Mixed cumulative probit: a multivariate generalization of transition analysis that accommodates variation in the shape, spread and structure of data

Biological data are frequently nonlinear, heteroscedastic and conditionally dependent, and often researchers deal with missing data. To account for characteristics common in biological data in one algorithm, we developed the mixed cumulative probit (MCP), a novel latent trait model that is a formal generalization of the cumulative probit model usually used in transition analysis. Specifically, the MCP accommodates heteroscedasticity, mixtures of ordinal and continuous variables, missing values, conditional dependence and alternative specifications of the mean response and noise response. Cross-validation selects the best model parameters (mean response and the noise response for simple models, as well as conditional dependence for multivariate models), and the Kullback-Leibler divergence evaluates information gain during posterior inference to quantify mis-specified models (conditionally dependent versus conditionally independent). Two continuous and four ordinal skeletal and dental variables collected from 1296 individuals (aged birth to 22 years) from the Subadult Virtual Anthropology Database are used to introduce and demonstrate the algorithm. In addition to describing the features of the MCP, we provide material to help fit novel datasets using the MCP. The flexible, general formulation with model selection provides a process to robustly identify the modelling assumptions that are best suited for the data at hand.

A new Bayesian procedure for the estimation of the referees' decision thresholds and agreement. The case of professional handball refereeing

In double refereeing, agreement between referees is fundamental for the achievement of a flawless and smooth refereeing activity. Nonetheless, the agreeement can be affected by several external and internal factors, with a negative impact on the consistency of the refereeing and the fluidity of the game. The referee's Decision Threshold (DT) is the limit above which the evidence of a foul results in the call of an infraction by the referee. It represents the individual refereeing style, and it is one of the factors that can contribute to low agreement between the referees. We present an application of a new Bayesian procedure to estimate referee's DT in a typical refereeing task. To this end, 56 italian professional handball (FIGH) referees were asked to evaluate 96 potential foul plays, belonging to four different infraction types: 7-m throw, passive play, offensive foul, disciplinary sanctions. The proposed method provides information about: (i) referee's individual DT; (ii) the agreement between pairs of referees (i.e., one-to-one); (iii) the agreement between each referee and all the other referees (i.e., one-to-total); (iv) the agreement between each referee and a reference referee (i.e., one-to-expert); (v) the proportion of agreement between the referees and a reference referee for each potential foul play. Sport federations would profit by this procedure in different ways: by using the information about the DT to train referees, by detecting referees with a low agreement with their colleagues or with the reference referee, by focusing training on specific plays to improve the arbitration class internal consistency.

Root dentin translucency and age at death estimation in adults using single rooted teeth: Update of the Forensic International Dental Database

Since the publication of Lamendin's age estimation technique, the root dentin translucency has received increasing attention as an important indicator of age. Recently, Parra and colleagues presented the Forensic International Dental Database (FIDB), a proposal to estimate age at death in adults based on Bayes theorem by applying the criteria of Lamendin's technique. The present study aims to update the procedure and to evaluate a new version of the method (named FIDBv2) using two control samples from Colombia and Greece. The performance of this new version was acceptable and suggests that the method is suitable for age at death estimation in adult individuals from different forensic contexts. The best approximations to chronological age were obtained for individuals between 30 and 60 years old, with errors less than 10 years. The age estimations calculated on control samples suggest the adequate performance of FIDBv2 on individuals from varied populations. It can be stated that the FIDBv2 constitutes a solid alternative to be used in contexts where no additional data are available. Here we reinforce the initial idea that this model for estimating age at death in adults may be generalizable to any forensic context in the world.

Retrospective Bayesian Evidence of Null Effect in Two Decades of Alzheimer's Disease Clinical Trials

Despite intense research on Alzheimer's disease, no validated treatment able to reverse symptomatology or stop disease progression exists. A recent systematic review by Kim and colleagues evaluated possible reasons behind the failure of the majority of the clinical trials. As the focus was on methodological factors, no statistical trends were examined in detail. Here, we aim to complete this picture leveraging on Bayesian analysis. In particular, we tested whether the failure of those clinical trials was essentially due to insufficient statistical power or to lack of a true effect. The strong Bayes' Factor obtained supported the latter hypothesis.

