Using Mathematical Models to Understand Causal Mechanisms Underlying Counterintuitive Epidemiological Data

Abstract

Analyzing epidemiological data (e.g., from observational studies or surveillance) can reveal results contrary to what might be expected given a priori knowledge about the study question. In these cases, a clear mechanistic understanding of why counterintuitive results are observed is critical to minimize bias in study designs and implement effective interventions targeting diseases. Mathematical modeling approaches provide a flexible way to connect mechanisms with real-world data. In this dissertation, we describe the use of mathematical models to explore 3 cases in which seemingly counterintuitive results have been observed. First, we examined the obesity paradox or the apparent protective effect of obesity on mortality among certain high-risk groups, e.g. diabetic ever-smokers. Second, we examined how to leverage spatial and contact heterogeneity to optimize tuberculosis screening interventions in a variety of settings including those with high incidence-levels where household-based interventions have unexpectedly limited population-level effects. Finally, we examined why norovirus outbreaks are explosive in nature, but result in relatively low attack rates (the percentage of individuals who become diseased) in school and daycare settings.

In Aim 1, we developed a method to simulate epidemiological studies using compartmental models (CMs) derived from directed acyclic graphs (DAGs). We illustrated our approach using the obesity paradox as a case study. Specifically, we examined how altering underlying causal mechanisms (i.e. CM structure), can cause spurious associations in the data. We found that incorporating study design bias (e.g., including covariates in the causal mechanism and not adjusting for them), can lead to the obesity paradox. Overall, we showed how mathematical modeling of DAGs can be used to inform analyses, and explore underlying biases which may be helpful for designing sound observational studies and obtaining accurate measures of effect.

In Aim 2, we explored how variation in community contact and endemic incidence levels can affect the impact of household or community-targeted screening interventions using an individually-based network model. Overall, we found that the community drives transmission in high incidence settings. In general, more protection was conferred by targeted interventions and in lower incidence settings within networks that had fewer numbers of contacts, or shorter distance between contacts. Ultimately, these results may help identify the settings in which household or community targeted screening interventions will be effective.

In Aim 3, we explored mechanisms that underlie norovirus outbreak dynamics using a disease transmission model. We compared different scenarios, including a partially immune population, stochastic extinction, and individual exclusion, and calibrated our model to daycare and school outbreaks from surveillance data. We found that incorporating both a partially immune population and individual exclusion was sufficient to recreate explosive norovirus dynamics, more realistic outbreak durations (compared with immunity alone), and relatively low attack rates in school and daycare venues.

Ultimately, epidemiological findings only appear counterintuitive when there is a lack of understanding about the underlying mechanisms leading to what is observed in data. This dissertation highlights the importance of resolving this lack of understanding, and the use of models as a tool in this process. We used mathematical models as in silico laboratories to compare competing causal mechanisms, understand transmission patterns across different settings, and reveal key features of the natural history of disease. Gaining insight into causal mechanisms underlying seemingly counterintuitive data is critical to be able to minimize bias in study designs and implement effective disease targeting interventions.