Mean and variance of ratios of proportions from categories of a multinomial distribution

Ďuriš, František; Gazdarica, Juraj; Gazdaricova, Iveta; Striešková, Lucia; Budiš, Jaroslav; Turña, Ján; Szemes, Tomáš

doi:10.1186/s40488-018-0083-x

Cited by 14 publications

(9 citation statements)

References 31 publications

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“…We will confine ourselves to a first-order Taylor expansion around (µ v , µ w ) to make the analytic derivation of the approximation of Var[θ k ] feasible. The same observation has been made by [25,12] and [26, p. 351] to approximate the variance for a ratio random variable. We obtain:…”

Section: A Appendix: Proofssupporting

confidence: 60%

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DEvIANT: Discovering Significant Exceptional (Dis-)Agreement Within Groups

Belfodil

Duivesteijn

Plantevit

et al. 2020

Machine Learning and Knowledge Discovery in Databases

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We strive to find contexts (i.e., subgroups of entities) under which exceptional (dis-)agreement occurs among a group of individuals, in any type of data featuring individuals (e.g., parliamentarians, customers) performing observable actions (e.g., votes, ratings) on entities (e.g., legislative procedures, movies). To this end, we introduce the problem of discovering statistically significant exceptional contextual intra-group agreement patterns. To handle the sparsity inherent to voting and rating data, we use Krippendorff's Alpha measure for assessing the agreement among individuals. We devise a branch-and-bound algorithm, named DEvIANT, to discover such patterns. DEvIANT exploits both closure operators and tight optimistic estimates. We derive analytic approximations for the confidence intervals (CIs) associated with patterns for a computationally efficient significance assessment. We prove that these approximate CIs are nested along specialization of patterns. This allows to incorporate pruning properties in DEvIANT to quickly discard non-significant patterns. Empirical study on several datasets demonstrates the efficiency and the usefulness of DEvIANT.

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Section: A Appendix: Proofssupporting

confidence: 60%

“…An elegant way to deal with a ratio of two random variables is to approximate its moments using the Taylor series following the line of reasoning of [12] and [26, p.351], since no easy analytic expression of E[θ k ] and Var[θ k ] can be derived.…”

Section: Exceptional Contexts: Evaluation and Pruningmentioning

confidence: 99%

DEvIANT: Discovering Significant Exceptional (Dis-)Agreement Within Groups

Belfodil

Duivesteijn

Plantevit

et al. 2020

Machine Learning and Knowledge Discovery in Databases

View full text Add to dashboard Cite

show abstract

“…Count based methods of FF determination calculate disproportion of number of reads mapped to chromosomes that differ in mother and fetus genotypes. Although they are quite reliable, they can be used only on samples with male (XX vs. XY genotype) [12] or trisomic (2 copies vs. 3 copies of an aberrant chromosome) fetuses [13,14]. In pregnancy with a healthy female fetus, the FF have to be estimated by alternative methods.…”

Section: Introductionmentioning

confidence: 99%

Combination of Fetal Fraction Estimators Based on Fragment Lengths and Fragment Counts in Non-Invasive Prenatal Testing

Gazdarica

Hekel

Budiš

et al. 2019

IJMS

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The reliability of non-invasive prenatal testing is highly dependent on accurate estimation of fetal fraction. Several methods have been proposed up to date, utilizing different attributes of analyzed genomic material, for example length and genomic location of sequenced DNA fragments. These two sources of information are relatively unrelated, but so far, there have been no published attempts to combine them to get an improved predictor. We collected 2454 single euploid male fetus samples from women undergoing NIPT testing. Fetal fractions were calculated using several proposed predictors and the state-of-the-art SeqFF method. Predictions were compared with the reference Y-based method. We demonstrate that prediction based on length of sequenced DNA fragments may achieve nearly the same precision as the state-of-the-art methods based on their genomic locations. We also show that combination of several sample attributes leads to a predictor that has superior prediction accuracy over any single approach. Finally, appropriate weighting of samples in the training process may achieve higher accuracy for samples with low fetal fraction and so allow more reliability for subsequent testing for genomic aberrations. We propose several improvements in fetal fraction estimation with a special focus on the samples most prone to wrong conclusion.

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“…With p=(p1,p2,…,p22), q1=p·u, and q2=normalp·normalv, ref. [22] showed that for sufficiently large n the following approximations of mean and standard deviation of Y holds μADA(Y)≈q1q2+q1q22n σADA(Y)≈1n(q1q2)2(1q1+1q2) where n is the total autosomal read count of a given sample (more robust approximations can be found in the paper). Observe that while the numbers q1 and …”

Section: Methodsmentioning

confidence: 99%

Adaptable Model Parameters in Non-Invasive Prenatal Testing Lead to More Stable Predictions

Gazdarica

Budiš

Ďuriš

et al. 2019

IJMS

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Recent advances in massively parallel shotgun sequencing opened up new options for affordable non-invasive prenatal testing (NIPT) for fetus aneuploidy from DNA material extracted from maternal plasma. Tests typically compare chromosomal distributions of a tested sample with a control set of healthy samples with unaffected fetuses. Deviations above certain threshold levels are concluded as positive findings. The main problem with this approach is that the variance of the control set is dependent on the number of sequenced fragments. The higher the amount, the more precise the estimation of actual chromosomal proportions is. Testing a sample with a highly different number of sequenced reads as used in training may thus lead to over- or under-estimation of their variance, and so lead to false predictions. We propose the calculation of a variance for each tested sample adaptively, based on the actual number of its sequenced fragments. We demonstrate how it leads to more stable predictions, mainly in real-world diagnostics with the highly divergent inter-sample coverage.

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Mean and variance of ratios of proportions from categories of a multinomial distribution

Cited by 14 publications

References 31 publications

DEvIANT: Discovering Significant Exceptional (Dis-)Agreement Within Groups

DEvIANT: Discovering Significant Exceptional (Dis-)Agreement Within Groups

Combination of Fetal Fraction Estimators Based on Fragment Lengths and Fragment Counts in Non-Invasive Prenatal Testing

Adaptable Model Parameters in Non-Invasive Prenatal Testing Lead to More Stable Predictions

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