'Single-subject studies'-derived analyses unveil altered biomechanisms between very small cohorts: implications for rare diseases.

MOTIVATION: Identifying altered transcripts between very small human cohorts is particularly challenging and is compounded by the low accrual rate of human subjects in rare diseases or sub-stratified common disorders. Yet, single-subject studies (S3) can compare paired transcriptome samples drawn from the same patient under two conditions (e.g. treated versus pre-treatment) and suggest patient-specific responsive biomechanisms based on the overrepresentation of functionally defined gene sets. These improve statistical power by: (i) reducing the total features tested and (ii) relaxing the requirement of within-cohort uniformity at the transcript level. We propose Inter-N-of-1, a novel method, to identify meaningful differences between very small cohorts by using the effect size of 'single-subject-study'-derived responsive biological mechanisms. RESULTS: In each subject, Inter-N-of-1 requires applying previously published S3-type N-of-1-pathways MixEnrich to two paired samples (e.g. diseased versus unaffected tissues) for determining patient-specific enriched genes sets: Odds Ratios (S3-OR) and S3-variance using Gene Ontology Biological Processes. To evaluate small cohorts, we calculated the precision and recall of Inter-N-of-1 and that of a control method (GLM+EGS) when comparing two cohorts of decreasing sizes (from 20 versus 20 to 2 versus 2) in a comprehensive six-parameter simulation and in a proof-of-concept clinical dataset. In simulations, the Inter-N-of-1 median precision and recall are > 90% and >75% in cohorts of 3 versus 3 distinct subjects (regardless of the parameter values), whereas conventional methods outperform Inter-N-of-1 at sample sizes 9 versus 9 and larger. Similar results were obtained in the clinical proof-of-concept dataset. AVAILABILITY AND IMPLEMENTATION: R software is available at Lussierlab.net/BSSD.

Benchmark dose risk analysis with mixed-factor quantal data in environmental risk assessment.

Benchmark analysis is a general risk estimation strategy for identifying the benchmark dose (BMD) past which the risk of exhibiting an adverse environmental response exceeds a fixed, target value of benchmark response (BMR). Estimation of BMD and of its lower confidence limit (BMDL) is well understood for the case of an adverse response to a single stimulus. In many environmental settings, however, one or more additional, secondary, qualitative factor(s) may collude to affect the adverse outcome, such that the risk changes with differential levels of the secondary factor. This paper extends the single-dose BMD paradigm to a mixed-factor setting with a secondary qualitative factor possessing two levels. With focus on quantal-response data and using a generalized linear model with a complementary-log link function, we derive expressions for BMD and BMDL. We study the operating characteristics of six different multiplicity-adjusted approaches to calculate the BMDL, using Monte Carlo evaluations. We illustrate the calculations via an example data set from environmental carcinogenicity testing.

Quantal Risk Assessment Database: A Database for Exploring Patterns in Quantal Dose-Response Data in Risk Assessment and its Application to Develop Priors for Bayesian Dose-Response Analysis.

Quantitative risk assessments for physical, chemical, biological, occupational, or environmental agents rely on scientific studies to support their conclusions. These studies often include relatively few observations, and, as a result, models used to characterize the risk may include large amounts of uncertainty. The motivation, development, and assessment of new methods for risk assessment is facilitated by the availability of a set of experimental studies that span a range of dose-response patterns that are observed in practice. We describe construction of such a historical database focusing on quantal data in chemical risk assessment, and we employ this database to develop priors in Bayesian analyses. The database is assembled from a variety of existing toxicological data sources and contains 733 separate quantal dose-response data sets. As an illustration of the database's use, prior distributions for individual model parameters in Bayesian dose-response analysis are constructed. Results indicate that including prior information based on curated historical data in quantitative risk assessments may help stabilize eventual point estimates, producing dose-response functions that are more stable and precisely estimated. These in turn produce potency estimates that share the same benefit. We are confident that quantitative risk analysts will find many other applications and issues to explore using this database.