Efficacy and safety associated with immune checkpoint inhibitors in unresectable hepatocellular carcinoma: A re-analysis of a meta-analysis

We identified analytic limitations in a recent meta-analysis and re-examined the efficacy and safety associated with immune checkpoint inhibitors (ICIs) in unresectable hepatocellular carcinoma (HCC) compared with standard therapies. Our findings mostly contradict conclusions from the previous study, suggesting the need for continuing the investigation of ICIs in HCC with additional clinical evidence.

Bayesian modelling of phosphorus content in wheat grain using hyperspectral reflectance data

BACKGROUND

As a result of the technological progress, the use of sensors for crop survey has substantially increased, generating valuable information for modelling agricultural data. Plant spectroscopy jointly with statistical modeling can potentially help to assess certain chemical components of interest present in plants, which may be laborious and expensive to obtain by direct measurements. In this research, the phosphorus content in wheat grain is modeled using reflectance information measured by a hyperspectral sensor at different wavelengths. A Bayesian procedure for selecting variables was used to identify the set of the most important spectral bands. Additionally, three different models were evaluated: the first model assumes that the observations are independent, the other two models assume that the observations are spatially correlated: one of the proposed models, assumes spatial dependence using a Conditionally Autoregressive Model (CAR), and the other through an exponential correlogram. The goodness of fit of the models was evaluated by means of the Deviance Information Criterion, and the predictive power is evaluated using cross validation.

RESULTS

We have found that CAR was the model that best fits and predicts the data. Additionally, the selection variable procedure in the CAR model reveals which wavelengths in the range of 500-690 nm are the most important. Comparing the vegetative indices with the CAR model, it was observed that the average correlation of the CAR model exceeded that of the vegetative indices by 23.26%, - 1.2% and 22.78% for the year 2010, 2011 and 2012 respectively; therefore, the use of the proposed methodology outperformed the vegetative indices in prediction.

CONCLUSIONS

The proposal to predict the phosphorus content in wheat grain using Bayesian approach, reflect with the results as a good alternative.

The effect of physician density on colorectal cancer stage at diagnosis: causal inference methods for spatial data applied on regional-level data

BACKGROUND

The early detection of colorectal cancer (CRC) through regular screening decreases its incidence and mortality rates and improves survival rates. Norway has an extremely high percentage of CRC cases diagnosed at late stages, with large variations across municipalities and hospital catchment areas. This study examined whether the availability of physicians related to CRC primary diagnosis and preoperative investigations, or physician density, contributes to the observed geographical differences in late-stage incidence rates.

METHOD

Municipality-level data on CRC stage at diagnosis were obtained from the Cancer Registry of Norway for the period 2012-2020. Physician density was calculated as the number of physicians related to CRC investigations, general practitioners (GPs) and specialists per 10,000 people, using physician counts per municipality and hospital areas from Statistics Norway. The relationship was examined using a novel causal inference method for spatial data-neighbourhood adjustment method via spatial smoothing (NA approach)-which allowed for studying the region-level effect of physician supply on CRC outcome by using spatially referenced data and still providing causal relationships.

RESULTS

According to the NA approach, an increase in one general practitioner per 10,000 people will result in a 3.6% (CI -0.064 to -0.008) decrease in late-stage CRC rates. For specialists, there was no evidence of a significant correlation with late-stage CRC distribution, while for both groups, GPs and specialists combined, an increase of 1 physician per 10,000 people would be equal to an average decrease in late-stage incidence rates by 2.79% (CI -0.055 to -0.001).

CONCLUSION

The study confirmed previous findings that an increase in GP supply will significantly improve CRC outcomes. In contrast to previous research, this study identified the importance of accessibility to both groups of physicians-GPs and specialists. If GPs encounter insufficient workforces in hospitals and long delays in colonoscopy scheduling, they will less often recommend colonoscopy examinations to patients. This study also highlighted the efficiency of the novel methodology for spatially referenced data, which allowed us to study the effect of physician density on cancer outcomes within a causal inference framework.

