Abstract
Human health risk assessments for complex mixtures can address real-world exposures and protect public health. While risk assessors typically prefer whole mixture approaches over component-based approaches, data from the precise exposure of interest are often unavailable and surrogate data from a sufficiently similar mixture(s) are required. This review describes recent advances in determining sufficient similarity of whole, complex mixtures spanning the comparison of chemical features, bioactivity profiles, and statistical evaluation to determine “thresholds of similarity”. Case studies, including water disinfection byproducts, botanical ingredients, and wildfire emissions, are used to highlight tools and methods. Limitations to application of sufficient similarity in risk-based decision making are reviewed and recommendations presented for developing best practice guidelines.
Keywords: complex mixtures, new approach methodologies, non-targeted chemical analysis, water disinfection byproducts, botanicals, wildfire smoke
Graphical Abstract

1. Introduction to Mixtures Risk Assessment
The evaluation of health risks associated with exposure to mixtures begins with problem formulation, which requires first identifying the mixture of interest (i.e., exposure of concern) (Figure 1). This initial task can be complicated by ambiguity surrounding mixtures terminology, different options for approaching mixtures risk assessment, and regulatory constraints (e.g., legislative mandates, siloed jurisdictions). The term “mixture” can be divided into defined mixtures containing relatively few active chemicals with known quantities (e.g., combination pharmaceuticals, pesticide formulations, research mixtures), and complex mixtures, synonymous with UVCBs (Unknown or Variable composition, Complex reaction products, or Biological materials) [1], with many constituents and some uncharacterized fraction. The mixture of interest can range from a commercial formulation to the totality of chemicals present in the body (i.e., exposome) [2].
Figure 1. Risk assessment context for whole mixtures evaluation and sufficient similarity determination.

Data on the exact whole mixture of interest are rarely available, so methods to determine sufficient similarity of a data-rich surrogate mixture(s) are required.
Following identification of a mixture, data available for characterizing hazard are evaluated. If there are adequate data for conducting a quantitative risk assessment, analysts are faced with a decision between: (a) evaluating the mixture as a single entity using data from a whole mixture, or (b) estimating mixture effects using data from a subset of individual mixture components input into predictive mixture models (i.e., a component-based approach) [3]. Criteria for making this decision are not firmly established, and decisions on a whole mixture versus component-based approach are typically made on a case-by-case basis. For example, diesel exhaust has been evaluated as a whole mixture [4], while other mixtures containing polycyclic aromatic hydrocarbons have defaulted to a component-based approach, despite numerous associated uncertainties and limitations [5].
Generally, risk analysts prefer the use of whole mixture data because all constituents and interactions are accounted for in the evaluation, and assumptions about joint action among components are unnecessary (as opposed to component-based approaches). However, data for the precise mixture of interest are rarely available. In these data-poor cases, data from sufficiently similar whole mixtures can theoretically be used [3], but methods for determining sufficient similarity are required. The term “sufficient similarity” indicates that a mixture with adequate toxicity data can be used to evaluate the risk associated with a related data-poor mixture of interest. Thus, this method could be thought of as a mixtures-based read-across, a method that is commonly implemented to gap-fill toxicity data for data-poor chemicals that are structurally similar to chemicals with toxicity data during hazard evaluation [6]. Though, unlike traditional single chemical read-across, mixtures sufficient similarity also uses toxicological response data. The basic process of determining sufficient similarity involves comparing across mixtures using chemical composition and toxicological data along with data analysis approaches to observe the relatedness among mixtures (Figure 2).
Figure 2. Sufficient similarity assessments for whole mixtures represent integrative approaches that bridge exposure, toxicology, and data science to inform human health risk assessments.

Illustrated here are proposed conceptual steps involved in such assessments. (A) First the primary question of whether or not a mixture is sufficiently similar to a known reference mixture is posed. Data surrounding the mixtures’ (B) exposure chemistry and (C) biological response profiles are (D) integrated and compared to inform the manner in which health risks are ultimately quantified. Figure generation in Biorender Software.
In this opinion article, we focus on complex mixtures in the context of whole mixtures risk assessment. Defined mixtures and component-based approaches are outside of the scope of this review and are discussed elsewhere [3,7]. Herein, we provide an overview of recent advances in chemical analysis and bioactivity screening of complex mixtures, as well as data analysis approaches that can be used to interpret and integrate across these datastreams. Next, we briefly review recent literature on determining sufficient similarity of whole, complex mixtures. Challenges are discussed in the context of available case studies and integration into risk assessments. We conclude by providing recommendations for advancing the application of sufficient similarity methods to assess risk from exposure to complex mixtures.
