Variance decomposition: a tool enabling strategic improvement of the precision of analytical recovery and concentration estimates associated with microorganism enumeration methods

Framework to Quantify Uncertainty in Microplastic Concentrations in Wastewaters and Sludges Incorporating Analytical Recovery Information into Data Analysis

Wastewater treatment plants (WWTPs) serve a pivotal role in transferring microplastics (MPs) from wastewater to sludge streams, thereby exerting a significant influence on their release into the environment and establishing wastewater and biosolids as vectors for MP transport and delivery. Hence, an accurate understanding of the fate and transport of MPs in WWTPs is vital. Enumeration is commonly used to estimate concentrations of MPs in performance evaluations of treatment processes, and risk assessment also typically involves MP enumeration. However, achieving high accuracy in concentration estimates is challenging due to inherent uncertainty in the analytical workflow to collect and process samples and count MPs. Here, sources of random error in MP enumeration in wastewater and other matrices were investigated using a modeling approach that addresses the sources of error associated with each step of the analysis. In particular, losses are reflected in data analysis rather than merely being measured as a validation step for MP extraction methods. A model for addressing uncertainty in the enumeration of microorganisms in water was adapted to include key assumptions relevant to the enumeration of MPs in wastewater. Critically, analytical recovery, the capacity to successfully enumerate particles considering losses and counting error, may be variable among MPs due to differences in size, shape, and type (differential analytical recovery) in addition to random variability between samples (nonconstant analytical recovery). Accordingly, differential analytical recovery among the categories of MPs was added to the existing model. This model was illustratively applied to estimate MP concentrations from simulated data and quantify uncertainty in the resulting estimates. Increasing the number of replicates, counting categories of MPs separately, and accounting for both differential and nonconstant analytical recovery improved the accuracy of MP enumeration. This work contributes to developing guidelines for analytical procedures quantifying MPs in diverse types of samples and provides a framework for enhanced interpretation of enumeration data, thereby facilitating the collection of more accurate and reliable MP data in environmental studies.

Realizing the value in "non-standard" parts of the qPCR standard curve by integrating fundamentals of quantitative microbiology

The real-time polymerase chain reaction (PCR), commonly known as quantitative PCR (qPCR), is increasingly common in environmental microbiology applications. During the COVID-19 pandemic, qPCR combined with reverse transcription (RT-qPCR) has been used to detect and quantify SARS-CoV-2 in clinical diagnoses and wastewater monitoring of local trends. Estimation of concentrations using qPCR often features a log-linear standard curve model calibrating quantification cycle (Cq) values obtained from underlying fluorescence measurements to standard concentrations. This process works well at high concentrations within a linear dynamic range but has diminishing reliability at low concentrations because it cannot explain "non-standard" data such as Cq values reflecting increasing variability at low concentrations or non-detects that do not yield Cq values at all. Here, fundamental probabilistic modeling concepts from classical quantitative microbiology were integrated into standard curve modeling approaches by reflecting well-understood mechanisms for random error in microbial data. This work showed that data diverging from the log-linear regression model at low concentrations as well as non-detects can be seamlessly integrated into enhanced standard curve analysis. The newly developed model provides improved representation of standard curve data at low concentrations while converging asymptotically upon conventional log-linear regression at high concentrations and adding no fitting parameters. Such modeling facilitates exploration of the effects of various random error mechanisms in experiments generating standard curve data, enables quantification of uncertainty in standard curve parameters, and is an important step toward quantifying uncertainty in qPCR-based concentration estimates. Improving understanding of the random error in qPCR data and standard curve modeling is especially important when low concentrations are of particular interest and inappropriate analysis can unduly affect interpretation, conclusions regarding lab performance, reported concentration estimates, and associated decision-making.

Ensuring That Fundamentals of Quantitative Microbiology Are Reflected in Microbial Diversity Analyses Based on Next-Generation Sequencing

Diversity analysis of amplicon sequencing data has mainly been limited to plug-in estimates calculated using normalized data to obtain a single value of an alpha diversity metric or a single point on a beta diversity ordination plot for each sample. As recognized for count data generated using classical microbiological methods, amplicon sequence read counts obtained from a sample are random data linked to source properties (e.g., proportional composition) by a probabilistic process. Thus, diversity analysis has focused on diversity exhibited in (normalized) samples rather than probabilistic inference about source diversity. This study applies fundamentals of statistical analysis for quantitative microbiology (e.g., microscopy, plating, and most probable number methods) to sample collection and processing procedures of amplicon sequencing methods to facilitate inference reflecting the probabilistic nature of such data and evaluation of uncertainty in diversity metrics. Following description of types of random error, mechanisms such as clustering of microorganisms in the source, differential analytical recovery during sample processing, and amplification are found to invalidate a multinomial relative abundance model. The zeros often abounding in amplicon sequencing data and their implications are addressed, and Bayesian analysis is applied to estimate the source Shannon index given unnormalized data (both simulated and experimental). Inference about source diversity is found to require knowledge of the exact number of unique variants in the source, which is practically unknowable due to library size limitations and the inability to differentiate zeros corresponding to variants that are actually absent in the source from zeros corresponding to variants that were merely not detected. Given these problems with estimation of diversity in the source even when the basic multinomial model is valid, diversity analysis at the level of samples with normalized library sizes is discussed.

Recognizing Structural Nonidentifiability: When Experiments Do Not Provide Information About Important Parameters and Misleading Models Can Still Have Great Fit

In the quest to model various phenomena, the foundational importance of parameter identifiability to sound statistical modeling may be less well appreciated than goodness of fit. Identifiability concerns the quality of objective information in data to facilitate estimation of a parameter, while nonidentifiability means there are parameters in a model about which the data provide little or no information. In purely empirical models where parsimonious good fit is the chief concern, nonidentifiability (or parameter redundancy) implies overparameterization of the model. In contrast, nonidentifiability implies underinformativeness of available data in mechanistically derived models where parameters are interpreted as having strong practical meaning. This study explores illustrative examples of structural nonidentifiability and its implications using mechanistically derived models (for repeated presence/absence analyses and dose-response of Escherichia coli O157:H7 and norovirus) drawn from quantitative microbial risk assessment. Following algebraic proof of nonidentifiability in these examples, profile likelihood analysis and Bayesian Markov Chain Monte Carlo with uniform priors are illustrated as tools to help detect model parameters that are not strongly identifiable. It is shown that identifiability should be considered during experimental design and ethics approval to ensure generated data can yield strong objective information about all mechanistic parameters of interest. When Bayesian methods are applied to a nonidentifiable model, the subjective prior effectively fabricates information about any parameters about which the data carry no objective information. Finally, structural nonidentifiability can lead to spurious models that fit data well but can yield severely flawed inferences and predictions when they are interpreted or used inappropriately.