Sample size calculation for clinical trials analyzed with the meta-analytic-predictive approach

The meta-analytic-predictive (MAP) approach is a Bayesian method to incorporate historical controls in new trials that aims to increase the statistical power and reduce the required sample size. Here we investigate how to calculate the sample size of the new trial when historical data is available, and the MAP approach is used in the analysis. In previous applications of the MAP approach, the prior effective sample size (ESS) acted as a metric to quantify the number of subjects the historical information is worth. However, the validity of using the prior ESS in sample size calculation (i.e., reducing the number of randomized controls by the derived prior ESS) is questionable, because different approaches may yield different values for prior ESS. In this work, we propose a straightforward Monte Carlo approach to calculate the sample size that achieves the desired power in the new trial given available historical controls. To make full use of the available historical information to simulate the new trial data, the control parameters are not taken as a point estimate but sampled from the MAP prior. These sampled control parameters and the MAP prior based on the historical data are then used to derive the statistical power for the treatment effect and the resulting required sample size. The proposed sample size calculation approach is illustrated with real-life data sets with different outcomes from three studies. The results show that this approach to calculating the required sample size for the MAP analysis is straightforward and generic.

IRAA: A statistical tool for investigating a protein-protein interaction interface from multiple structures

Understanding protein-protein interactions (PPIs) is fundamental to infer how different molecular systems work. A major component to model molecular recognition is the buried surface area (BSA), that is, the area that becomes inaccessible to solvent upon complex formation. To date, many attempts tried to connect BSA to molecular recognition principles, and in particular, to the underlying binding affinity. However, the most popular approach to calculate BSA is to use a single (or in some cases few) bound structures, consequently neglecting a wealth of structural information of the interacting proteins derived from ensembles corresponding to their unbound and bound states. Moreover, the most popular method inherently assumes the component proteins to bind as rigid entities. To address the above shortcomings, we developed a Monte Carlo method-based Interface Residue Assessment Algorithm (IRAA), to calculate a combined distribution of BSA for a given complex. Further, we apply our algorithm to human ACE2 and SARS-CoV-2 Spike protein complex, a system of prime importance. Results show a much broader distribution of BSA compared to that obtained from only the bound structure or structures and extended residue members of the interface with implications to the underlying biomolecular recognition. We derive that specific interface residues of ACE2 and of S-protein are consistently highly flexible, whereas other residues systematically show minor conformational variations. In effect, IRAA facilitates the use of all available structural data for any biomolecular complex of interest, extracting quantitative parameters with statistical significance, thereby providing a deeper biophysical understanding of the molecular system under investigation.

Integrating Identification and Quantification Uncertainty for Differential Protein Abundance Analysis with Triqler

Protein quantification for shotgun proteomics is a complicated process where errors can be introduced in each of the steps. Triqler is a Python package that estimates and integrates errors of the different parts of the label-free protein quantification pipeline into a single Bayesian model. Specifically, it weighs the quantitative values by the confidence we have in the correctness of the corresponding PSM. Furthermore, it treats missing values in a way that reflects their uncertainty relative to observed values. Finally, it combines these error estimates in a single differential abundance FDR that not only reflects the errors and uncertainties in quantification but also in identification. In this tutorial, we show how to (1) generate input data for Triqler from quantification packages such as MaxQuant and Quandenser, (2) run Triqler and what the different options are, (3) interpret the results, (4) investigate the posterior distributions of a protein of interest in detail, and (5) verify that the hyperparameter estimations are sensible.

A size-constrained feeding-niche model distinguishes predation patterns between aquatic and terrestrial food webs

Understanding the formation of feeding links provides insights into processes underlying food webs. Generally, predators feed on prey within a certain body-size range, but a systematic quantification of such feeding niches is lacking. We developed a size-constrained feeding-niche (SCFN) model and parameterized it with information on both realized and non-realized feeding links in 72 aquatic and 65 terrestrial food webs. Our analyses revealed profound differences in feeding niches between aquatic and terrestrial predators and variation along a temperature gradient. Specifically, the predator-prey body-size ratio and the range in prey sizes increase with the size of aquatic predators, whereas they are nearly constant across gradients in terrestrial predator size. Overall, our SCFN model well reproduces the feeding relationships and predation architecture across 137 natural food webs (including 3878 species and 136,839 realized links). Our results illuminate the organisation of natural food webs and enables novel trait-based and environment-explicit modelling approaches.

