Estimation and construction of confidence intervals for biomarker cutoff-points under the shortest Euclidean distance from the ROC surface to the perfection corner.

Pancreatic ductal adenocarcinoma (PDAC) is an aggressive type of cancer with a 5-year survival rate of less than 5%. As in many other diseases, its diagnosis might involve progressive stages. It is common that in biomarker studies referring to PDAC, recruitment involves three groups: healthy individuals, patients that suffer from chronic pancreatitis, and PDAC patients. Early detection and accurate classification of the state of the disease are crucial for patients' successful treatment. ROC analysis is the most popular way to evaluate the performance of a biomarker and the Youden index is commonly employed for cutoff derivation. The so-called generalized Youden index has a drawback in the three-class case of not accommodating the full data set when estimating the optimal cutoffs. In this article, we explore the use of the Euclidean distance of the ROC to the perfection corner for the derivation of cutoffs in trichotomous settings. We construct an inferential framework that involves both parametric and nonparametric techniques. Our methods can accommodate the full information of a given data set and thus provide more accurate estimates in terms of the decision-making cutoffs compared with a Youden-based strategy. We evaluate our approaches through extensive simulations and illustrate them on a PDAC biomarker study.

Combining multiple biomarkers linearly to minimize the Euclidean distance of the closest point on the receiver operating characteristic surface to the perfection corner in trichotomous settings.

The performance of individual biomarkers in discriminating between two groups, typically the healthy and the diseased, may be limited. Thus, there is interest in developing statistical methodologies for biomarker combinations with the aim of improving upon the individual discriminatory performance. There is extensive literature referring to biomarker combinations under the two-class setting. However, the corresponding literature under a three-class setting is limited. In our study, we provide parametric and nonparametric methods that allow investigators to optimally combine biomarkers that seek to discriminate between three classes by minimizing the Euclidean distance from the receiver operating characteristic surface to the perfection corner. Using this Euclidean distance as the objective function allows for estimation of the optimal combination coefficients along with the optimal cutoff values for the combined score. An advantage of the proposed methods is that they can accommodate biomarker data from all three groups simultaneously, as opposed to a pairwise analysis such as the one implied by the three-class Youden index. We illustrate that the derived true classification rates exhibit narrower confidence intervals than those derived from the Youden-based approach under a parametric, flexible parametric, and nonparametric kernel-based framework. We evaluate our approaches through extensive simulations and apply them to real data sets that refer to liver cancer patients.

Statistical assessment of the prognostic and the predictive value of biomarkers-A biomarker assessment framework with applications to traumatic brain injury biomarker studies.

Studies that investigate the performance of prognostic and predictive biomarkers are commonplace in medicine. Evaluating the performance of biomarkers is challenging in traumatic brain injury (TBI) and other conditions when both the time factor (i.e. time from injury to biomarker measurement) and different levels or doses of treatments are in play. Such factors need to be accounted for when assessing the biomarker's performance in relation to a clinical outcome. The Hyperbaric Oxygen in Brain Injury Treatment (HOBIT) trial, a phase II randomized control clinical trial seeks to determine the dose of hyperbaric oxygen therapy (HBOT) for treating severe TBI that has the highest likelihood of demonstrating efficacy in a phase III trial. Hyperbaric Oxygen in Brain Injury Treatment will study up to 200 participants with severe TBI. This paper discusses the statistical approaches to assess the prognostic and predictive performance of the biomarkers studied in this trial, where prognosis refers to the association between a biomarker and the clinical outcome while the predictiveness refers to the ability of the biomarker to identify patient subgroups that benefit from therapy. Analyses based on initial biomarker levels accounting for different levels of HBOT and other baseline clinical characteristics, and analyses of longitudinal changes in biomarker levels are discussed from a statistical point of view. Methods for combining biomarkers that are of complementary nature are also considered and the relevant algorithms are illustrated in detail along with an extensive simulation study that assesses the performance of the statistical methods. Even though the discussed approaches are motivated by the HOBIT trial, their applications are broader. They can be applied in studies assessing the predictiveness and prognostic ability of biomarkers in relation to a well-defined therapeutic intervention and clinical outcome.

Rheostat functional outcomes occur when substitutions are introduced at nonconserved positions that diverge with speciation.

When amino acids vary during evolution, the outcome can be functionally neutral or biologically-important. We previously found that substituting a subset of nonconserved positions, "rheostat" positions, can have surprising effects on protein function. Since changes at rheostat positions can facilitate functional evolution or cause disease, more examples are needed to understand their unique biophysical characteristics. Here, we explored whether "phylogenetic" patterns of change in multiple sequence alignments (such as positions with subfamily specific conservation) predict the locations of functional rheostat positions. To that end, we experimentally tested eight phylogenetic positions in human liver pyruvate kinase (hLPYK), using 10-15 substitutions per position and biochemical assays that yielded five functional parameters. Five positions were strongly rheostatic and three were non-neutral. To test the corollary that positions with low phylogenetic scores were not rheostat positions, we combined these phylogenetic positions with previously-identified hLPYK rheostat, "toggle" (most substitution abolished function), and "neutral" (all substitutions were like wild-type) positions. Despite representing 428 variants, this set of 33 positions was poorly statistically powered. Thus, we turned to the in vivo phenotypic dataset for E. coli lactose repressor protein (LacI), which comprised 12-13 substitutions at 329 positions and could be used to identify rheostat, toggle, and neutral positions. Combined hLPYK and LacI results show that positions with strong phylogenetic patterns of change are more likely to exhibit rheostat substitution outcomes than neutral or toggle outcomes. Furthermore, phylogenetic patterns were more successful at identifying rheostat positions than were co-evolutionary or eigenvector centrality measures of evolutionary change.