Partial order relation-based gene ontology embedding improves protein function prediction.

Protein annotation has long been a challenging task in computational biology. Gene Ontology (GO) has become one of the most popular frameworks to describe protein functions and their relationships. Prediction of a protein annotation with proper GO terms demands high-quality GO term representation learning, which aims to learn a low-dimensional dense vector representation with accompanying semantic meaning for each functional label, also known as embedding. However, existing GO term embedding methods, which mainly take into account ancestral co-occurrence information, have yet to capture the full topological information in the GO-directed acyclic graph (DAG). In this study, we propose a novel GO term representation learning method, PO2Vec, to utilize the partial order relationships to improve the GO term representations. Extensive evaluations show that PO2Vec achieves better outcomes than existing embedding methods in a variety of downstream biological tasks. Based on PO2Vec, we further developed a new protein function prediction method PO2GO, which demonstrates superior performance measured in multiple metrics and annotation specificity as well as few-shot prediction capability in the benchmarks. These results suggest that the high-quality representation of GO structure is critical for diverse biological tasks including computational protein annotation.

Dual-agent dose-finding in Phase I clinical trial-An extension of rapid enrollment design.

Dual-agent treatment has become more and more popular in clinical trials. We have developed an approach called rapid enrollment dual-agent design (REDD) for dose-finding in Phase I clinical trials. This approach aims to administer treatment to patients using a dose combination that is highly probable to be the target dose combination. Unlike other non-model-based designs, rapid enrollment designs (RED and REDD) do not require waiting for all patients to complete an assessment before the assignment of the next participant. Simulations showed that across several scenarios, the average performance of REDD is comparable to that of the Bayesian optimal interval (BOIN) design and the partial order continual reassessment method (POCRM). The simulation results of REDD for late-onset toxicity assessments demonstrated that assigning patients to a dose combination as they are being enrolled, without waiting for the most recent cohort of patients to complete their follow-up, does not significantly compromise the quality of the maximum tolerated dose (MTD) estimation. Instead, it saves a considerable amount of time in clinical trial enrollment. User-friendly online applications have also been created to further facilitate the adoption of rapid enrollment designs in Phase I trials. In summary, being similar to BOIN and POCRM in performance, REDD is an approach that is easily comprehensible, straightforward to implement and offers an advantage of enrolling patients without having to wait for all current patients to complete their follow-ups for toxicity.

CRM and partial order CRM with adaptive rescaling for dose-finding in immunotherapy trials with a continuous outcome.

In many phase 1 oncology trials of immunotherapies, no dose-limiting toxicities are observed and the maximum tolerated dose cannot be identified. In these settings, dose-finding can be guided by a biomarker of response rather than the occurrences of dose-limiting toxicity. The recommended phase 2 dose can be defined as the dose with mean response equal to a prespecified value of a continuous response biomarker. To target the mean of a continuous biomarker, we build on the idea of the continual reassessment method and the quasi-Bernoulli likelihood. We extend the design to a problem of finding the recommended phase 2 dose combination in a trial with multiple immunotherapies.

Sample size formula for general win ratio analysis.

Originally proposed for the analysis of prioritized composite endpoints, the win ratio has now expanded into a broad class of methodology based on general pairwise comparisons. Complicated by the non-i.i.d. structure of the test statistic, however, sample size estimation for the win ratio has lagged behind. In this article, we develop general and easy-to-use formulas to calculate sample size for win ratio analysis of different outcome types. In a nonparametric setting, the null variance of the test statistic is derived using U-statistic theory in terms of a dispersion parameter called the standard rank deviation, an intrinsic characteristic of the null outcome distribution and the user-defined rule of comparison. The effect size can be hypothesized either on the original scale of the population win ratio, or on the scale of a "usual" effect size suited to the outcome type. The latter approach allows one to measure the effect size by, for example, odds/continuation ratio for totally/partially ordered outcomes and hazard ratios for composite time-to-event outcomes. Simulation studies show that the derived formulas provide accurate estimates for the required sample size across different settings. As illustration, real data from two clinical studies of hepatic and cardiovascular diseases are used as pilot data to calculate sample sizes for future trials.

Consistency of the CRM when the dose-toxicity curve is not monotone and its application to the POCRM.