Having a ball: evaluating scoring streaks and game excitement using in-match trend estimation

Many popular sports involve matches between two teams or players where each team have the possibility of scoring points throughout the match. While the overall match winner and result is interesting, it conveys little information about the underlying scoring trends throughout the match. Modeling approaches that accommodate a finer granularity of the score difference throughout the match is needed to evaluate in-game strategies, discuss scoring streaks, teams strengths, and other aspects of the game. We propose a latent Gaussian process to model the score difference between two teams and introduce the Trend Direction Index as an easily interpretable probabilistic measure of the current trend in the match as well as a measure of post-game trend evaluation. In addition we propose the Excitement Trend Index-the expected number of monotonicity changes in the running score difference-as a measure of overall game excitement. Our proposed methodology is applied to all 1143 matches from the 2019-2020 National Basketball Association season. We show how the trends can be interpreted in individual games and how the excitement score can be used to cluster teams according to how exciting they are to watch.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10182-022-00452-w.

Quantifying the Magnitude and Longevity of the Effect of Repetitive Head Impacts in Adolescent Soccer Players: Deleterious Effect of Long Headers Extend Beyond a Month

There is growing interest in the effects of sports-related repetitive head impacts (RHIs) on athletes' cognitive capabilities. This study examines the effect of RHIs in data collected from adolescent athletes to estimate the magnitude and longevity of RHIs on sensorimotor and cognitive performance. A non-linear regression model estimated the longevity of RHI effects by adding a half-life parameter embedded in an exponential decay function. A model estimate of this parameter allows the possibility of RHI effects to attenuate over time and introduces a mechanism to study the cumulative effect of RHIs. The posterior distribution of the half-life parameter associated with short-distance headers (<30 m) is centered around 6 days, whereas the posterior distribution of the half-life parameter associated with long-distance headers extends beyond a month. Additionally, the magnitude of the effect of each short header is around 3 times smaller than that of a long header. The results indicate that, on both tasks, response time (RT) changes after long headers are bigger in magnitude and last longer compared to the effects of short headers. Most important, we demonstrate that deleterious effects of long headers extend beyond 1 month. Although estimates are based on data from a relatively short-duration study with a relatively small sample size, the proposed model provides a mechanism to estimate long-term behavioral slowing from RHIs, which may be helpful to reduce the risk of additional injury. Finally, differences in the longevity of the effects of short and long RHIs may help to explain the large variance found between biomechanical input and clinical outcome in studies of concussion tolerance.

Spectral EEG correlations from the different phases of general anesthesia

Introduction

Electroencephalography (EEG) signals contain transient oscillation patterns commonly used to classify brain states in responses to action, sleep, coma or anesthesia.

Methods

Using a time-frequency analysis of the EEG, we search for possible causal correlations between the successive phases of general anesthesia. We hypothesize that it could be possible to anticipate recovery patterns from the induction or maintenance phases. For that goal, we track the maximum power of the α-band and follow its time course.

Results and discussion

We quantify the frequency shift of the α-band during the recovery phase and the associated duration. Using Pearson coefficient and Bayes factor, we report non-significant linear correlation between the α-band frequency and duration shifts during recovery and the presence of the δ or the α rhythms during the maintenance phase. We also found no correlations between the α-band emergence trajectory and the total duration of the flat EEG epochs (iso-electric suppressions) induced by a propofol bolus injected during induction. Finally, we quantify the instability of the α-band using the mathematical total variation that measures possible deviations from a flat line. To conclude, the present correlative analysis shows that EEG dynamics extracted from the initial and maintenance phases of general anesthesia cannot anticipate both the emergence trajectory and the extubation time.

Spatiotemporal Evolution and Drivers of Total Health Expenditure across Mainland China in Recent Years

A substantially growing health expenditure has become an important global issue. Thus, how and why health expenditure is rising should be urgently investigated in systematic research. The Bayesian space-time model and the Bayesian least absolute shrinkage and selection operator (LASSO) model were employed in this study to investigate the spatiotemporal trends and influence patterns of total health expenditure per capita (THEPC) and total health expenditure (THEE) as a share of the gross domestic product (GDP) on the Chinese mainland from 2009 to 2018. The spatial distribution of THEE as a share of GDP in mainland China has shaped a distinct geographical structure with the characteristic of 'west high/east low'. Its local increasing trends formed a geographical structure that exhibited a 'north high/south low' feature. The heterogeneity of the influence patterns of health expenditure was observed from east to west across China. Natural environmental factors, such as air pollution and green coverage, along with changes in dietary structures, have increasingly influenced the growth of health expenditures.

