Bayesian Imputation Research Articles

Abstract TMP95: Context Matters: Geographic Decision-Making Could Improve Prehospital Stroke Triage

Introduction: Emergency medical services (EMS) play a key role in stroke outcomes, as triage decisions made under diagnostic uncertainty impact availability of time sensitive treatments. Quantifying both time varying effects and uncertainty allows for optimized algorithms to improve destination decisions for stroke patients. We developed a Bayesian model of neurological outcomes and an algorithm for hospital triage based on clinical trials data. Methods: We used data from Virtual International Stroke Trials Archive (VISTA), RACECAT, and FAST-MAG. To model prehospital diagnosis, we included patients with any stroke-like illness (ischemic/hemorrhagic stroke, and mimics). Primary outcome was 90-day modified Rankin scale (mRS). Due to variability in reported measures from each trial, model-based Bayesian imputation was used. Our model accepts time-from symptoms, location, and capability of all local hospitals as inputs. Results: We included 9048 participants with 8600 (95%) ischemic strokes, 1801 (20%) had large vessel occlusion, and 4064 (45%) had a 90-day mRS of 0-2 (good neurologic outcome). We evaluated the impact of our algorithm using 1,320 stroke events from RACECAT. The estimated median absolute difference in chance of good mRS score between bypass and non local hospital bypass was 2.3% (ranging from 0 to 7.4%) among 1,320 stroke events in the RACECAT data set; covariate-adjusted patient scenarios predicted a preference for local hospital bypass of -2.9% to 7.4%. Destination maps for Catalonia show important patterns of bypass optimality. Conclusion: We found that no uniform destination selection approach is likely to be optimal under all circumstances. This finding is important, because it suggests that a personalized approach considering diagnostic uncertainty, patient characteristics, and geospatial factors could outperform simpler approaches. Predicted time-to-treatment targets may be insufficient for appropriate system optimization.

Trajectory Statistical Learning of the Potential Mean of Force and Diffusion Coefficient from Molecular Dynamics Simulations.

Central to studying the conformational changes of a complex protein is understanding the dynamics and energetics involved. Phenomenologically, structural dynamics can be formulated using an overdamped Langevin model along an observable, e.g., the distance between two residues in the protein. The Langevin model is specified by the deterministic force (the potential of mean force, PMF) and stochastic force (characterized by the diffusion coefficient, D). It is therefore of great interest to be able to extract both PMF and D from an observable time series but under the same computational framework. Here, we approach this challenge in molecular dynamics (MD) simulations by treating it as a missing-data Bayesian estimation problem. An important distinction in our methodology is that the entire MD trajectory, as opposed to the individual data elements, is used as the statistical variable in Bayesian imputation. This idea is implemented through an eigen-decomposition procedure for a time-symmetrized Fokker-Planck equation, followed by maximizing the likelihood for parameter estimation. The mathematical expressions for the functional derivatives used in learning PMF and D also provide new physical insights for the manner by which the information on both the deterministic and stochastic forces is encoded in the dynamics data. An all-atom MD simulation of a nontrivial biomolecule case is used to illustrate the application of this approach. We show that, interestingly, the results of trajectory statistical learning can motivate new order parameters for an improved description of the kinetic bottlenecks in conformational changes. Complementing purely data-driven or black-box methods, this work underscores the advantages of physics-based machine learning in gaining chemical insights from quantitative parameter estimation.

System Identification of User Engagement in mHealth Behavioral Interventions

Digital behavior change interventions (DBCIs) such as “just-in-time” adaptive interventions (JITAIs) have demonstrated efficacy for increasing physical activity behavior. However, the effectiveness of these interventions is heavily dependent upon user engagement. Despite the inherent dynamic nature of engagement, as it varies over time based on an individual’s changing environment, context, and psychological state, the current understanding of engagement primarily comes from static snapshots of the behavior. The availability of intensive longitudinal data from JITAIs provides a unique opportunity to build and test dynamic models of behavior change from a process systems lens, relying on prediction-error methods from system identification. However, data missingness is a significant practical consideration in this process. Therefore, in this work we address missingness using a Bayesian imputation approach, which we evaluate using data from the HeartSteps II JITAI. Ultimately, the methods presented support the discovery of key factors that impact engagement behavior over time and can play an important role in the development of large-scale personalized interventions.