The continual reassessment method (CRM) is a well-known design for dose-finding trials with the goal of estimating the maximum tolerated dose (MTD), the dose with a given probability of toxicity. The standard assumption is that the probability of toxicity monotonically increases with dose. We show that the CRM can still be consistent and correctly identify the MTD even when the dose-toxicity curve is not monotone as long as there is monotonicity of the true toxicity probabilities right below and right above the true MTD. In the case of multiple therapies, where it is unclear how to order combinations of dose levels of multiple therapies, our findings provide insight into the performance of the partial order CRM (POCRM). To select the correct dose combination at the end of a trial, the POCRM does not have to select a monotone ordering of drug combinations. We illustrate the connection between our results for the CRM with a nonmonotone dose-toxicity curve and the POCRM via simulations.

A partial order and cluster-similarity metric on rooted phylogenetic trees.

Metrics on rooted phylogenetic trees are integral to a number of areas of phylogenetic analysis. Cluster-similarity metrics have recently been introduced in order to limit skew in the distribution of distances, and to ensure that trees in the neighbourhood of each other have similar hierarchies. In the present paper we introduce a new cluster-similarity metric on rooted phylogenetic tree space that has an associated local operation, allowing for easy calculation of neighbourhoods, a trait that is desirable for MCMC calculations. The metric is defined by the distance on the Hasse diagram induced by a partial order on the set of rooted phylogenetic trees, itself based on the notion of a hierarchy-preserving map between trees. The partial order we introduce is a refinement of the well-known refinement order on hierarchies. Both the partial order and the hierarchy-preserving maps may also be of independent interest.

An efficient, large-scale, non-lattice-detection algorithm for exhaustive structural auditing of biomedical ontologies.

One of the basic challenges in developing structural methods for systematic audition on the quality of biomedical ontologies is the computational cost usually involved in exhaustive sub-graph analysis. We introduce ANT-LCA, a new algorithm for computing all non-trivial lowest common ancestors (LCA) of each pair of concepts in the hierarchical order induced by an ontology. The computation of LCA is a fundamental step for non-lattice approach for ontology quality assurance. Distinct from existing approaches, ANT-LCA only computes LCAs for non-trivial pairs, those having at least one common ancestor. To skip all trivial pairs that may be of no practical interest, ANT-LCA employs a simple but innovative algorithmic strategy combining topological order and dynamic programming to keep track of non-trivial pairs. We provide correctness proofs and demonstrate a substantial reduction in computational time for two largest biomedical ontologies: SNOMED CT and Gene Ontology (GO). ANT-LCA achieved an average computation time of 30 and 3 sec per version for SNOMED CT and GO, respectively, about 2 orders of magnitude faster than the best known approaches. Our algorithm overcomes a fundamental computational barrier in sub-graph based structural analysis of large ontological systems. It enables the implementation of a new breed of structural auditing methods that not only identifies potential problematic areas, but also automatically suggests changes to fix the issues. Such structural auditing methods can lead to more effective tools supporting ontology quality assurance work.

Implementing the DF4 in a robust model, allowing for enhanced comparison, prioritisation and grouping of Nanomaterials.

It is here shown how partial order can be used to provide a robust and consistent implementation of the DF4 approach which provides unbiased information enabling comparison and open up the possibility for grouping. The approach is based on few assumptions, works well with the data, can include different types of input parameters, and can provide fundamental information about the ranks of tested materials. It is shown that the materials in many cases are below one threshold within a tier, but above another threshold within the same tier. It is also observed that the ranks of the materials can differ between tiers, although this is less relevant for DF4 since parameters evaluation may be hierarchical.

Isotonic designs for phase I trials in partially ordered groups.

BACKGROUND/AIMS: Dose-finding trials can be conducted such that patients are first stratified into multiple risk groups before doses are allocated. The risk groups are often completely ordered in that, for a fixed dose, the probability of toxicity is monotonically increasing across groups. In some trials, the groups are only partially ordered. For example, one of several groups in a trial may be known to have the least risk of toxicity for a given dose, but the ordering of the risk among the remaining groups may not be known. The aim of the article is to introduce a method for designing dose-finding trials of cytotoxic agents in completely or partially ordered groups of patients. METHODS: This article presents a method for dose-finding that combines previously proposed mathematical models, augmented with results using order restricted inference. The resulting method is computationally convenient and allows for dose-finding in trials with completely or partially ordered groups. Extensive simulations are done to evaluate the performance of the method, using randomly generated dose-toxicity curves where, within each group, the risk of toxicity is an increasing function of dose. RESULTS: Our simulations show that the hybrid method, in which order-restricted estimation is applied to parameters of a parsimonious mathematical model, gives results that are similar to previously proposed methods for completely ordered groups. Our method generalizes to a wide range of partial orders among the groups. CONCLUSION: The problem of dose-finding in partially ordered groups has not been extensively studied in the statistical literature. The proposed method is computationally feasible, and provides a potential solution to the design of dose-finding studies in completely or partially ordered groups.

