Date of Award:


Document Type:


Degree Name:

Doctor of Philosophy (PhD)


Mathematics and Statistics

Committee Chair(s)

John R. Stevens


John R. Stevens


Chris Corcoran


Daniel Coster


Adele Cutler


Abby D. Benninghoff


The research objective of this dissertation was to provide novel statistical methods to fill potential gaps in the analyses of micro-ribonucleic acid (miRNA) data, and consequently to identify the miRNAs that contribute to cancer development. Mainly, this dissertation addressed the statistical issues raised by the statistical dependence of imputed (i.e., the missing data were replaced with substituted values) miRNA data in the colorectal cancer study. This dissertation presented a modified imputation method, the weighted KNN imputation accounting for dependence, that predicted the expression levels of missing normal samples with greater imputation accuracy than other imputation methods, and had moderate power to identify the differentially expressed miRNAs. The dissertation also improved the differential expression tests that do not assume a specific distribution of the miRNAs and account for the dependence structure of the data. Particularly, it provided an effective computational solution for the nonparametric permutation t-test by increasing its computational efficiency more than 100 times. Moreover, this dissertation contributed to the normalization literature, which includes a critical data analysis step in detecting differentially expressed miRNA features, by developing a new normalization method that removes not only technical variation but also the variation caused by the characteristics of subjects, and maintains true biological differences between arrays.



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Mathematics Commons