MS07 - MEPI-1
Cartoon Room 1 (#3145) in The Ohio Union

Recent advances in parameter identifiability of mathematical models in mathematical biology

Thursday, July 20 at 04:00pm

SMB2023 SMB2023 Follow Thursday during the "MS07" time block.
Room assignment: Cartoon Room 1 (#3145) in The Ohio Union.
Note: this minisymposia has multiple sessions. The other session is MS06-MEPI-1 (click here).

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Organizers:

Omar Saucedo, Bren Case, Lauren Childs

Description:

Parameter estimation is common practice when determining unknown parameters of a mathematical model. However, whether estimated parameters are reliable depends on the quantity and quality of available data, as well as the complexity of the model. Although models in mathematical biology tend to be highly nonlinear and can interact with data in unexpected ways, identifiability is rarely assessed prior to model fitting. Identifiability analysis comes in two flavors, the first focusing on whether there exists a unique set of parameters for all possible model output, and the second focusing the set of plausible parameters inferred from noisy data. Both approaches employ a range of geometric and statistical techniques. The goal of this mini-symposium is to bring in experts working throughout the immense field of mathematical biology to discuss the most recent advancements in identifiability.



Madeline A. E. Peters

Michigan State University (Microbiology and Molecular Genetics)
"Challenges in forming inferences from limited data: a case study of malaria parasite maturation"
Inferring biological processes from population dynamics is a common challenge in ecology, particularly when faced with incomplete data. This challenge extends to inferring parasite traits from within-host infection dynamics. We focus on rodent malaria infections (Plasmodium berghei), a system for which previous work inferred an immune-mediated extension in the length of the parasite development cycle within red blood cells. By developing a system of delay-differential equations to describe within-host infection dynamics and simulating data, we demonstrate the potential to obtain biased estimates of parasite (and host) traits when key biological processes are not considered. Despite generating infection dynamics using a fixed parasite developmental cycle length, we find that known sources of measurement bias in parasite stage and abundance data can affect estimates of parasite developmental duration, with stage misclassification driving inferences about extended cycle length. We discuss alternative protocols and statistical methods that can mitigate such misestimation.
Additional authors: Megan Greischar, Department of Ecology and Evolutionary Biology, Cornell University; Nicole Mideo, Department of Ecology and Evolutionary Biology, University of Toronto



Bren Case

University of Vermont (Computer Science)
"Restricted Marginal Divergence: an efficient Bayesian measure of practical identifiability for nonlinear systems in biology and epidemiology"
Practical identifiability (PI) analysis seeks to quantify the reliability in estimates a researcher can expect when fitting a mathematical model to data. Such analyses generally reflect an intrinsic property of a particular model and proposed experimental design, rather than uncertainty in any single realization of data. Traditionally, PI has been studied using the variance-covariance matrix of an estimator for the true parameter values. However, such second-order approximations underestimate uncertainty in limited data settings, where the distribution of plausible values may be incorrectly centered or highly skewed. Here we introduce a novel method, the Restricted Marginal Divergence, which reflects the average amount of posterior shrinkage that would occur in a Bayesian analysis, without requiring computationally expensive methods such as MCMC. We show the method has attractive properties in both limited and big data regimes, and discuss its relationship to other PI methods. An in-depth application of the method follows, illustrating the amount of time that is required to learn different model-based summary statistics in an emerging epidemic, such as the basic reproductive number or fraction of individuals who will become infected.
Additional authors: Jean-Gabriel Young, Department of Mathematics & Statistics, University of Vermont; Laurent H├ębert-Dufresne, Department of Computer Science, University of Vermont



All Participants

"Open Forum"
The last 30 minutes of this session will include an open forum for discussion with speakers and participants.



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Annual Meeting for the Society for Mathematical Biology, 2023.