Some principles for using epidemiologic study results to parameterize transmission models

Abstract

Background: Infectious disease models, including individual based models (IBMs), can be used to inform public health response. For these models to be effective, accurate estimates of key parameters describing the natural history of infection and disease are needed. However, obtaining these parameter estimates from epidemiological studies is not always straightforward. We aim to 1) outline challenges to parameter estimation that arise due to common biases found in epidemiologic studies and 2) describe the conditions under which careful consideration in the design and analysis of the study could allow us to obtain a causal estimate of the parameter of interest. In this discussion we do not focus on issues of generalizability and transportability.

Methods: Using examples from the COVID-19 pandemic, we first identify different ways of parameterizing IBMs and describe ideal study designs to estimate these parameters. Given real-world limitations, we describe challenges in parameter estimation due to confounding and conditioning on a post-exposure observation. We then describe ideal study designs that can lead to unbiased parameter estimates. We finally discuss additional challenges in estimating progression probabilities and the consequences of these challenges.

Results: Causal estimation can only occur if we are able to accurately measure and control for all confounding variables that create non-causal associations between the exposure and outcome of interest, which is sometimes challenging given the nature of the variables we need to measure. In the absence of perfect control, non-causal parameter estimates should still be used, as sometimes they are the best available information we have.

Conclusions: Identifying which estimates from epidemiologic studies correspond to the quantities needed to parameterize disease models, and determining whether these parameters have causal interpretations, can inform future study designs and improve inferences from infectious disease models. Understanding the way in which biases can arise in parameter estimation can inform sensitivity analyses or help with interpretation of results if the magnitude and direction of the bias is understood.

Figure 1:

(A) Disease progression after exposure to COVID-19. (B) Combination of outcomes that can occur post exposure. The ordering described above is approximate in time, though some may coincide (e.g., hospitalization and diagnosis might be the same event) and some may be in the opposite order (e.g., diagnosis may precede symptom onset). This should not be taken as a compartmental model because the transitions are typically not Markov. That is, the probability of hospitalization given diagnosis will depend on symptoms (as well as on covariates).

Figure 2:. Distortion of VEH|S estimates due to selection bias induced by conditioning on a collider, symptomatic infection.

Directed acyclic graph (DAG) showing variables that can impact the relationship between vaccination and hospitalization among individuals with symptomatic disease. Blue box means a variable is conditioned upon. Variables with a solid box around them can be fully controlled for using stratification-based approaches. Variables with dashed lines can be controlled for, but likely with some error resulting in residual confounding.