Compartmental Model Diagrams as Causal Representations in Relation to DAGs.

Compartmental model diagrams have been used for nearly a century to depict causal relationships in infectious disease epidemiology. Causal directed acyclic graphs (DAGs) have been used more broadly in epidemiology since the 1990s to guide analyses of a variety of public health problems. Using an example from chronic disease epidemiology, the effect of type 2 diabetes on dementia incidence, we illustrate how compartmental model diagrams can represent the same concepts as causal DAGs, including causation, mediation, confounding, and collider bias. We show how to use compartmental model diagrams to explicitly depict interaction and feedback cycles. While DAGs imply a set of conditional independencies, they do not define conditional distributions parametrically. Compartmental model diagrams parametrically (or semiparametrically) describe state changes based on known biological processes or mechanisms. Compartmental model diagrams are part of a long-term tradition of causal thinking in epidemiology and can parametrically express the same concepts as DAGs, as well as explicitly depict feedback cycles and interactions. As causal inference efforts in epidemiology increasingly draw on simulations and quantitative sensitivity analyses, compartmental model diagrams may be of use to a wider audience. Recognizing simple links between these two common approaches to representing causal processes may facilitate communication between researchers from different traditions.

Body mass index and cognitive function: the potential for reverse causation.

OBJECTIVE: Higher late life body mass index (BMI) is unrelated to or even predicts lower risk of dementia in late life, a phenomenon that may be explained by reverse causation due to weight loss during preclinical phases of dementia. We aim to investigate the association of baseline BMI and changes in BMI with dementia in a large prospective cohort, and to examine whether weight loss predicts cognitive function. METHODS: Using a national cohort of adults average age 58 years at baseline in 1994 (n=7029), we investigated the associations between baseline BMI in 1994 and memory scores from 2000 to 2010. We also examined the association of BMI change from 1994 to 1998 with memory scores from 2000 to 2010. Last, to investigate reverse causation, we examined whether memory scores in 1996 predicted BMI trajectories from 2000 to 2010. RESULTS: Baseline overweight predicted better memory scores 6 to 16 years later (ß=0.012, 95% confidence interval (CI)=0.001; 0.023). Decline in BMI predicted lower memory scores over the subsequent 12 years (ß=-0.026, 95% CI= -0.041; -0.011). Lower memory scores at mean age 60 years in 1996 predicted faster annual rate of BMI decline during follow-up (ß=-0.158 kg m(-2) per year, 95% CI= -0.223; -0.094). CONCLUSION: Consistent with reverse causation, greater decline in BMI over the first 4 years of the study was associated with lower memory scores over the next decade and lower memory scores was associated with a decline in BMI. These findings suggest that preclinical dementia predicts weight loss for people as early as their late 50s.