Modeling basal body temperature data using horseshoe process regression.

Biomedical data often exhibit jumps or abrupt changes. For example, women's basal body temperature may jump at ovulation, menstruation, implantation, and miscarriage. These sudden changes make these data challenging to model: many methods will oversmooth the sharp changes or overfit in response to measurement error. We develop horseshoe process regression (HPR) to address this problem. We define a horseshoe process as a stochastic process in which each increment is horseshoe-distributed. We use the horseshoe process as a nonparametric Bayesian prior for modeling a potentially nonlinear association between an outcome and its continuous predictor, which we implement via Stan and in the R package HPR. We provide guidance and extensions to advance HPR's use in applied practice: we introduce a Bayesian imputation scheme to allow for interpolation at unobserved values of the predictor within the HPR; include additional covariates via a partial linear model framework; and allow for monotonicity constraints. We find that HPR performs well when fitting functions that have sharp changes. We apply HPR to model women's basal body temperatures over the course of the menstrual cycle.

Survival analysis of recurrent breast cancer patients using mix Bayesian network

IntroductionBreast cancer (BC) is the most common cancer among women. Iranians have an 11% BC recurrence rate, which lowers their survival rates. Few studies have investigated cancer recurrence survival rates. This study's major purpose is to use a mixed Bayesian network (BN) to analyze recurrent patients' survival. Material and methodsThis study aimed to evaluate the pathobiological features, age, gender, final status, and survival time of the patients. Bayesian imputation was used for missing data. The performance of BN was optimized through the utilization of a blacklist and prior probability. After structural and parametric learning, posterior conditional probabilities and mean survival periods for the node arcs were predicted. The hold-out technique based on the posterior classification error was used to investigate the model's validation. ResultsThe study included 220 cancer recurrence patients. These patients averaged 47 years old. The BN with a blacklist and prior probability has a higher network score than other networks. The hold-out technique verified structural learning. The Directed Acyclic Graph showed a statistically significant relationship between cancer biomarkers (ER, PR, and HER2 receptors), cancer stage, and tumor grade and patient survival duration. Patient death was also significantly associated with education, ER, PR, HER2, and tumor grade. The BN reports that HER2 negative, ER positive, and PR positive patients had a higher survival rate. ConclusionSurvival and death of relapsed patients depend on biomarkers. Based on the findings, patient survival can be predicted with their features.

Maximum Likelihood Estimation of Hierarchical Linear Models from Incomplete Data: Random Coefficients, Statistical Interactions, and Measurement Error

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data and . However, if the model for R given C includes random coefficients, interactions, or polynomial terms, their joint distribution will be nonstandard. We propose a family of unique factorizations involving selected “provisionally known random effects” u such that is normally distributed and u is a low-dimensional normal random vector; we approximate via adaptive Gauss-Hermite quadrature. For polynomial models, the approximation is exact but, in any case, can be made as accurate as required given sufficient computation time. The model incorporates random effects as explanatory variables, reducing bias due to measurement error. By construction, our factorizations solve problems of compatibility among fully conditional distributions that have arisen in Bayesian imputation based on the Gibbs Sampler. We spell out general rules for selecting u, and show that our factorizations can support fully compatible Bayesian methods of imputation using the Gibbs Sampler. Supplementary materials for this article are available online.

Better data for decision-making through Bayesian imputation of suppressed provisional COVID-19 death counts.