2. Elements of Mixtures Evaluations for Sufficient Similarity
2.1. Mixtures Exposure Chemistry and Advances through Non-Targeted Analysis
Sufficient similarity analyses rely upon evaluation and comparison across whole mixture exposure profiles, often leveraging chemistry-based characterizations (Figure 2B). The overall field of exposure science has experienced a dramatic shift in recent years due to advances in technologies aimed at better characterizing the “exposome” [8]. A method that has significantly contributed to this rapid advancement and is particularly useful in evaluating whole, complex mixtures is non-targeted analysis (NTA). NTA represents a compilation of technologies reliant upon high resolution mass spectrometry, chemical databases, and computational/software tools to enable quicker identification of hundreds-to-thousands of chemicals within environmental/biological samples [9].
NTA has contributed to our knowledge of chemicals present in many different environmental and biological samples [8]. Due to its global unbiased chemical coverage, NTA can serve a critical role in the evaluation of sufficient similarity in mixtures assessments, as in the botanical case studies described below. The advantage to conducting a sufficient similarity analysis based upon NTA is that observed molecular features do not necessarily require full chemical-specific annotation/identification, representing a common rate-limiting step in NTA research [10–13]. Instead, molecular feature signatures (also referred to as “fingerprints”) can be evaluated for similarities based upon spectral patterns, relative abundance/peak intensities, retention time, and other attributes that are outputted from mass spectrometry measures that are now routinely collected.
NTA is an important tool contributing to mixtures analyses, with capabilities that are continually expanding [8,9]. However, limitations surround instrument- and/or lab-specificity of molecular feature data, where sharing spectral output and providing structure for data interpretation and downstream analyses outside of the originating lab remain difficult. These challenges underscore a recommendation to analyze whole, complex mixtures in parallel (e.g., under the same laboratory conditions, on the same day(s)) when evaluating sufficient similarity. Recent progress surrounding universal data standards, data deposition, and reporting are now beginning to address this issue [14], though improvements are still needed to instill Findability, Accessibility, Interoperability, and Reusability (FAIR) data principles [15]. NTA also typically produces chemical quantification estimates based on relative abundance, as opposed to chemical concentrations. Furthermore, the identification of specific chemicals remains difficult, where most have limited confidence levels, requiring chemical-specific follow-up analysis through further refined MS2 fragmentation and/or chemical standards [16]. Given the overall momentum behind NTA, these methods will inevitably become more streamlined.
2.2. Mixtures Biological Activity Profiling
Biological activity profiling is an important part of determining sufficient similarity of whole, complex mixtures (Figure 2C). New approach methods (NAMs) that allow for evaluating numerous complex mixtures in parallel are already being successfully used to characterize complex mixture toxicity [17]. Significant collaborative efforts are intentionally expanding the application domain of in vitro assays from single chemicals to complex mixtures and building confidence in their use. For example, the PANORAMIX project, is aimed at advancing mixtures risk assessment by applying a high-throughput in vitro screening approach to complex, real-world mixtures [18] and the Botanical Safety Consortium, is a public-private partnership dedicated to evaluating the performance of in vitro assays with complex botanical ingredients [19].
Many universal issues associated with the use of in vitro bioassays in hazard characterization are being explored in a mixtures context. The first challenge is differentiating between detectable changes in sensitive in vitro systems and adverse responses that reflect potential human health hazards. Toward the goal of better defining this inflection point, effect-based trigger values have been established for specific effects (e.g., steroid hormone activity) [20] and less specific activity (e.g., stress response, xenobiotic metabolizing enzyme activity) [21]. These effect-based trigger values, developed using individual chemical data, have been applied to the evaluation of complex environmental mixtures, such as wastewater treatment effluent [20,21], to determine water quality.
Another important challenge is in adequately capturing the biological complexity of humans using in vitro systems. Different approaches for bridging the divide have been applied to mixtures. The Tox21 and ToxCast efforts include a wide array of cell-based assays to capture diverse biological targets on an individual chemical basis and have been used to evaluate complex botanical mixtures [22] and vegetable/fruit extracts [23]. Higher-order in vitro models that better reflect complex biological systems, such as organoids [24] and organotypic human stem cells [25], have been used to evaluate mixtures. Multiple mixtures-related efforts have used adverse outcome pathways and networks to link molecular initiating events that represent typical in vitro endpoints, such as receptor activation, to apical, adverse outcomes [26,27].