Analysis of aggregated cell-cell statistical distances within pathways unveils therapeutic-resistance mechanisms in circulating tumor cells.

MOTIVATION: As 'omics' biotechnologies accelerate the capability to contrast a myriad of molecular measurements from a single cell, they also exacerbate current analytical limitations for detecting meaningful single-cell dysregulations. Moreover, mRNA expression alone lacks functional interpretation, limiting opportunities for translation of single-cell transcriptomic insights to precision medicine. Lastly, most single-cell RNA-sequencing analytic approaches are not designed to investigate small populations of cells such as circulating tumor cells shed from solid tumors and isolated from patient blood samples. RESULTS: In response to these characteristics and limitations in current single-cell RNA-sequencing methodology, we introduce an analytic framework that models transcriptome dynamics through the analysis of aggregated cell-cell statistical distances within biomolecular pathways. Cell-cell statistical distances are calculated from pathway mRNA fold changes between two cells. Within an elaborate case study of circulating tumor cells derived from prostate cancer patients, we develop analytic methods of aggregated distances to identify five differentially expressed pathways associated to therapeutic resistance. Our aggregation analyses perform comparably with Gene Set Enrichment Analysis and better than differentially expressed genes followed by gene set enrichment. However, these methods were not designed to inform on differential pathway expression for a single cell. As such, our framework culminates with the novel aggregation method, cell-centric statistics (CCS). CCS quantifies the effect size and significance of differentially expressed pathways for a single cell of interest. Improved rose plots of differentially expressed pathways in each cell highlight the utility of CCS for therapeutic decision-making. AVAILABILITY AND IMPLEMENTATION: http://www.lussierlab.org/publications/CCS/ CONTACT: yves@email.arizona.edu or piegorsch@math.arizona.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Dynamic changes of RNA-sequencing expression for precision medicine: N-of-1-pathways Mahalanobis distance within pathways of single subjects predicts breast cancer survival.

MOTIVATION: The conventional approach to personalized medicine relies on molecular data analytics across multiple patients. The path to precision medicine lies with molecular data analytics that can discover interpretable single-subject signals (N-of-1). We developed a global framework, N-of-1-pathways, for a mechanistic-anchored approach to single-subject gene expression data analysis. We previously employed a metric that could prioritize the statistical significance of a deregulated pathway in single subjects, however, it lacked in quantitative interpretability (e.g. the equivalent to a gene expression fold-change). RESULTS: In this study, we extend our previous approach with the application of statistical Mahalanobis distance (MD) to quantify personal pathway-level deregulation. We demonstrate that this approach, N-of-1-pathways Paired Samples MD (N-OF-1-PATHWAYS-MD), detects deregulated pathways (empirical simulations), while not inflating false-positive rate using a study with biological replicates. Finally, we establish that N-OF-1-PATHWAYS-MD scores are, biologically significant, clinically relevant and are predictive of breast cancer survival (P < 0.05, n = 80 invasive carcinoma; TCGA RNA-sequences). CONCLUSION: N-of-1-pathways MD provides a practical approach towards precision medicine. The method generates the magnitude and the biological significance of personal deregulated pathways results derived solely from the patient's transcriptome. These pathways offer the opportunities for deriving clinically actionable decisions that have the potential to complement the clinical interpretability of personal polymorphisms obtained from DNA acquired or inherited polymorphisms and mutations. In addition, it offers an opportunity for applicability to diseases in which DNA changes may not be relevant, and thus expand the 'interpretable 'omics' of single subjects (e.g. personalome). AVAILABILITY AND IMPLEMENTATION: http://www.lussierlab.net/publications/N-of-1-pathways.

Benchmark Dose Analysis via Nonparametric Regression Modeling.

