Date of Award
2019
Embargo Period
8-1-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Public Health Sciences
College
College of Graduate Studies
First Advisor
Paul J. Nietert
Second Advisor
Viswanathan Ramakrishnan
Third Advisor
Bethany J. Wolf
Fourth Advisor
Diane L. Kamen
Fifth Advisor
Jim C. Oates
Abstract
Computing unbiased parameter estimates from a distribution using a sample with observations appearing below a lower limit of detection (LLOD) can be challenging. Frequently, LLOD observations are excluded from calculations for parameter estimates, or the LLOD observations are replaced with arbitrary values (LLOD, LLOD/2, LLOD/√2) prior to the calculations. Despite the frequent use of these simple approaches, the approaches are known to provide biased parameter estimates. Alternative approaches include implementing a left truncation or left censoring approach. In the first dissertation aim, we will explore and establish a general theoretical relationship between accurately estimating parameters under left truncated and left censored models. Estimation methods under both models require iterative algorithms. The left truncation approach is applied through an Expectation-Maximization (EM) algorithm. While the left censoring approach is implemented by the Newton-Raphson method. We conclude in the first aim that the left truncation and left censoring approaches yielded equivalent parameter estimates. Computationally, we favored the left truncation approach that is implemented through an EM algorithm. The left truncation approach for estimating parameters is utilized in the remaining aims. In the second aim of this dissertation, we propose an EM algorithm for estimating parameters from a normal distribution when there are multiple LLOD values present. The third aim includes solutions to an EM algorithm for estimating bivariate normal distribution parameters. In the third aim, the data under the left truncation approach can be categorized into 24 scenarios. The construction of the EM algorithm includes the scenarios. All dissertation aims are motivated by toxicology and serology data collected in the Systemic Lupus Erythematosus in Gullah Health study.
Recommended Citation
Muhammad, Lutfiyya NaQiyba, "Parameter Estimation for Data with Lower Limit of Detection Values under the Truncated Model – EM Solutions" (2019). MUSC Theses and Dissertations. 225.
https://medica-musc.researchcommons.org/theses/225
Rights
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