2.3. Mixtures Data Analysis and Integration
Data science and computational approaches serve as the basis for integrating across chemical and biological datastreams, ultimately influencing how mixtures are evaluated for health risks (Figure 2D). Here, we posit that high dimensional analysis approaches that are now routine when evaluating mixture exposures and toxicology can often be leveraged for this additional focus on sufficient similarity. Example approaches include machine learning (ML), mixtures statistical models, and similarity indices to inform risk quantitation. These methods are discussed below in the context of recent mixtures studies, while highlighting current/future utilities towards sufficient similarity.
2.3.1. Unsupervised and Supervised ML
ML represents a growing field of computational approaches that can ascertain patterns and/or predictions from large datasets often spanning high dimensionalities, including data types that are typical in mixtures-based evaluations. A common unsupervised ML method is clustering, which has been used in recent mixtures studies to elucidate patterns of chemical co-exposures relevant to breast cancer in women [28] and neurodevelopment and thyroid effects in infants [29], among many other applications. Such clustering methods are reliant upon the identification of similarities vs differences amongst datasets, and thus can be leveraged to inform sufficient similarity analyses [30]. Frequent itemset mining [31] and comparative network analysis [32] have also been used to identify common sets of chemical mixtures detected in human biomonitoring studies. These pattern recognition methods can notably be combined with data reduction techniques (e.g., principal component analysis) to identify patterns between groups of exposures/toxicological responses relevant to whole mixtures [28,30,33]. Other methods include predictive modeling using supervised ML, as implemented by researchers combining environmental and social stressors to predict community-level vulnerabilities to the COVID-19 pandemic [34]. Supervised ML has yet to be integrated into sufficient similarity analyses, to our knowledge. Though, as this field continues to evolve and datasets continue to expand, it is feasible that enough data may exist for a particular group of mixtures to build models predicting whether or not mixtures exposure conditions are similar.
2.3.2. Mixtures Statistical Models
Mixtures (or multivariable) statistical models are also commonly implemented in mixtures research, particularly within epidemiological designs. Recent examples include a study evaluating breast cancer risk in association with toxic metals in air using weighted quantile sum regression modeling [35]. Bayesian Kernel Machine Regression modeling is also commonly implemented, as exemplified by a recent study showing relationships between endocrine disrupting chemical mixtures and reduced birth weight within a large pregnancy cohort [36]. Quantile-based g-computation represents a newer method that is becoming increasingly popular in mixtures-based epidemiological studies, for instance in the recent analysis of crude oil-originating airborne chemical mixtures and asthma incidence [37]. We have translated this method into toxicological assessments, including a study that used quantile-based g-computation to evaluate chemical groups that co-occur across wildfire-relevant exposure scenarios as discussed below [38]. Future study designs could incorporate output of statistical results into sufficient similarity analyses, either quantitatively based upon model fit parameters (e.g., similarities across beta coefficients) or by prioritizing future experimentation based upon relationships derived in silico through mixtures modeling.
2.3.3. Similarity Indices and Data Integration to Inform Risk
Similarity indices can also be derived to inform the degree to which one mixture is similar to another. For example, groups of exposure conditions can be compared upon visual inspection of summarized values based upon dimensionality reduction, as was carried out using visualizations across dietary supplements’ chemical and biological response signature data [39]. There are also many similarity metrics that have been used to compare datasets of binarized values. For instance, chemical structure features are commonly compared using the Jaccard distance metric (also known as the Tanimoto method) [28,40]. A recent metric of mixtures-specific similarity was posed, namely the Similar Mixture Risk Indicator (SMRI) [41]. This metric represents a hybrid approach, first identifying a reference mixture of prioritized chemicals that is characterized for animal toxicity to derive a point of departure. Then, other mixtures measured through human biomonitoring are compared by calculating the differences between prioritized chemical concentrations, and if the differences are small, mixtures are determined to be sufficiently similar. Resulting SMRI values are then calculated using component-based methods [41].
There notably exist limitations surrounding the development, use, and training of data analysis methods for mixtures. We recently aimed to address this gap through the dissemination of data science training materials relevant to environmental health, including mixtures sufficient similarity analyses [6]. Regardless of the data analysis method, the ultimate goal of sufficient similarity is to inform whole mixture human health risk assessments.
