Statistical Artifacts in the Ratio of Discrete Quantities

Johnston, Roger G.; Schroder, Shayla D.; Mallawaaratchy, A. Rajika

doi:10.2307/2684202

Cited by 9 publications

(14 citation statements)

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“…The distribution of the raw ratios show high level of discreteness, and only a small number of values between 0 and 1 have non-zero probability, which is an artifact of dividing a small integer by another slightly larger integer (Johnson, Shayla et al, [10]). As a result, the frequencies of some values are very high (Figure 3.A).…”

Section: Resultsmentioning

confidence: 99%

“…In fact, the discreteness of the raw ratio distribution is largely a statistical artifact due to small λ s (Johnson, Shayla et al, [10]). Assuming that the total of the paired counts is fixed, then the ratio of one count, for example, tumor sample count, over the total count provides a more accurate estimate for the probability of being tumor if additional count(s) is obtained.…”

Section: Resultsmentioning

confidence: 99%

“…In fact, even if a closed form can be obtained, it is computationally expensive to apply the complex exact distribution to derive statistical inferences, due to its discrete and multi-modality nature, given the enormous size of sequencing data. On the other hand, as pointed out by Johnston, Shayla et al, [10], the discrete nature of the ratio of two random integers is in fact caused by some statistical artifacts, and is independent of the underlying distribution. Motivated by this observation, in this paper we propose a feasible solution to approximate the distribution of read count ratio, especially for NGS data analysis.…”

Section: Introductionmentioning

confidence: 99%

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Beta approximation of ratio distribution and its application to next generation sequencing read counts

Yang

Fang

2016

Journal of Applied Statistics

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Paired sequencing data are commonly collected in genomic studies to control biological variation. However, existing data processing strategies suffer at low coverage regions, which are unavoidable due to the limitation of current sequencing technology. Furthermore, information contained in the absolute values of the read counts is commonly ignored. We propose a read count ratio processing/modification method, to not only incorporate information contained in the absolute values of paired counts into one variable, but also mitigate the discrete artifact, especially when both counts are small. Simulation shows that the processed variable fits well with a Beta distribution, thus providing an easy tool for down-stream inference analysis.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Beta approximation of ratio distribution and its application to next generation sequencing read counts

Yang

Fang

2016

Journal of Applied Statistics

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“…Although the presence of irregular shapes and spikes in empirically occuring distributions of ratios of natural numbers was reported before as a statistical artifact8, the authors of this previous work failed to acknowledge the interesting mathematical structure of the underlying distributions. In this work we propose the study of those naturally occurring distributions of rational numbers as an interesting mathematical topic with important clinical and biological applications.…”

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confidence: 85%

Fractal-like Distributions over the Rational Numbers in High-throughput Biological and Clinical Data

Трифонов

Pasqualucci

Dalla‐Favera

et al. 2011

Sci Rep

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Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing (HTS), expression profiles, proteomics, and electronic health records (EHR) are some examples of such technologies. Extracting meaningful information from those technologies requires careful analysis of the large volumes of data they produce. In this note, we present a set of fractal-like distributions that commonly appear in the analysis of such data. The first set of examples are drawn from a HTS experiment. Here, the distributions appear as part of the evaluation of the error rate of the sequencing and the identification of tumorogenic genomic alterations. The other examples are obtained from risk factor evaluation and analysis of relative disease prevalence and co-mordbidity as these appear in EHR. The distributions are also relevant to identification of subclonal populations in tumors and the study of quasi-species and intrahost diversity of viral populations.

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“…2 demonstrates, the pdf described by equation (4) is dominated by fine structure when n is small. Some of the possible values of s 2 will rarely be observed despite the fact that both smaller and larger values may be common because there happen to be very few combinations that lead to them (a statistical artifact common to ratios of discrete quantities, see Johnston et al 1995). The pdf becomes smoother and more values of s 2 become possible as n increases, but the odds of s 2 being very much greater than its expected value, x (n -1)/n, remain small.…”

Section: Constraints On Sample Variancementioning

confidence: 99%

A Monte Carlo Evaluation of the Stock Synthesis Assessment Program

Sampson¹,

Yin²

1998

Fishery Stock Assessment Models

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Stock assessments for many U.S. Pacific coast groundfish stocks are developed using the catch at age method known as Stock Synthesis. The Stock Synthesis computer program attempts to reconstruct the demographic history of a stock from observed changes in fish age or size distributions, coupled with auxiliary information such as an index of stock biomass developed from a research survey or an index of fishing mortality based on fishing effort. In this study Monte Carlo simulation techniques were used to generate fishery and survey data with known characteristics. The simulated data were then analyzed with the age-structured version of the Stock Synthesis program and results from the program were compared with the true values to evaluate the influence of measurement errors on the accuracy of the Stock Synthesis results. Data sets were constructed with low and high levels of random error in each of four types of sample data (fishery age composition, a fishing effort index, survey age composition, and a survey index of stock biomass). A series of experiments, based on a fractional factorial design, was conducted to examine the importance of eight factors: low versus high rates of natural mortality; constant versus variable annual recruitment; low versus high rates of increase in fishing mortality; dome-shaped versus asymptotic fishery selectivity; short versus long data series; low versus high variability in the fishing effort index; low versus high variability in the survey biomass index; and small versus large samples for age composition. On average the Stock Synthesis estimates for total biomass, exploitable biomass, recruitment, and fishing mortality in the ending year were slightly positively biased (3.5-6.1%) but less variable than the input data. In general, the number of years in the data series and the size of the age samples were the most influential factors, with increased amounts of data producing less biased and less variable estimates.

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Statistical Artifacts in the Ratio of Discrete Quantities

Cited by 9 publications

References 0 publications

Beta approximation of ratio distribution and its application to next generation sequencing read counts

Beta approximation of ratio distribution and its application to next generation sequencing read counts

Fractal-like Distributions over the Rational Numbers in High-throughput Biological and Clinical Data

A Monte Carlo Evaluation of the Stock Synthesis Assessment Program

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