Award Date
August 2023
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
First Committee Member
Petros Hadjicostas
Second Committee Member
Amei Amei
Third Committee Member
Kaushik Ghosh
Fourth Committee Member
Ann Vuong
Number of Pages
327
Abstract
Synergy and antagonism have been extensively studied in the context of the statistical analysis of drug combinations given to treat a disease. “Synergy” (“antagonism”, resp.) in a drug combination occurs when the desirable effect of two drugs given together for treating a disease is greater than (less than, resp.) the effect of each drug given separately.
In this dissertation, however, we study “synergy” and “antagonism” in log-linear models. We also give a thorough review and extend several epidemiological definitions of synergy and antagonism for categorical data, and we connect these definitions to the definitions of synergy and antagonism in log-linear models.
In particular, we discuss in great detail Worcester’s (1971) synergistic multiplicative model. Worcester’s (1971) model was used to model “synergy” between the binary factors “smoking” and “use of oral contraceptive” in affecting the response variable “presence or absence of thromboembolism”. We also provide asymptotic standard errors for a measure of synergy provided by Worcester. These allow us to perform tests of hypotheses and construct confidence intervals for this measure of synergy.
In a series of articles, Japanese statistician E. Funo (2002 to 2007) studied and generalized the log-linear versions of Worcester’s (1971) models to multiway tables. We review Funo’s non-standard log-linear models and suggest generalizations of Worcester’s measure of synergy that are appropriate for multiway contingency tables.
Keywords
Antagonism; Contingency table; Log-linear; Relative risk; Synergy; Worcester
Disciplines
Statistics and Probability
File Format
File Size
1640 KB
Degree Grantor
University of Nevada, Las Vegas
Language
English
Repository Citation
Hasan, Md Nahid, "Synergy and Antagonism in Log-Linear Models" (2023). UNLV Theses, Dissertations, Professional Papers, and Capstones. 4833.
http://dx.doi.org/10.34917/36948183
Rights
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