Estimation of benchmark doses (BMDs) in quantitative risk assessment traditionally is based upon parametric dose-response modeling. It is a well-known concern, however, that if the chosen parametric model is uncertain and/or misspecified, inaccurate and possibly unsafe low-dose inferences can result. We describe a nonparametric approach for estimating BMDs with quantal-response data based on an isotonic regression method, and also study use of corresponding, nonparametric, bootstrap-based confidence limits for the BMD. We explore the confidence limits' small-sample properties via a simulation study, and illustrate the calculations with an example from cancer risk assessment. It is seen that this nonparametric approach can provide a useful alternative for BMD estimation when faced with the problem of parametric model uncertainty.

Benchmark dose profiles for joint-action continuous data in quantitative risk assessment.

Benchmark analysis is a widely used tool in biomedical and environmental risk assessment. Therein, estimation of minimum exposure levels, called benchmark doses (BMDs), that induce a prespecified benchmark response (BMR) is well understood for the case of an adverse response to a single stimulus. For cases where two agents are studied in tandem, however, the benchmark approach is far less developed. This paper demonstrates how the benchmark modeling paradigm can be expanded from the single-agent setting to joint-action, two-agent studies. Focus is on continuous response outcomes. Extending the single-exposure setting, representations of risk are based on a joint-action dose-response model involving both agents. Based on such a model, the concept of a benchmark profile-a two-dimensional analog of the single-dose BMD at which both agents achieve the specified BMR-is defined for use in quantitative risk characterization and assessment.

Information-theoretic model-averaged benchmark dose analysis in environmental risk assessment.

An important objective in environmental risk assessment is estimation of minimum exposure levels, called Benchmark Doses (BMDs), that induce a pre-specified Benchmark Response (BMR) in a dose-response experiment. In such settings, representations of the risk are traditionally based on a specified parametric model. It is a well-known concern, however, that existing parametric estimation techniques are sensitive to the form employed for modeling the dose response. If the chosen parametric model is in fact misspecified, this can lead to inaccurate low-dose inferences. Indeed, avoiding the impact of model selection was one early motivating issue behind development of the BMD technology. Here, we apply a frequentist model averaging approach for estimating benchmark doses, based on information-theoretic weights. We explore how the strategy can be used to build one-sided lower confidence limits on the BMD, and we study the confidence limits' small-sample properties via a simulation study. An example from environmental carcinogenicity testing illustrates the calculations. It is seen that application of this information-theoretic, model averaging methodology to benchmark analysis can improve environmental health planning and risk regulation when dealing with low-level exposures to hazardous agents.

Accounting for extra-binomial variability with differentially expressed genetic pathway data: a collaborative bioinformatic study.

We describe a collaborative project involving faculty and students in a university bioinformatics/biostatistics center. The project focuses on identification of differentially expressed gene sets ("pathways") in subjects expressing a disease state, medical intervention, or other distinguishable condition. The key feature of the endeavor is the data structure presented to the team: a single cohort of subjects with two samples taken from each subject - one for each of two differing conditions without replication. This particular structure leads to essentially a cohort of 2×2 contingency tables, where each table compares the differential gene state with the pathway condition. Recognizing that correlations both within and between pathway responses can disrupt standard 2×2 table analytics, we develop methods for analyzing this data structure in the presence of complicated intra-table correlations. These provide some convenient approaches for this problem, using design effect adjustments from sample survey theory and manipulations of the summary 2×2 table counts. Monte Carlo simulations show that the methods operate extremely well, validating their use in practice. In the end, the collaborative connections among the team members led to solutions no one of us would have envisioned separately.

Benchmark dose profiles for joint-action quantal data in quantitative risk assessment.