Comparing the Efficiency of Hospitals in Italy and Germany: Nonparametric Conditional Approach Based on Partial Frontier.

Traditional nonparametric frontier techniques to measure hospital efficiency have been criticized for their deterministic nature and the inability to incorporate external factors into the analysis. Moreover, efficiency estimates represent a relative measure meaning that the implications from a hospital efficiency analysis based on a single-country dataset are limited by the availability of suitable benchmarks. Our first objective is to demonstrate the application of advanced nonparametric methods that overcome the limitations of the traditional nonparametric frontier techniques. Our second objective is to provide guidance on how an international comparison of hospital efficiency can be conducted using the example of two countries: Italy and Germany. We rely on a partial frontier of order-m to obtain efficiency estimates robust to outliers and extreme values. We use the conditional approach to incorporate hospital and regional characteristics into the estimation of efficiency. The obtained conditional efficiency estimates may deviate from the traditional unconditional efficiency estimates, which do not account for the potential influence of operational environment on the production possibilities. We nonparametrically regress the ratios of conditional to unconditional efficiency estimates to examine the relation of hospital and regional characteristics with the efficiency performance. We show that the two countries can be compared against a common frontier when the challenges of international data compatibility are successfully overcome. The results indicate that there are significant differences in the production possibilities of Italian and German hospitals. Moreover, hospital characteristics, particularly bed-size category, ownership status, and specialization, are significantly related to differences in efficiency performance across the analyzed hospitals.

CombiSimilarity, an innovative method to compare environmental and health data sets with different attribute sizes example: eighteen Organochlorine Pesticides in soil and human breast milk samples.

Human health and the health of the environment have entwined. In this paper we underpin this position by presenting a modeling approach named CombiSimilarity, which has been developed by the first author in the software tool PyHasse comprising a wide variety of partial ordering tools. A case study of 18 Organochlorine Pesticides (OCPs) detected in soil as well as in human breast milk samples in the Taurus Mountains in Turkey is carried out. Seven soil samples and 44 breast milk samples were measured. We seek to answer the question whether the contamination pattern in breast milk is associated with the contamination pattern in soil by studying the mutual quantitative relationships of the chemicals involved. We could demonstrate that there is a similarity with respect to the concentration profiles between the soil and breast milk pollution. Therefore the hypothesis may be formulated that the concentrations of chemicals in the milk samples are strongly related to the soil contamination. This supports the concept that soil could be a surrogate for human exposure at background locations.

Adaptive penalty-based neurodynamic approach for nonsmooth interval-valued optimization problem.

The complex and diverse practical background drives this paper to explore a new neurodynamic approach (NA) to solve nonsmooth interval-valued optimization problems (IVOPs) constrained by interval partial order and more general sets. On the one hand, to deal with the uncertainty of interval-valued information, the LU-optimality condition of IVOPs is established through a deterministic form. On the other hand, according to the penalty method and adaptive controller, the interval partial order constraint and set constraint are punished by one adaptive parameter, which is a key enabler for the feasibility of states while having a lower solution space dimension and avoiding estimating exact penalty parameters. Through nonsmooth analysis and Lyapunov theory, the proposed adaptive penalty-based neurodynamic approach (APNA) is proven to converge to an LU-solution of the considered IVOPs. Finally, the feasibility of the proposed APNA is illustrated by numerical simulations and an investment decision-making problem.

Ranking of concern, based on environmental indexes, for pharmaceutical and personal care products: an application to the Spanish case.

