Assessing the bivariate time-varying association between two binary variables in a longitudinal study

In many biomedical studies, researchers want to know the relationship between two "yes/no" variables. Longitudinal studies, in which the variables are measured more than once over a period of time, would help researchers understand how the relationship changes over time. I propose the bivariate time-varying odds ratio and relative risk model, which measures how strong the relationship between two variables is at different times. Estimating the odds ratio and relative risk at a given time is challenging when the variables are measured at different times. The challenge occurs because the two variables are not sampled concurrently at the time of interest. I propose a model to estimate the odds ratio and relative risk in longitudinal samples where the two variables are measured at different time points. The proposed estimation method is tested in two situations: samples of the two variables are taken at the same time or at different time points. Estimation bias could happen in research about the end of life when data is censored due to someone’s death. I propose a missingness model and suggest an estimation method based on the predicted probability as a weight. Simulation studies show that the estimation method can be used to fix the bias. In biological studies, there are times when you need to figure out how dependent two random variables are on each other based on what you know about other random variables. I propose ways to determine the relationship based on some other variables. I will use the proposed method in the Framingham Heart Study and look at how the link between parents and children with high blood pressure has changed over 45 years for both genders.