Fundamental Identifiability Limits in Molecular Epidemiology

Abstract

Viral phylogenies provide crucial information on the spread of infectious diseases, and many studies fit mathematical models to phylogenetic data to estimate epidemiological parameters such as the effective reproduction ratio (Re) over time. Such phylodynamic inferences often complement or even substitute for conventional surveillance data, particularly when sampling is poor or delayed. It remains generally unknown, however, how robust phylodynamic epidemiological inferences are, especially when there is uncertainty regarding pathogen prevalence and sampling intensity. Here we use recently developed mathematical techniques to fully characterize the information that can possibly be extracted from serially collected viral phylogenetic data, in the context of the commonly used birth-death-sampling model. We show that for any candidate epidemiological scenario, there exists a myriad of alternative, markedly different and yet plausible “congruent” scenarios that cannot be distinguished using phylogenetic data alone, no matter how large the dataset. In the absence of strong constraints or rate priors across the entire study period, neither maximum-likelihood fitting nor Bayesian inference can reliably reconstruct the true epidemiological dynamics from phylogenetic data alone; rather, estimators can only converge to the “congruence class” of the true dynamics. We propose concrete and feasible strategies for making more robust epidemiological inferences from viral phylogenetic data.

Miniaturization during a Silurian environmental crisis generated the modern brittle star body plan

“…Careful attention to fossil sampling is necessary for several reasons. For example, parameter identifiability in birth-death-sampling models may be a concern for methods simultaneously estimating origination, extinction, and sampling rates, but identifiability can be improved when parameter constraints are available 60 . In addition, we could not plausibly include all known Phanerozoic brittle star taxa in our phylogenetic analysis, but highly incomplete taxon sampling may bias FBD parameter estimation, which in turn may influence macroevolutionary inferences, including ancestor-descendant probabilities.…”

Unifying Phylogenetic Birth–Death Models in Epidemiology and Macroevolution

“…The unification of these models clarifies the connections between BDS variants, facilitates the development of new variants tailored to specific scenarios, and provides a structure for understanding how results depend on model assumptions ( Kirkpatrick et al 2002 ; Lafferty et al 2015 ; Louca and Pennell 2020a ). And importantly, given the recent discovery of widespread nonidentifiability in birth–death processes fit to extant-only ( Louca and Pennell 2020a ) and serially sampled ( Louca et al 2021 ) phylogenetic data, there is a critical need to explore a much broader range of BDS models than were previously considered and the mathematical generalization presented here will be enable this.…”

“…Furthermore, despite their apparent similarities, these models have been derived on a case-by-case basis using different notation and techniques; this creates a substantial barrier for researchers working to develop novel models for new situations. And critically, it is imperative that we understand the general properties of BDS phylogenetic models and the limits of inferences from them ( Louca and Pennell 2020a ; Louca et al 2021 ), and this is difficult to do without considering the full breadth of possible scenarios. Here, we address all of these challenges by unifying the whole class of phylogenetic BDS models.…”

“…We do so by first deriving a likelihood for general single- and multitype BDS models; in the general case, we do not assume anything about the functional forms (i.e., temporal dynamics) of the various parameters including the sampling rate through time, the possibility of sampling ancestors (or not), or how the process was conditioned. While such general models may be useful for studying the mathematical properties of BDS models as a whole ( Lambert and Stadler 2013 ; Louca and Pennell 2020a ; Louca et al 2021 ), statistical inference from these models requires researchers to make further constraints on the process. We prove that existing BDS model variants are indeed submodels of the more general case—and thereby clarify the specific assumptions made by different models—and provide a standardized notation and technique for deriving these and other submodels that have not previously been considered in the literature.…”

A computationally tractable birth-death model that combines phylogenetic and epidemiological data

“…Rates are given in units of per day, the average duration of infectiousness is 10 days and the basic reproduction number is 1.85. When estimating model parameters the death rate μ was fixed to the true value used while simulating the data, since not fixing one of the parameters makes the likelihood unidentifiable and estimates of μ may be obtained from additional data sources [13,42]. A uniform prior distribution was used for all parameters.…”