A wide range of Pharmaceuticals and Personal Care Products (PPCPs) are present in the environment, and many of their adverse effects are unknown. The emergence of new compounds or changes in regulations have led to dynamical studies of occurrence, impact and treatment, which consider geographical areas and trends in consumption and innovation in the pharmaceutical industry. A Quantitative study of Structure-Activity Relationship ((Q)SAR) was performed to assess the possible adverse effects of ninety six PPCPs and metabolites with negligible experimental data and establish a ranking of concern, which was supported by the EPA EPI Suite™ interface. The environmental and toxicological indexes, the persistence (P), the bioaccumulation (B), the toxicity (T) (extensive) and the occurrence in Spanish aquatic environments (O) (intensive) were evaluated. The most hazardous characteristics in the largest number of compounds were generated by the P index, followed by the T and B indexes. A high number of metabolites has a concern score equal to or greater than their parent compounds. Three PBT and OPBT rankings of concern were proposed using the total and partial ranking method (supported by a Hasse diagram) by the Decision Analysis by Ranking Techniques (DART) tool, which was recently recommended by the European Commission. An analysis of the sensibility of the relative weights of these indexes has been conducted. Hormones, antidepressants (and their metabolites), blood lipid regulators and all of the personal care products considered in this study were at the highest levels of risk according to the PBT and OPBT total rankings. Furthermore, when the OPBT partial ranking was performed, X-ray contrast media, H2 blockers and some antibiotics were included at the highest level of concern. It is important to improve and incorporate useful indexes for the predicted environmental impact of PPCPs and metabolites and thus focus experimental analysis on the compounds that require urgent attention.

Visualizing genomic data: The mixing perspective.

We report on a novel way to visualize genomic data. By considering genome coding sequences, cds, as sets of the N=61 non-stop codons, one obtains a partition of the total number of codons in each cds. Partitions exhibit a statistical property known as mixing character which characterizes how mixed the partition is. Mixing characters have been shown mathematically to exhibit a partial order known as majorization (Ruch, 1975). In previous work (Seitz and Kirwan, 2022) we developed an approach that combined mixing and entropy that is visualized as a scatter plot. If we consider all 1,121,505 partitions of 61 codons, this produces a plot we call the theoretical mixing space, TGMS. A normalization procedure is developed here and applied to real genomic data to produce the genome mixing signature, GMS. Example GMS's of 19 species, including Homo sapiens, are shown and discussed.

[Development and application of visual analysis teaching software for acupoint compatibility laws].

A user-friendly teaching software for visual analysis of acupoint compatibility laws has been developed based on the principles of partial order mathematics. This software is designed to provide auxiliary teaching of structured organization and visualization of law knowledge of compatibility data of acupuncture and moxibustion prescriptions from ancient texts, textbooks, and clinical case records. The software is installed as a plugin in the Microsoft Office Excel, allowing the generation of visually appealing graphs and associated rules that align with the cognitive patterns of teachers and students majoring in acupuncture and moxibustion. Its aim is to facilitate the discovery and analysis of underlying patterns and structured knowledge embedded in acupoint compatibility data, thus contributing to the enhancement of teaching effectiveness in acupoint compatibility.

Towards a partial order graph for interactive pharmacophore exploration: extraction of pharmacophores activity delta.

This paper presents a novel approach called Pharmacophore Activity Delta for extracting outstanding pharmacophores from a chemogenomic dataset, with a specific focus on a kinase target known as BCR-ABL. The method involves constructing a Hasse diagram, referred to as the pharmacophore network, by utilizing the subgraph partial order as an initial step, leading to the identification of pharmacophores for further evaluation. A pharmacophore is classified as a 'Pharmacophore Activity Delta' if its capability to effectively discriminate between active vs inactive molecules significantly deviates (by at least δ standard deviations) from the mean capability of its related pharmacophores. Among the 1479 molecules associated to BCR-ABL binding data, 130 Pharmacophore Activity Delta were identified. The pharmacophore network reveals distinct regions associated with active and inactive molecules. The study includes a discussion on representative key areas linked to different pharmacophores, emphasizing structure-activity relationships.

Quasi-partial order continual reassessment method: Applying toxicity scores to cancer dose-finding drug combination trials.

