: Talih M

PROVIDER: S-EPMC4643429 | biostudies-literature | 2013

REPOSITORIES: biostudies-literature

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A REFERENCE-INVARIANT HEALTH DISPARITY INDEX BASED ON RÉNYI DIVERGENCE.

Talih Makram M

The annals of applied statistics 20131209 2

One of four overarching goals of Healthy People 2020 (HP2020) is to achieve health equity, eliminate disparities, and improve the health of all groups. In health disparity indices (HDIs) such as the mean log deviation (MLD) and Theil index (TI), disparities are relative to the population average, whereas in the index of disparity (IDisp) the reference is the group with the least adverse health outcome. Although the latter may be preferable, identification of a reference group can be affected by ...[more]

PMID: 26568778

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Project description:Parallels between phylogeny and ontogeny have been discussed since almost two centuries and a number of theories have been proposed to explain such patterns. Especially elusive is the so-called phylotypic stage, a phase during development where species within a phylum are particularly similar to each other. While this has formerly been interpreted as a recapitulation of phylogeny, it is nowadays thought to reflect an ontogenetic progression phase, where strong constraints on developmental regulation and gene interactions exist. Several studies have shown that genes expressed during this stage evolve slower, but it has so far not been possible to derive an unequivocal molecular signature associated with this stage. We use here a combination of phylostratigraphy and stage specific gene expression data to generate a cumulative index that reflects the evolutionary age of the transcriptome at given ontogenetic stages. Using zebrafish ontogeny and adult development as a model, we find that the phylotypic stage does indeed express the oldest transcriptome set and that younger sets are expressed during early and late development, thus faithfully mirroring the hourglass model of morphological divergence. Reproductively active animals show the youngest transcriptome, with major differences between males and females. Intriguingly, aging animals express also increasingly older genes. Comparisons with similar datasets from flies and nematodes show that this pattern occurs across phyla. Our results suggest that an old transcriptome marks the phylotypic phase and that phylogenetic differences at other ontogenetic stages correlate with the expression of newly evolved genes. Zebrafish (Danio rerio) were kept in 12L flow-through tanks at 26.5 °C (around 60 animals per tank). For accurate staging, fertilized eggs were collected within 15 min intervalls and incubated in Petri dishes at 28.5°C with water changes every 2-6 hours. After hatching, larvae were transferred to 1 liter tanks and kept at 28.5 °C. We took 72 samples in at least two biological replicates (147 experiments in total) that correspond to 61 stages across zebrafish ontogeny (50 stages before the sex could be clearly recognized plus 11 adult stages of males and females each). Staging was done according to post-fertilization time. Embryos were additionally staged under the dissecting microscope to check for the consistency of post-fertilization timing and morphological development at standard temperature (28.5 °C). Only healthy animals that showed the expected morphological features for a given post-fertilization time were sampled. Each sample contained around 50 individuals until the 1 day and 3 hour embryo stage, 15 individuals until the 10 day larval stage, 10 individuals until the 18 day larval stage, 5 individuals until the 45 days juvenile stage, while in later juvenile and adult stages we sampled males and females separately and each sample contained 2 individuals. All samples were snap frozen in liquid nitrogen and stored at -80 °C until RNA extraction. To avoid severe biases due to the excess of unfertilized eggs we squeezed eggs from adult females before freezing them in liquid nitrogen.

Dataset Information

A REFERENCE-INVARIANT HEALTH DISPARITY INDEX BASED ON RENYI DIVERGENCE.

Publications

A REFERENCE-INVARIANT HEALTH DISPARITY INDEX BASED ON RÉNYI DIVERGENCE.

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