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A novel generalized normal distribution for human longevity and other negatively skewed data.

ABSTRACT: Negatively skewed data arise occasionally in statistical practice; perhaps the most familiar example is the distribution of human longevity. Although other generalizations of the normal distribution exist, we demonstrate a new alternative that apparently fits human longevity data better. We propose an alternative approach of a normal distribution whose scale parameter is conditioned on attained age. This approach is consistent with previous findings that longevity conditioned on survival to the modal age behaves like a normal distribution. We derive such a distribution and demonstrate its accuracy in modeling human longevity data from life tables. The new distribution is characterized by 1. An intuitively straightforward genesis; 2. Closed forms for the pdf, cdf, mode, quantile, and hazard functions; and 3. Accessibility to non-statisticians, based on its close relationship to the normal distribution.

SUBMITTER: Robertson HT

PROVIDER: S-EPMC3356396 | biostudies-other | 2012

REPOSITORIES: biostudies-other

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A novel generalized normal distribution for human longevity and other negatively skewed data.

Robertson Henry T HT Allison David B DB

PloS one 20120518 5

Negatively skewed data arise occasionally in statistical practice; perhaps the most familiar example is the distribution of human longevity. Although other generalizations of the normal distribution exist, we demonstrate a new alternative that apparently fits human longevity data better. We propose an alternative approach of a normal distribution whose scale parameter is conditioned on attained age. This approach is consistent with previous findings that longevity conditioned on survival to the ...[more]

PMID: 22623974

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Project description:Genome-wide analysis of gene expression or protein binding patterns using different array or sequencing based technologies is now routinely performed to compare different populations, such as treatment and reference groups. It is often necessary to normalize the data obtained to remove technical variation introduced in the course of conducting experimental work, but standard normalization techniques are not capable of eliminating technical bias in cases where the distribution of the truly altered variables is skewed, i.e. when a large fraction of the variables are either positively or negatively affected by the treatment. However, several experiments are likely to generate such skewed distributions, including ChIP-chip experiments for the study of chromatin, gene expression experiments for the study of apoptosis, and SNP-studies of copy number variation in normal and tumour tissues. A preliminary study using spike-in array data established that the capacity of an experiment to identify altered variables and generate unbiased estimates of the fold change decreases as the fraction of altered variables and the skewness increases. We propose the following work-flow for analyzing high-dimensional experiments with regions of altered variables: (1) Pre-process raw data using one of the standard normalization techniques. (2) Investigate if the distribution of the altered variables is skewed. (3) If the distribution is not believed to be skewed, no additional normalization is needed. Otherwise, re-normalize the data using a novel HMM-assisted normalization procedure. (4) Perform downstream analysis. Here, ChIP-chip data and simulated data were used to evaluate the performance of the work-flow. It was found that skewed distributions can be detected by using the novel DSE-test (Detection of Skewed Experiments). Furthermore, applying the HMM-assisted normalization to experiments where the distribution of the truly altered variables is skewed results in considerably higher sensitivity and lower bias than can be attained using standard and invariant normalization methods.

Project description:BackgroundInfant morbidity is a topic of interest because it is used globally as an indicator of the status of health care in a country. A large body of evidence supports an association between bacterial vaginosis (BV) and infant morbidity. When estimating the relationship between the predictors and the estimated variable of morbidity severity, the latter exhibits imbalanced data, which means that violation of symmetry is expected. Two competing methods of analysis, that is, (1) probit and (2) logit techniques, can be considered in this context and have been applied to model such outcomes. However, these models may yield inconsistent results. While non-normal modeling approaches have been embraced in the recent past, the skewed logit model has been given little attention. In this study, we exemplify its usefulness in analyzing imbalanced longitudinal responses data.MethodologyWhile numerous non-normal methods for modeling binomial responses are well established, there is a need for comparison studies to assess their usefulness in different scenarios, especially under a longitudinal setting. This is addressed in this study. We use a dataset from Kenya about infants born to human immunodeficiency virus (HIV) positive mothers, who are also screened for BV. We aimed to investigate the effect of BV on infant morbidity across time. We derived a score for morbidity incidences depending on illnesses reported during the month of reference. By adjusting for the mother's BV status, the child's HIV status, sex, feeding status, and weight for age, we estimated the standard binary logit and skewed logit models, both using Generalized Estimating Equations.ResultsResults show that accounting for skewness in imbalanced binary data can show associations between variables in line with expectations documented by the literature. In addition, an in-depth analysis accounting for skewness has shown that, over time, maternal BV is associated with multiple health conditions in infants.InterpretationMaternal BV status was positively associated with infant morbidity incidences, which highlights the need for early intervention in cases of HIV-infected pregnant women.

Dataset Information

A novel generalized normal distribution for human longevity and other negatively skewed data.

Publications

A novel generalized normal distribution for human longevity and other negatively skewed data.

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