Award Date

August 2023

Degree Type


Degree Name

Doctor of Philosophy (PhD)


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



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.


Antagonism; Contingency table; Log-linear; Relative risk; Synergy; Worcester


Statistics and Probability

Degree Grantor

University of Nevada, Las Vegas




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