Date of Graduation

5-2025

Document Type

Thesis

Degree Name

Master of Science in Statistics and Analytics (MS)

Degree Level

Graduate

Department

Statistics and Analytics

Advisor/Mentor

Lewis, Jeffrey A.

Committee Member

Zhang, Qingyang

Second Committee Member

Alverson, Andrew J.

Third Committee Member

Chakraborty, Avishek A.

Keywords

Cell Biology; Ordinal Regression; Statistical Methods; Stress Assay; Yeast

Abstract

This thesis explores the application of ordinal regression to the analysis of semi-quantitative growth assays often used when comparing fitness for different strains of the model yeast Saccharomyces cerevisiae. For stress survival assays, yeast stress resistance is measured using an ordered survival score that ranges from 0 (no growth) to 4 (confluent growth). Traditional approaches to analyze this type of data either treats data as a nominal categorical variable or as a continuous numerical variable. These approaches risk loss of information or violation of testing assumptions. In contrast, cumulative logit ordinal regression uses the information contained in the order of the data scores without requiring equal spacing between scores. This work also compares censored Poisson regression for colony count data while accounting for overlapping colonies.

Through simulation and example datasets, the performance of ordinal regression is compared to nominal-based tests (chi-sq, fisher’s exact) and summary approaches (t- test of score sums) for identifying differences in effect of treatment according to genotype. Results show ordinal modeling is a powerful technique that is manages to control Type I (false positive) error. Additionally, proposed here is a biologically intuitive summary statistic, minimum inhibitory concentration (MIC), derived from ordinal model estimates to quantify the lowest dose of stress that prevents survival.

Application of ordinal regression to example datasets further demonstrates advantages of ordinal regression for quantifying stress resistance. In one dataset, the effect deleting CTT1, a key gene for stress protection, is quantitatively assessed across different conditions. A second dataset evaluates hybrid yeast strains crossed from stress- sensitive and stress-resistant parents, allowing for quantification of resistance profiles across genetically diverse isolates. This thesis highlights the merits of ordinal regression for analyzing semi-quantitative survival data. By utilizing model-based estimation of effects with interpretable metrics, this thesis supports wider adoption of ordinal regression in cell and molecular biology research.

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