Benchmark analysis is a widely used tool in public health risk analysis. Therein, estimation of minimum exposure levels, called Benchmark Doses (BMDs), that induce a prespecified Benchmark Response (BMR) is well understood for the case of an adverse response to a single stimulus. For cases where two agents are studied in tandem, however, the benchmark approach is far less developed. This article demonstrates how the benchmark modeling paradigm can be expanded from the single-dose setting to joint-action, two-agent studies. Focus is on response outcomes expressed as proportions. Extending the single-exposure setting, representations of risk are based on a joint-action dose-response model involving both agents. Based on such a model, the concept of a benchmark profile (BMP) - a two-dimensional analog of the single-dose BMD at which both agents achieve the specified BMR - is defined for use in quantitative risk characterization and assessment. The resulting, joint, low-dose guidelines can improve public health planning and risk regulation when dealing with low-level exposures to combinations of hazardous agents.

Nonparametric estimation of benchmark doses in environmental risk assessment.

An important statistical objective in environmental risk analysis is estimation of minimum exposure levels, called benchmark doses (BMDs), that induce a pre-specified benchmark response in a dose-response experiment. In such settings, representations of the risk are traditionally based on a parametric dose-response model. It is a well-known concern, however, that if the chosen parametric form is misspecified, inaccurate and possibly unsafe low-dose inferences can result. We apply a nonparametric approach for calculating benchmark doses, based on an isotonic regression method for dose-response estimation with quantal-response data (Bhattacharya and Kong, 2007). We determine the large-sample properties of the estimator, develop bootstrap-based confidence limits on the BMDs, and explore the confidence limits' small-sample properties via a short simulation study. An example from cancer risk assessment illustrates the calculations.

The Impact of Model Uncertainty on Benchmark Dose Estimation.

We study the popular benchmark dose (BMD) approach for estimation of low exposure levels in toxicological risk assessment, focusing on dose-response experiments with quantal data. In such settings, representations of the risk are traditionally based on a specified, parametric, dose-response model. It is a well-known concern, however, that uncertainty can exist in specification and selection of the model. If the chosen parametric form is in fact misspecified, this can lead to inaccurate, and possibly unsafe, lowdose inferences. We study the effects of model selection and possible misspecification on the BMD, on its corresponding lower confidence limit (BMDL), and on the associated extra risks achieved at these values, via large-scale Monte Carlo simulation. It is seen that an uncomfortably high percentage of instances can occur where the true extra risk at the BMDL under a misspecified or incorrectly selected model can surpass the target BMR, exposing potential dangers of traditional strategies for model selection when calculating BMDs and BMDLs.

Adjusting statistical benchmark risk analysis to account for non-spatial autocorrelation, with application to natural hazard risk assessment.

We develop and study a quantitative, interdisciplinary strategy for conducting statistical risk analyses within the 'benchmark risk' paradigm of contemporary risk assessment when potential autocorrelation exists among sample units. We use the methodology to explore information on vulnerability to natural hazards across 3108 counties in the conterminous 48 US states, applying a place-based resilience index to an existing knowledgebase of hazardous incidents and related human casualties. An extension of a centered autologistic regression model is applied to relate local, county-level vulnerability to hazardous outcomes. Adjustments for autocorrelation embedded in the resiliency information are applied via a novel, non-spatial neighborhood structure. Statistical risk-benchmarking techniques are then incorporated into the modeling framework, wherein levels of high and low vulnerability to hazards are identified.

A sensitivity analysis of the social vulnerability index.

