Date of Award


Document Type

Open Access Thesis


Epidemiology and Biostatistics


The Norman J. Arnold School of Public Health

First Advisor

Jiajia Zhang


In an observational longitudinal study, there can be time-varying exposure/treatment and time-varying confounders. When the confounders affect the exposure and prior exposure also has an impact on levels of confounders, there is treatment confounder feedback. To admit estimation of unbiased causal effects, these conditions need to be hold, exchangeability, positivity, consistency. The traditional method of conditioning on potential confounders does not meet these 3 conditions. Therefore, parameter estimates from traditional Cox model are biased casual effect estimates when the treatment confounder feedback exists. The marginal structural Cox model can be used to address this issue. By calculating and including inverse probability (IP) weights, the impact of confounding can be removed. Estimates from models with IP weights are interpreted as the causal effect that comparing always in treatment group vs. never in treatment group.

In this study, first, I introduced basic concepts of causal inference, treatment confounder feedback and the marginal structural model; detailed steps of calculating IP weights and model fitting. In simulation study, I compared the time-dependent Cox models and the marginal structural Cox model; Also, for the marginal model, results using three types of IP weights were compared: un-stabilized weight, stabilized weight, and stabilized weight considering censoring. Performance metrics of each method were evaluated based on their bias, percentage bias, empirical standard deviation, standard error and coverage probability of 95% confidence intervals. Aerobics Center Longitudinal Study (ACLS) data were used to explore the causal effect of cardiorespiratory fitness on hypertension incidence. Overweight or obese is a risk factor of hypertension. We hypothesized that cardiorespiratory fitness may help lower BMI via physical exercise, while reduced BMI or improved overweight status may promote cardiorespiratory fitness. Thus, there exists cardiorespiratory (treatment) overweight (confounder) feedback, and the marginal structural Cox model may deepen our understanding of association between hypertension and CRF through ACLS data.