The primary endpoint of most dose-finding cancer trials is patient toxicity, and the primary goal is to identify the maximum tolerated dose (MTD), that is, the highest dose that falls below or within a pre-specified toxicity tolerability threshold. Conventionally, dose-finding methods have utilized a binary toxicity endpoint based on whether or not a patient experiences a dose limiting-toxicity (DLT). Improving upon this, in recent years several methods have been developed for modeling toxicity scores, a novel continuous endpoint designed to more precisely estimate patient toxicity burden. Separately, drug-combination trials have become increasingly prevalent, and due to added complexities regarding estimating 'true' dose ordering and potential for more complex patient toxicity profiles, provide an ideal setting which may benefit from the improved precision of toxicity scores. In this paper, we merge two frameworks based on the Continual Reassessment Method (CRM) - the Quasi-CRM and the Partial Order CRM (POCRM) - to propose a novel approach for modeling toxicity scores in a combination-trial setting. We demonstrate that utilizing toxicity scores has the potential to greatly improve correct dose-selection over a variety of trial scenarios. We further present a simple adaptation to the toxicity-score model to control for potential over-dosing issues such that it adheres to the conventional DLT definition and will, at worst, perform equivalently to that of the traditional binary DLT framework. We demonstrate that extending toxicity scores to the combination-trial setting offers potential for improvement over the conventional binary endpoint models.

[Visualization and application method of acupuncture-moxibustion knowledge of senile dementia in ancient books based on partial order structure].

Acupuncture-moxibustion has affirmative curative effect in the prevention and treatment of senile dementia. Starting from the literature research, a visualization and application method of acupuncture-moxibustion knowledge of senile dementia in ancient books based on partial order structure is proposed. This method could extract and integrate the acupuncture-moxibustion knowledge of senile dementia contained in ancient books of traditional Chinese medicine, and establish a standardized, structured and visual knowledge graph. Applying this method to knowledge visual analysis and clinical auxiliary guidance could provide reference for combing the knowledge of ancient books of traditional Chinese medicine and transforming the knowledge of ancient books into clinical application.

Using the Evolutionary History of Proteins to Engineer Insertion-Deletion Mutants from Robust, Ancestral Templates Using Graphical Representation of Ancestral Sequence Predictions (GRASP).

Analyzing the natural evolution of proteins by ancestral sequence reconstruction (ASR) can provide valuable information about the changes in sequence and structure that drive the development of novel protein functions. However, ASR has also been used as a protein engineering tool, as it often generates thermostable proteins which can serve as robust and evolvable templates for enzyme engineering. Importantly, ASR has the potential to provide an insight into the history of insertions and deletions that have occurred in the evolution of a protein family. Indels are strongly associated with functional change during enzyme evolution and represent a largely unexplored source of genetic diversity for designing proteins with novel or improved properties. Current ASR methods differ in the way they handle indels; inclusion or exclusion of indels is often managed subjectively, based on assumptions the user makes about the likelihood of each recombination event, yet most currently available ASR tools provide limited, if any, opportunities for evaluating indel placement in a reconstructed sequence. Graphical Representation of Ancestral Sequence Predictions (GRASP) is an ASR tool that maps indel evolution throughout a reconstruction and enables the evaluation of indel variants. This chapter provides a general protocol for performing a reconstruction using GRASP and using the results to create indel variants. The method addresses protein template selection, sequence curation, alignment refinement, tree building, ancestor reconstruction, evaluation of indel variants and approaches to library development.

Psi-Caller: A Lightweight Short Read-Based Variant Caller With High Speed and Accuracy.

With the rapid development of short-read sequencing technologies, many population-scale resequencing studies have been carried out to study the associations between human genome variants and various phenotypes in recent years. Variant calling is one of the core bioinformatics tasks in such studies to comprehensively discover genomic variants in sequenced samples. Many efforts have been made to develop short read-based variant calling approaches; however, state-of-the-art tools are still computationally expensive. Meanwhile, cutting-edge genomics studies also have higher requirements on the yields of variant calling. Herein, we propose Partial-Order Alignment-based single nucleotide polymorphism (SNV) and Indel caller (Psi-caller), a lightweight variant calling algorithm that simultaneously achieves high performance and yield. Mainly, Psi-caller recognizes and divides the candidate variant site into three categories according to the complexity and location of the signatures and employs various methods including binomial model, partial-order alignment, and de Bruijn graph-based local assembly to handle various categories of candidate variant sites to call and genotype SNVs/Indels, respectively. Benchmarks on simulated and real short-read sequencing data sets demonstrate that Psi-caller is times faster than state-of-the-art tools with higher or equal sensitivity and accuracy. It has the potential to well handle large-scale data sets in cutting-edge genomics studies.