Suggesting disease associations for overlooked metabolites using literature from metabolic neighbors

In human health research, metabolic signatures extracted from metabolomics data have a strong added value for stratifying patients and identifying biomarkers. Nevertheless, one of the main challenges is to interpret and relate these lists of discriminant metabolites to pathological mechanisms. This task requires experts to combine their knowledge with information extracted from databases and the scientific literature. However, we show that most compounds (>99%) in the PubChem database lack annotated literature. This dearth of available information can have a direct impact on the interpretation of metabolic signatures, which is often restricted to a subset of significant metabolites. To suggest potential pathological phenotypes related to overlooked metabolites that lack annotated literature, we extend the "guilt-by-association" principle to literature information by using a Bayesian framework. The underlying assumption is that the literature associated with the metabolic neighbors of a compound can provide valuable insights, or an a priori, into its biomedical context. The metabolic neighborhood of a compound can be defined from a metabolic network and correspond to metabolites to which it is connected through biochemical reactions. With the proposed approach, we suggest more than 35,000 associations between 1,047 overlooked metabolites and 3,288 diseases (or disease families). All these newly inferred associations are freely available on the FORUM ftp server (see information at https://github.com/eMetaboHUB/Forum-LiteraturePropagation).

Reliability as Lindley Information

This paper introduces a definition of reliability based on Lindley information, which is the mutual information between an observed measure and latent attribute. This definition reduces to the traditional definition of reliability in the case of normal variables, but can be applied to any joint distribution of observed and latent variables. Importantly, unlike traditional definitions of reliability, this formulation of reliability applies to vector- or matrix-valued estimates and summaries of responses, and therefore generalizes reliability to sets of scores and estimates in addition to individual scores and estimates. This formulation also leads to new bounds for reliability, as well as newly reported relationships between reliability and the traditional Fisher information function familiar in item response theory literature. This form of reliability can be estimated using formulae, or methods used in Bayesian inference such as Markov Chain Monte Carlo (MCMC) depending on the case. Examples based on well-studied datasets are provided, as well as applications to drift-diffusion modeling and randomly-varying intraindividual covariance structures.

BISC: accurate inference of transcriptional bursting kinetics from single-cell transcriptomic data

Gene expression in mammalian cells is inherently stochastic and mRNAs are synthesized in discrete bursts. Single-cell transcriptomics provides an unprecedented opportunity to explore the transcriptome-wide kinetics of transcriptional bursting. However, current analysis methods provide limited accuracy in bursting inference due to substantial noise inherent to single-cell transcriptomic data. In this study, we developed BISC, a Bayesian method for inferring bursting parameters from single cell transcriptomic data. Based on a beta-gamma-Poisson model, BISC modeled the mean-variance dependency to achieve accurate estimation of bursting parameters from noisy data. Evaluation based on both simulation and real intron sequential RNA fluorescence in situ hybridization data showed improved accuracy and reliability of BISC over existing methods, especially for genes with low expression values. Further application of BISC found bursting frequency but not bursting size was strongly associated with gene expression regulation. Moreover, our analysis provided new mechanistic insights into the functional role of enhancer and superenhancer by modulating both bursting frequency and size. BISC also formulated a downstream framework to identify differential bursting (in frequency and size separately) genes in samples under different conditions. Applying to multiple datasets (a mouse embryonic cell and fibroblast dataset, a human immune cell dataset and a human pancreatic cell dataset), BISC identified known cell-type signature genes that were missed by differential expression analysis, providing additional insights in understanding the cell-specific stochastic gene transcription. Applying to datasets of human lung and colon cancers, BISC successfully detected tumor signature genes based on alterations in bursting kinetics, which illustrates its value in understanding disease development regarding transcriptional bursting. Collectively, BISC provides a new tool for accurately inferring bursting kinetics and detecting differential bursting genes. This study also produced new insights in the role of transcriptional bursting in regulating gene expression, cell identity and tumor progression.

Using Prior Toxicological Data to Support Dose-Response Assessment─Identifying Plausible Prior Distributions for Dichotomous Dose-Response Models

The benchmark dose (BMD) methodology has significantly advanced the practice of dose-response analysis and created substantial opportunities to enhance the plausibility of BMD estimation by synthesizing dose-response information from different sources. Particularly, integrating existing toxicological information via prior distribution in a Bayesian framework is a promising but not well-studied strategy. The study objective is to identify a plausible way to incorporate toxicological information through informative prior to support BMD estimation using dichotomous data. There are four steps in this study: determine appropriate types of distribution for parameters in common dose-response models, estimate the parameters of the determined distributions, investigate the impact of alternative strategies of prior implementation, and derive endpoint-specific priors to examine how prior-eliciting data affect priors and BMD estimates. A plausible distribution was estimated for each parameter in the common dichotomous dose-response models using a general database. Alternative strategies for implementing informative prior have a limited impact on BMD estimation, but using informative prior can significantly reduce uncertainty in BMD estimation. Endpoint-specific informative priors are substantially different from the general one, highlighting the necessity for guidance on prior elicitation. The study developed a practical way to employ informative prior and laid a foundation for advanced Bayesian BMD modeling.

