Sensitivity analysis of longitudinal count responses: a local influence approach and application to medical data

Tapia, Alejandra; Giampaoli, Viviana; Díaz, María del Pilar; Leiva, Víctor

doi:10.1080/02664763.2018.1531978

Cited by 7 publications

(7 citation statements)

References 41 publications

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“…Further investigation to be continued from the present study is related to asymptotic estimation, Bayesian and shape methods, as well as mixture models. [31][32][33] Also, calculation of sample sizes for the new distribution 34 as well as count spatial/temporal regressions, partial least squares structures, and their diagnostics 3,[35][36][37][38][39] are relevant. A multivariate r-hypergeometric distribution is of interest as well considering the following ideas.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

“…(M − 1)! ( N − M n − x ) Note that E((Y + 1) 3 ) = E(Y 3 ) + 3𝜇 Y E(Y 2 ) + 3𝜇 2 Y E(Y ) + 𝜇 3 Y , E((Y + 1) 3 ) = E(Y 3 ) + 3𝜇 Y (𝜎 2 Y + 𝜇 2 Y ) + 3𝜇 3 Y + 𝜇 3 Y , and E((Y + 1) 3 ) = E(Y 3 ) + 3𝜇 Y 𝜎 2 Y + 7𝜇 3 Y .As Y is an r-hypergeometric distributed random variable, its mean and variance are stated and so we getE(Y 3 ) = (n − 1)(M + 1) N + E(Y 3), 𝜇 Y and 𝜎 2 Y , the expression E((Y + 1)3 ) can be calculated and based on it, we may get…”

mentioning

confidence: 93%

“…Diverse phenomena in nature can be modeled by discrete statistical distributions 1,2 . Such distributions may be classified as count models for finite and infinite ranges 3 . One of the most popular and oldest finite‐range discrete distributions is the binomial model, which is used when the following conditions are met: (i) the trials have only two possible outcomes (success or failure), and (ii) the sample must be random and selected from an infinite population so that the probability of success is constant through the trials.…”

Section: Introductionmentioning

confidence: 99%

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The r‐hypergeometric distribution: Characterization, mathematical methods, simulations, and applications in sciences and engineering

Díaz‐Rodríguez

Leiva

Martín-Barreiro

et al. 2022

Math Methods in App Sciences

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In this article, we introduce a novel univariate discrete distribution called the r‐hypergeometric model. This distribution has the sampling characteristics with replacement of the binomial distribution and no‐order sampling of the hypergeometric distribution. Mathematical expressions are obtained for computing probabilities, the mode, and moments of the new distribution. Two simulation algorithms are proposed using the acceptance‐rejection and inverse‐transform methods and computational features to generate values of an r‐hypergeometric distributed random variable. Python and R codes are implemented to perform computational experiments. Applications of mathematical methods based on the new distribution in sciences and engineering employing simulated and real‐world data sets are provided. A comparison with existing distributions is also included. In addition to the mathematical results, some findings obtained from our study are related to a better computational performance of the inverse‐transform method. Also, we identify applications of our model that are not covered by the traditional count distributions. In addition, we establish distinct probabilities for the same event under the binomial, hypergeometric, and r‐hypergeometric distributions, with their means also being distinct, but their variances, skewness, and kurtosis converge to the same value.

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Section: Conclusion and Future Researchmentioning

confidence: 99%

mentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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The r‐hypergeometric distribution: Characterization, mathematical methods, simulations, and applications in sciences and engineering

Díaz‐Rodríguez

Leiva

Martín-Barreiro

et al. 2022

Math Methods in App Sciences

Self Cite

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“…The second one corresponds to local influence diagnostics that allows us to identify cases that, under small perturbations in the model or in the data, may cause disproportionate changes in the estimates of the model parameters; see details in, for example, Refs. [22,[24][25][26][27][28]30,[37][38][39].…”

Section: Data-influence Analytics In Mixed-effects Logistic Regressiomentioning

confidence: 99%

“…There are several manners to make this validation in models for binary data [19]. Recent advances in model checking and diagnostics have been developed by several authors [20][21][22][23][24][25][26][27][28][29][30]. For more details and references regarding to statistical diagnostics, see Section 3.…”

Section: Introduction and Context Of The Empirical Applicationmentioning

confidence: 99%

Data-Influence Analytics in Predictive Models Applied to Asthma Disease

et al. 2020

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Asthma is one of the most common chronic diseases around the world and represents a serious problem in human health. Predictive models have become important in medical sciences because they provide valuable information for data-driven decision-making. In this work, a methodology of data-influence analytics based on mixed-effects logistic regression models is proposed for detecting potentially influential observations which can affect the quality of these models. Global and local influence diagnostic techniques are used simultaneously in this detection, which are often used separately. In addition, predictive performance measures are considered for this analytics. A study with children and adolescent asthma real data, collected from a public hospital of São Paulo, Brazil, is conducted to illustrate the proposed methodology. The results show that the influence diagnostic methodology is helpful for obtaining an accurate predictive model that provides scientific evidence when data-driven medical decision-making.

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Global and local diagnostic analytics for a geostatistical model based on a new approach to quantile regression

Leiva

Sánchez

Galea

et al. 2020

Stoch Environ Res Risk Assess

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Sensitivity analysis of longitudinal count responses: a local influence approach and application to medical data

Cited by 7 publications

References 41 publications

The r‐hypergeometric distribution: Characterization, mathematical methods, simulations, and applications in sciences and engineering

The r‐hypergeometric distribution: Characterization, mathematical methods, simulations, and applications in sciences and engineering

Data-Influence Analytics in Predictive Models Applied to Asthma Disease

Global and local diagnostic analytics for a geostatistical model based on a new approach to quantile regression

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