To facilitate use of timely, granular, and publicly available data on COVID-19 mortality, we provide a method for imputing suppressed COVID-19 death counts in the National Center for Health Statistic's 2020 provisional mortality data by quarter, county, and age. We used a Bayesian approach to impute suppressed COVID-19 death counts by quarter, county, and age in provisional data for 3,138 US counties. Our model accounts for multilevel data structures; numerous zero death counts among persons aged <50 years, rural counties, early quarters in 2020; highly right-skewed distributions; and different levels of data granularity (county, state or locality, and national levels). We compared three models with different prior assumptions of suppressed COVID-19 deaths, including noninformative priors (M1), the same weakly informative priors for all age groups (M2), and weakly informative priors that differ by age (M3) to impute the suppressed death counts. After the imputed suppressed counts were available, we assessed three prior assumptions at the national, state/locality, and county level, respectively. Finally, we compared US counties by two types of COVID-19 death rates, crude (CDR) and age-standardized death rates (ASDR), which can be estimated only through imputing suppressed death counts. Without imputation, the total COVID-19 death counts estimated from the raw data underestimated the reported national COVID-19 deaths by 18.60%. Using imputed data, we overestimated the national COVID-19 deaths by 3.57% (95% CI: 3.37%-3.80%) in model M1, 2.23% (95% CI: 2.04%-2.43%) in model M2, and 2.96% (95% CI: 2.76%-3.16%) in model M3 compared with the national report. The top 20 counties that were most affected by COVID-19 mortality were different between CDR and ASDR. Bayesian imputation of suppressed county-level, age-specific COVID-19 deaths in US provisional data can improve county ASDR estimates and aid public health officials in identifying disparities in deaths from COVID-19.

#6569 PREDICTION OF ALL-CAUSE MORTALITY FOR CHRONIC KIDNEY DISEASE PATIENTS USING FOUR MODELS OF MACHINE LEARNING

Abstract Background and Aims Prediction tools developed from general population data to predict all-cause mortality are not adapted to patients with chronic kidney disease (CKD), as this population has a higher risk of mortality. This study aimed to create a clinical prediction tool with good predictive performance to predict 2-year all-cause mortality in patients with stage 4 or 5 CKD using an innovative approach with machine learning models and a synthetic population. Method The national, observational, descriptive and prospective Photo-Graphe 3 study was used to create the learning database. Four models (i) logistic regression; (ii) deep learning; (iii) random forest and (iv) Bayesian network were used to create four prediction tools. The performance of each model, including the area under the receiver operating characteristic curve (AUC-ROC) value, accuracy, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV), was evaluated and compared using 10-fold cross-validation. The prediction tool with the best performance was selected and optimized using a synthetic population and the explanatory variables most related to mortality. The synthetic population was created by the Bayesian imputation method. The variables most associated with 2-year all-cause mortality were determined by compromising the number of variables selected and the AUC-ROC value when successively adding the variable according to its percentage variance value. The performance of the optimized prediction tool in predicting 2-year mortality was then evaluated by 10-fold cross validation. Results All prediction tools except the one developed with the random forest model showed satisfactory discrimination (AUC-ROC ≥ 0.70). Overall, the prediction tools developed using the Bayesian network and logistic regression tended to have better performance. Although not significantly different from logistic regression, the prediction tool developed using the Bayesian network was chosen for further development because of its advantages. From the 534 patients in the study population, a synthetic population of 2000 patients (survivor:death ratio = 1:1) was created. The seven most informative variables ranked in descending order were: age, ESA, CV history, smoking status, 25-OH vitamin D level, PTH level, and ferritin level (Figure 1). The optimized clinical prediction tool had satisfactory internal performance. The mean accuracy was 73.8% (SD = 3.6), the mean AUC-ROC was 0.81 (SD = 0.03), the mean sensitivity was 71.0% (SD = 5.4), the mean specificity was 76.5% (SD = 3.0), the mean PPV was 75.1% (SD = 3.2), and the mean NPV was 72.6% (SD = 4.1). Conclusion Bayesian network model was used to create a seven-variable prediction tool to predict the 2-year all-cause mortality in patients with stage 4–5 CKD. This prediction tool has a satisfactory performance. Prior to external validation, the proposed prediction tool can be used at: https://bit.ly/3JPhrkh for research purpose. This is the first time that a synthetic population has been applied to create predictive models. In this study, the synthetic population showed its advantage in dealing with sample size issues in developing predictive models and in improving the performance of the prediction tool in terms of sensitivity and PPV.