A Bayesian perspective on Biogen's aducanumab trial

This perspective is a companion to a recent editorial on the use of Bayesian analysis in clinical research. We aim to introduce and highlight the relevance and advantages that Bayesian inference offers to clinical trials using the data on the amyloid antibody aducanumab presented at a Food and Drug Administration hearing in November 2020 as an applied example. We apply Bayesian analysis of model plausibility and effect sizes based on simulated data of the two phase 3 trials of aducanumab in prodromal and mild dementia stages of Alzheimer's disease (AD). Bayesian analysis can quantify evidence in favor of, or against, the presence of an effect (i.e., provide evidence of absence), as well as assess the strength of the effect. This is in contrast to the binary conclusions provided by frequentist tests.

Incorporating historical control information in ANCOVA models using the meta-analytic-predictive approach

The meta-analytic-predictive (MAP) approach is a Bayesian meta-analytic method to synthesize and incorporate information from historical controls in the analysis of a new trial. Classically, only a single parameter, typically the intercept or rate, is assumed to vary across studies, which may not be realistic in more complex models. Analysis of covariance (ANCOVA) is often used to analyze trials with a pretest-posttest design, where both the intercept and the baseline effect (coefficient of the outcome at baseline) affect the estimated treatment effect. We extended the MAP approach to ANCOVA, to allow for variation in the intercept and the baseline effect across studies, and possibly also correlation between these parameters. The method was illustrated using data from the Alzheimer's Disease Cooperative Study (ADCS) and assessed with a simulation study. In the ADCS data, the proposed multivariate MAP approach yielded a prior effective sample size of 79 and 58 for the intercept and the baseline effect respectively and reduced the posterior standard deviation of the treatment effect by 12.6%. The result was robust to the choice of prior for the between-study variation. In the simulations, the proposed approach yielded power gains with a good control of the type I error rate. Ignoring the between-study correlation of the parameters or assuming no variation in the baseline effect generally led to less power gain. In conclusion, the MAP approach can be extended to a multivariate version for ANCOVA, which may improve the estimation of the treatment effect.

Score-based measurement invariance checks for Bayesian maximum-a-posteriori estimates in item response theory

A family of score-based tests has been proposed in recent years for assessing the invariance of model parameters in several models of item response theory (IRT). These tests were originally developed in a maximum likelihood framework. This study discusses analogous tests for Bayesian maximum-a-posteriori estimates and multiple-group IRT models. We propose two families of statistical tests, which are based on an approximation using a pooled variance method, or on a simulation approach based on asymptotic results. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a categorical or continuous person covariate in the two- and three-parametric logistic models. Whereas the method based on pooled variance was found to be useful in practice with maximum likelihood as well as maximum-a-posteriori estimates, the simulation-based approach was found to require large sample sizes to lead to satisfactory results.

Sequences of Events from the Electronic Medical Record and the Onset of Infection

We present a novel model of time-series analysis to learn from electronic health record (EHR) data when infection occurred in the intensive care unit (ICU) by translating methods from proteomics and Bayesian statistics. Using 48,536 patients hospitalized in an ICU, we describe each hospital course as an 'alphabet' of 23 physician actions ('events') in temporal order. We analyze these as k-mers of length 3-12 events and apply a Bayesian model of (cumulative) relative risk (RR). The log2-transformed RR (median=0.248, mean=0.226) supported the conclusion that the events selected were individually associated with increased risk of infection. Selecting from all possible cutoffs of maximum gain (MG), MG>0.0244 predicts administration of antibiotics with PPV 82.0 %, NPV 44.4 %, and AUC 0.706. Our approach holds value for retrospective analysis of other clinical syndromes for which time-of-onset is critical to analysis but poorly marked in EHRs, including delirium and decompensation.