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Quantile Regression Approach for Analyzing Similarity of Gene Expressions under Multiple Biological Conditions

1
Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada
2
Department of Statistics, Mawlana Bhashani Science and Technology University, Santosh, Tangail 1902, Bangladesh
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Zhu Wei
Stats 2022, 5(3), 583-605; https://doi.org/10.3390/stats5030036
Received: 6 June 2022 / Revised: 27 June 2022 / Accepted: 29 June 2022 / Published: 2 July 2022
Temporal gene expression data contain ample information to characterize gene function and are now widely used in bio-medical research. A dense temporal gene expression usually shows various patterns in expression levels under different biological conditions. The existing literature investigates the gene trajectory using the mean function. However, temporal gene expression curves usually show a strong degree of heterogeneity under multiple conditions. As a result, rates of change for gene expressions may be different in non-central locations and a mean function model may not capture the non-central location of the gene expression distribution. Further, the mean regression model depends on the normality assumptions of the error terms of the model, which may be impractical when analyzing gene expression data. In this research, a linear quantile mixed model is used to find the trajectory of gene expression data. This method enables the changes in gene expression over time to be studied by estimating a family of quantile functions. A statistical test is proposed to test the similarity between two different gene expressions based on estimated parameters using a quantile model. Then, the performance of the proposed test statistic is examined using extensive simulation studies. Simulation studies demonstrate the good statistical performance of this proposed test statistic and show that this method is robust against normal error assumptions. As an illustration, the proposed method is applied to analyze a dataset of 18 genes in P. aeruginosa, expressed in 24 biological conditions. Furthermore, a minimum Mahalanobis distance is used to find the clustering tree for gene expressions. View Full-Text
Keywords: chi-square test; classification; linear mixed model; Mahalanobis distance; quantile analysis; temporal gene expressions chi-square test; classification; linear mixed model; Mahalanobis distance; quantile analysis; temporal gene expressions
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MDPI and ACS Style

Deng, D.; Chowdhury, M.H. Quantile Regression Approach for Analyzing Similarity of Gene Expressions under Multiple Biological Conditions. Stats 2022, 5, 583-605. https://doi.org/10.3390/stats5030036

AMA Style

Deng D, Chowdhury MH. Quantile Regression Approach for Analyzing Similarity of Gene Expressions under Multiple Biological Conditions. Stats. 2022; 5(3):583-605. https://doi.org/10.3390/stats5030036

Chicago/Turabian Style

Deng, Dianliang, and Mashfiqul Huq Chowdhury. 2022. "Quantile Regression Approach for Analyzing Similarity of Gene Expressions under Multiple Biological Conditions" Stats 5, no. 3: 583-605. https://doi.org/10.3390/stats5030036

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