The Social Vulnerability Index (SoVI), created by Cutter et al. (2003), examined the spatial patterns of social vulnerability to natural hazards at the county level in the United States in order to describe and understand the social burdens of risk. The purpose of this article is to examine the sensitivity of quantitative features underlying the SoVI approach to changes in its construction, the scale at which it is applied, the set of variables used, and to various geographic contexts. First, the SoVI was calculated for multiple aggregation levels in the State of South Carolina and with a subset of the original variables to determine the impact of scalar and variable changes on index construction. Second, to test the sensitivity of the algorithm to changes in construction, and to determine if that sensitivity was constant in various geographic contexts, census data were collected at a submetropolitan level for three study sites: Charleston, SC; Los Angeles, CA; and New Orleans, LA. Fifty-four unique variations of the SoVI were calculated for each study area and evaluated using factorial analysis. These results were then compared across study areas to evaluate the impact of changing geographic context. While decreases in the scale of aggregation were found to result in decreases in the variance explained by principal components analysis (PCA), and in increases in the variance of the resulting index values, the subjective interpretations yielded from the SoVI remained fairly stable. The algorithm's sensitivity to certain changes in index construction differed somewhat among the study areas. Understanding the impacts of changes in index construction and scale are crucial in increasing user confidence in metrics designed to represent the extremely complex phenomenon of social vulnerability.

Simultaneous Confidence Bands for Abbott-Adjusted Quantal Response Models.

We study use of a Scheffé-style simultaneous confidence band as applied to low-dose risk estimation with quantal response data. We consider two formulations for the dose-response risk function, an Abbott-adjusted Weibull model and an Abbott-adjusted log-logistic model. Using the simultaneous construction, we derive methods for estimating upper confidence limits on predicted extra risk and, by inverting the upper bands on risk, lower bounds on the benchmark dose, or BMD, at which a specific level of 'benchmark risk' is attained. Monte Carlo evaluations explore the operating characteristics of the simultaneous limits.

Testing for differentially expressed genetic pathways with single-subject N-of-1 data in the presence of inter-gene correlation.

Modern precision medicine increasingly relies on molecular data analytics, wherein development of interpretable single-subject ("N-of-1") signals is a challenging goal. A previously developed global framework, N-of-1- pathways, employs single-subject gene expression data to identify differentially expressed gene set pathways in an individual patient. Unfortunately, the limited amount of data within the single-subject, N-of-1 setting makes construction of suitable statistical inferences for identifying differentially expressed gene set pathways difficult, especially when non-trivial inter-gene correlation is present. We propose a method that exploits external information on gene expression correlations to cluster positively co-expressed genes within pathways, then assesses differential expression across the clusters within a pathway. A simulation study illustrates that the cluster-based approach exhibits satisfactory false-positive error control and reasonable power to detect differentially expressed gene set pathways. An example with a single N-of-1 patient's triple negative breast cancer data illustrates use of the methodology.

Autologistic models for benchmark risk or vulnerability assessment of urban terrorism outcomes.

We develop a quantitative methodology to characterize vulnerability among 132 U.S. urban centers ('cities') to terrorist events, applying a place-based vulnerability index to a database of terrorist incidents and related human casualties. A centered autologistic regression model is employed to relate urban vulnerability to terrorist outcomes and also to adjust for autocorrelation in the geospatial data. Risk-analytic 'benchmark' techniques are then incorporated into the modeling framework, wherein levels of high and low urban vulnerability to terrorism are identified. This new, translational adaptation of the risk-benchmark approach, including its ability to account for geospatial autocorrelation, is seen to operate quite flexibly in this socio-geographic setting.

Ergonomic decision-making: a conceptual framework for experienced practitioners from backgrounds in industrial engineering and physical therapy.

Ergonomists play an important role in preventing and controlling work-related injuries and illnesses, yet little is known about the decision-making processes that lead to their recommendations. This study (1) generated a data-grounded conceptual framework, based on schema theory, for ergonomic decision-making by experienced practitioners in the USA and (2) assessed the adequacy of that framework for describing the decision-making of ergonomics practitioners from backgrounds in industrial engineering (IE) and physical therapy (PT). A combination of qualitative and quantitative analyses, within and across 54 decision-making situations derived from in-depth interviews with 21 practitioners, indicated that a single framework adequately describes the decision-making of experienced practitioners from these backgrounds. Results indicate that demands of the practitioner environment and practitioner factors such as personality more strongly influence the decision-making of experienced ergonomics practitioners than does practitioner background in IE or PT.