Superiority of Bayesian Imputation to Mice in Logit Panel Data Models

Superiority of Bayesian Imputation to Mice in Logit Panel Data Models

Hierarchical, multiclass prediction of Alzheimer’s clinical diagnosis using imputed, multimodal NACC data

AbstractBackgroundEarly detection and diagnosis are critical for effective treatment of Alzheimer’s disease (AD). Statistical machine learning holds promise for disease prediction using large AD repositories, such as the National Alzheimer’s Coordinating Center (NACC) dataset. Past work has extensively explored binary classifications of AD diagnosis. Here, we extended this to address two major, remaining challenges: data imputation and multiclass classification (e.g., AD vs Mild Cognitive Impairment, MCI vs. Healthy Cognition, HC).MethodFor imputation, we tested single‐value (baseline), k‐NN, and Bayesian imputation on a subset of complete training data with artificially removed values (completely at random). Per modality of interest, a systematic search was conducted for the best input feature set to impute the missing values. The mean absolute deviation and mismatch rate between the imputed and true values were used to evaluate the methods on a held‐out test set. For classification, we then implemented both “flat” multiclass and hierarchical classification, an extension of multiclass classification that organizes classes into a tree, to predict clinical diagnosis using multimodal inputs. Several pipelines with combinations of imputation methods, classifiers, and input modalities were tested on different hierarchical classification strategies, e.g., HC vs [AD vs MCI], compared with the flat, multiclass baseline (AD vs MCI vs HC).ResultCompared to the baseline methods for both imputation and classification, the proposed alternatives performed better, as measured by the predetermined imputation and classification metrics evaluated on the test set. For imputation, behavioral and neuropsychiatric features were more easily and accurately imputed while ApoE genotype was more difficult to impute. For classification, using a combination of classifiers and input features in the hierarchy outperformed the baseline method and support the notion that select biomarkers are better able to characterize AD subpopulations within the hierarchy.ConclusionEstablishing a systematic imputation method tailored to AD biomarker modalities fills a critical gap in achieving more robust disease prediction. Building a hierarchical classifier parallels working through a differential diagnosis for AD, which offers greater translational value than binary classification of AD. In combination, these results form an important step toward developing reliable, holistic classifiers of AD disease status.

Solutions for surrogacy validation with longitudinal outcomes for a gene therapy.

Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate-dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed-start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout thetrial.

Bayesian imputation of COVID-19 positive test counts for nowcasting under reporting lag.

Obtaining up to date information on the number of UK COVID‐19 regional infections is hampered by the reporting lag in positive test results for people with COVID‐19 symptoms. In the UK, for ‘Pillar 2’ swab tests for those showing symptoms, it can take up to five days for results to be collated. We make use of the stability of the under reporting process over time to motivate a statistical temporal model that infers the final total count given the partial count information as it arrives. We adopt a Bayesian approach that provides for subjective priors on parameters and a hierarchical structure for an underlying latent intensity process for the infection counts. This results in a smoothed time‐series representation nowcasting the expected number of daily counts of positive tests with uncertainty bands that can be used to aid decision making. Inference is performed using sequential Monte Carlo.

Imputation of Below Detection Limit Missing Data in Chemical Mixture Analysis with Bayesian Group Index Regression.