3. Case Studies of Mixtures Sufficient Similarity Analyses
Sufficient similarity analyses of complex mixtures have been carried out by a few research teams, with select case studies described below. Common steps employed in these studies are displayed as a generic approach in Figure 3.
Figure 3. Steps that are commonly employed in a sufficient similarity analysis of complex mixtures.

(A) A comparison across chemical signatures is commonly implemented, showcased here using global, non-targeted chemistry methods to yield unannotated fingerprints of molecular features that can be compared across samples. A reference sample is bolded throughout and represents the data-rich sample to which all other mixtures are compared. (B) A comparison across biological response signatures can also be implemented, here using select toxicity endpoints (Tox Endpoints 1–5) that are displayed using a heat map based on clustered profiles. (C) Combined similarity metrics can be displayed using line plots, with distances between samples (dots) scaled according to similarity distance to the reference sample. In this generic example, a similarity intersect is shown indicating which samples are similar (left) vs dissimilar (right) to the reference sample.
3.1. Water Disinfection Byproducts
Understanding the risks posed by drinking water disinfection byproduct mixtures is a public health priority. One of the first case studies exploring sufficient similarity of complex, whole mixtures involved a comparison of water samples containing drinking water disinfection by products [42]. In this case study, 23 samples gathered from different points in 5 water treatment facilities were compared using targeted chemical analysis and an in vitro mutagenesis assay (i.e., Ames assay in Salmonella typhimurium strains TA98 and TA100) [43]. Multiple chemical features were measured including specific chemicals (e.g., 6 haloacetic acids), as well as several summary values (e.g., total organic halides). Two statistical approaches, principal component analysis [44] and a nonparametric bootstrap-based inference approach [45], were used to evaluate the similarity among samples. A key finding from the case study was that the differences between water treatment plants (i.e., processes) were more important than the collection points within each treatment site (i.e., finished versus distribution). Importantly, this case study involved comparison across all samples and did not include a reference mixture. Therefore, decisions would be highly reliant upon which treatment facilities were evaluated together, and thus may lack generalizability. A second point to consider was limited coverage of biological endpoints (namely, mutagenicity), where querying additional types of hazards (i.e., non-genotoxic carcinogenesis, noncancer endpoints) would enhance future mixtures safety assessments. Several more recent efforts have used alternative component-based approaches such as concentration addition to estimate mixture effects based on data from individual disinfection byproduct chemicals [46,47].
3.2. Wildfire Smoke
The study of wildfires is currently hindered due to the extreme variability in both exposure and biological response profiles that can result from these complex mixtures. Factors that contribute to this variability include the large differences in fuel types that can be burned during wildfire events, spanning limitless combinations of biomass fuels (e.g., tree species and other biogenic materials) and anthropogenic materials that can burn during wildfire events (e.g., building materials, vehicles, consumer products, and other materials relevant to human activities). Epidemiological studies have been conducted on wildfires, based largely on retrospective designs, and have established relationships between exposures and disease outcomes including respiratory disease, cardiovascular events, and mortality [48,49]. Toxicological studies have started to evaluate wildfire smoke as complex mixtures through lab-based simulations of wildfire events. For instance, our team has organized simulations of wildfire events, including the burning of various biomass fuels [38,50] and anthropogenic materials [33]. Resulting smoke samples have been used as exposures in mice and in vitro systems. Some notable findings include the identification of chemical groups that co-occur across burn scenarios through mixtures modeling [38]. Select chemical groups were associated with increased (e.g., inorganics and ionic constituents) and decreased (e.g., methoxyphenols) pulmonary responses in mice [38]. Expanding this study, a new bioinformatic method termed “Transcriptomic Similarity Analysis” was employed to bin exposure scenarios into groups based on the induction of similar lung transcriptomic response patterns across biomass smoke exposures [30]. Resulting groups were then posited to inform sufficient similarity, which were quantified via Jaccard based metrics of similarity and visualized using line plots similar to those illustrated in Figure 3C [30]. As in the disinfection byproducts example, reference mixtures for wildfire smoke are currently lacking. Future research will expand upon risk quantitation through the testing and analysis of individual chemicals, defined mixtures, and complex mixtures present in wildfire smoke.
