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Topic

Methods for Regression with Conditionally Poisson Measurement Error

Department of Mathematics and Statistics

Date & location

• Tuesday, April 7, 2026
• 12:00 P.M.
• Virtual Defence

Examining Committee

Supervisory Committee

• Dr. Farouk Nathoo, Department of Mathematics and Statistics, ̽��ϵ�� (Co-Supervisor)
• Dr. Mary Lesperance, Department of Mathematics and Statistics, UVic (Co-Supervisor)
• Dr. Julian Lum, Department of Biochemistry and Microbiology, UVic (Outside Member)
• Dr. Ibrahim Numanagic, Department of Computer Science, UVic (Outside Member)
• Dr. Dr. Finn Hamilton, Translational Bioinformatics, Pfizer Oncology Research Unit (Outside Member)

External Examiner

• Dr. Lang Wu, Department of Statistics, University of British Columbia

Chair of Oral Examination

• Dr. Timothy Iles, Department of Pacific and Asian Studies, UVic

Abstract

Measurement error in covariates is a pervasive challenge in regression and survival analysis, particularly when predictors are discrete biomarkers derived from cell counts or densities. Such data commonly arise in tumor tissue histology and tissue microarrays, where biomarkers are obtained by subsampling small tissue cores from larger sections, leading to non-Gaussian and heteroscedastic measurement error that is rarely accounted for in practice. In this paper, we develop a unified methodological framework for regression models with conditionally Poisson-distributed covariates, motivated by Poisson process models for the spatial distribution of marker-positive cells. 

We first extend the simulation–extrapolation (SIMEX) methodology to this setting, proposing POI-SIMEX, which accommodates conditional Poisson surrogates and enables correction for measurement error in the absence of internal validation data. Within a linear regression framework, we establish strong consistency of the POISIMEX estimator under suitable regularity conditions. Extensive simulation studies demonstrate that POI-SIMEX substantially reduces bias and improves estimation accuracy compared with naive analyses and alternative corrected likelihood approaches, for both linear regression and survival models.

To further enhance flexibility, we also introduce a Bayesian semiparametric joint modeling approach in which the latent covariate distribution is modeled using a Dirichlet process mixture. This framework naturally captures complex latent heterogeneity, induces appropriate heteroscedastic variance structures, and supports formal inference through Bayes factors. Simulation results show superior robustness and bias reduction relative to existing methods under realistic data-generating mechanisms. 

The proposed methods are illustrated using studies of high-grade serous ovarian carcinoma, examining associations between survival outcomes and immune cell densities measured from tissue microarrays. Together, these developments provide practical and theoretically grounded tools for analyzing regression and survival models with conditionally Poisson measurement error, addressing a critical need for methods for discrete biomarker data in cancer research.