Dissertations & Theses (Open Access)

Date of Award

Spring 5-2020

Degree Name

Doctor of Philosophy (PhD)

Advisor(s)

Wenyaw Chan, Phd

Second Advisor

Michael Swartz, Phd

Third Advisor

David Lairson Phd

Abstract

Mediation is a type of analysis used to determine the causal mechanism linking a predictor and an outcome through a mediator variable. Various research has examined the inclusion of different variable types for the predictor, mediator, and outcome. However, no studies include the presence of a continuous-time Markov chain (CTMC) as any of the components in a mediating model. If researchers wanted to design a study with a CTMC in the mediating process, one of the first steps would be to determine the minimum number of subjects or observations needed to detect a significant mediating effect. Therefore, in this study, we used simulations to determine that minimum sample size to achieve 80% power for a longitudinal mediation analysis that includes a two-state CTMC as one of the variables in the mediating model. We examined three mediation models with the following variable types: 1) A CTMC outcome with a binary predictor and continuous mediator, 2) a CTMC mediator with a binary predictor and continuous outcome, and 3) a CTMC predictor with continuous mediator and outcome. We calculated the power in simulations where we varied the sample size and effect sizes used to calculated the overall mediating effect. We found that all models required minimum sample sizes that ranged from 100 to 500 observations.

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