3.3. Botanical Supplements
Concerns for potential harm from botanical dietary supplements stem from a permissive regulatory structure and known issues with quality/adulteration in botanical products [34]. Unlike the example with water disinfection byproducts, botanical case studies typically involve comparison of a reference (i.e., well-characterized, data-rich sample) to samples representing the variability of products in the marketplace. In a case study with Ginkgo biloba extract, targeted and non-targeted chemical analysis, bioactivity profiling with liver-based in vitro models, and hierarchical clustering were used to determine the similarity of 26 Ginkgo samples to a reference that had been evaluated in rodent toxicity and carcinogenicity studies [51]. Multiple methods were applied to integrate chemical and biological activity datastreams and evaluate similarity, including a weight-of-evidence analysis, a visual interval approach, and empirical equivalence testing [51]. We found strong correlation between chemical similarity and bioactivity similarity-based results, with two-thirds of the samples determined to be sufficiently similar to the reference. Contrastingly, in a second case study with black cohosh extract, we found that feature differences observed via NTA did not correspond to differences in bioactivity profiles and all samples exhibited genotoxicity [39]. In the black cohosh case, biological similarity was more important than chemical similarity and all samples were deemed to be sufficiently similar for hazard identification purposes. We concluded that in vitro bioassays reflective of known toxicity associated with the mixture of interest (e.g., genotoxicity for black cohosh and constitutive androstane receptor [CAR] activity for Ginkgo) were more useful in sufficient similarity determinations than bioassays measuring general activity (e.g., a panel of receptor-associated genes for black cohosh). Specific activity linked to adverse outcomes observed in in vivo studies provides confidence that the determination of sufficient similarity is relevant to the hazard of concern.
4. Limitations in Mixtures Risk Evaluations
While a growing body of literature demonstrates the utility of methods for determining sufficient similarity, challenges remain, particularly when incorporating sufficient similarity into human health risk assessments and regulatory decision making. First, the determination of sufficient similarity requires expert input to determine what level of variation in chemistry and/or bioactivity translates into meaningful differences at the health outcome-level. Second, there are currently no formal guidelines or standardized methods for implementing sufficient similarity analyses. Building confidence in using the various sufficient similarity methods for risk evaluation and management will require careful review of the existing case studies and comparison of available options. Currently, there are limited examples of sufficient similarity determination in the literature, and they are investigative in nature, while examples of application in a regulatory framework are nonexistent. Future research will very likely expand on this topic, providing needed data for further case studies that can then be leveraged by policymakers in the evaluation and integration of sufficient similarity into regulatory action to protect public health.
5. Conclusions and Recommendations
A summary of overall conclusions and recommendations surrounding mixtures sufficient similarity analyses are presented in Table 1. The current body of evidence supports the future use of sufficient similarity determination in a whole mixture risk assessment framework. To our knowledge, there have yet to be instances when sufficient similarity analyses were formally used for risk-based decision making. However, the EPA is developing a sufficient similarity tool for assessment of polychlorinated biphenyl mixtures [52] based on methods originally proposed by Gennings and colleagues [53], representing an acknowledgement of the utility of these methods in a human health risk assessment context. We anticipate increasing research and development in sufficient similarity methods for evaluating complex mixtures and corresponding confidence in the integration of these methods into human health risk assessment to improve safety evaluations.
Table 1.
Summary of overall conclusions and recommendations for mixtures sufficient similarity research applications.
| Component of sufficient similarity analyses | Conclusion | Recommendation |
|---|---|---|
| Chemical analysis |
|
|
| Bioactivity profiling |
|
|
| Data analysis and integration |
|
|
| Use in risk context |
|
|
Highlights.
Sufficient similarity approaches are critical for whole mixture risk assessment.
Non-targeted chemical analysis is a promising approach for comparing mixtures.
New approach methodologies are useful for profiling the bioactivity of mixtures.
Review of sufficient similarity case studies demonstrates their utility.
Input from stakeholders and guidance on best practices is needed.
Funding
This review was supported by the National Institutes of Health (NIH), National Institute of Environmental Health Sciences (NIEHS) Intramural Research Program, Research Triangle Park, NC (ZIA ES103373-01), NIH extramural support (P42ES031007), and the U.S. Environmental Protection Agency (STAR 84045801). Additional support was provided by the Institute for Environmental Health Solutions at the Gillings School of Global Public Health.
Footnotes
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Competing interests
The authors declare that they have no competing interests.
Declaration of interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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