There is growing scientific interest in identifying the multitude of chemical exposures related to human diseases through mixture analysis. In this paper, we address the issue of below detection limit (BDL) missing data in mixture analysis using Bayesian group index regression by treating both regression effects and missing BDL observations as parameters in a model estimated through a Markov chain Monte Carlo algorithm that we refer to as pseudo-Gibbs imputation. We compare this with other Bayesian imputation methods found in the literature (Multiple Imputation by Chained Equations and Sequential Full Bayes imputation) as well as with a non-Bayesian single-imputation method. To evaluate our proposed method, we conduct simulation studies with varying percentages of BDL missingness and strengths of association. We apply our method to the California Childhood Leukemia Study (CCLS) to estimate concentrations of chemicals in house dust in a mixture analysis of potential environmental risk factors for childhood leukemia. Our results indicate that pseudo-Gibbs imputation has superior power for exposure effects and sensitivity for identifying individual chemicals at high percentages of BDL missing data. In the CCLS, we found a significant positive association between concentrations of polycyclic aromatic hydrocarbons (PAHs) in homes and childhood leukemia as well as significant positive associations for polychlorinated biphenyls (PCBs) and herbicides among children from the highest quartile of household income. In conclusion, pseudo-Gibbs imputation addresses a commonly encountered problem in environmental epidemiology, providing practitioners the ability to jointly estimate the effects of multiple chemical exposures with high levels of BDL missingness.

Bayesian Imputation with Optimal Look-Ahead-Bias and Variance Tradeoff

Missing time-series data is a prevalent problem in finance. Imputation methods for time-series data are usually applied to the full panel data with the purpose of training a model for a downstream out-of-sample task. For example, the imputation of missing returns may be applied prior to estimating a portfolio optimization model. However, this practice can result in a look-ahead-bias in the future performance of the downstream task. There is an inherent trade-off between the look-ahead-bias of using the full data set for imputation and the larger variance in the imputation from using only the training data. By connecting layers of information revealed in time, we propose a Bayesian consensus posterior that fuses an arbitrary number of posteriors to optimally control the variance and look-ahead-bias trade-off in the imputation. We derive tractable two-step optimization procedures for finding the optimal consensus posterior, with Kullback-Leibler divergence and Wasserstein distance as the measure of dissimilarity between posterior distributions. We demonstrate in simulations and an empirical study the benefit of our imputation mechanism for portfolio optimization with missing returns.

BIMAM—a tool for imputing variables missing across datasets using a Bayesian imputation and analysis model

MotivationCombination of multiple datasets is routine in modern epidemiology. However, studies may have measured different sets of variables; this is often inefficiently dealt with by excluding studies or dropping variables. Multilevel multiple imputation methods to impute these ‘systematically’ missing data (as opposed to ‘sporadically’ missing data within a study) are available, but problems may arise when many random effects are needed to allow for heterogeneity across studies. We show that the Bayesian IMputation and Analysis Model (BIMAM) implemented in our tool works well in this situation.General featuresBIMAM performs imputation and analysis simultaneously. It imputes both binary and continuous systematically and sporadically missing data, and analyses binary and continuous outcomes. BIMAM is a user-friendly, freely available tool that does not require knowledge of Bayesian methods. BIMAM is an R Shiny application. It is downloadable to a local machine and it automatically installs the required freely available packages (R packages, including R2MultiBUGS and MultiBUGS).AvailabilityBIMAM is available at [www.alecstudy.org/bimam].

Competition and invention quality: Evidence from Swiss firms

Existing literature investigates the effect of access to international markets on the technological activities of companies neglecting the issue of competition. It is not only the access to such markets, but in particular the competition in these markets that drives technological activities. This partly explains the divergent findings in the literature. We try to fill this research gap by investigating the relationship between competition in international technological markets, invention quality, and firm performance. We compile a unique time-series cross-section dataset combining patent and survey data covering the period 1990–2013. The survey data are based on stratified random sample of about 6000 companies drawn from the census data provided by the Swiss Federal Statistical Office. This data allows us to develop composite indicators for competition and invention quality, giving credit to their versatile features. We apply econometric procedures using international trade shocks as an instrument to identify invention quality and address selection issues with a Bayesian imputation approach. We find evidence that the positive effect of invention quality on domestic sales of innovative products is positively mediated by intensive competition in international markets. This has important implications for trade policy and underscores the meaningfulness of open markets for invention quality.

Accounting for the uncertainty due to chemicals below the detection limit in mixture analysis

Simultaneous exposure to a mixture of chemicals over a lifetime may increase an individual's risk of disease to a greater extent than individual exposures. Researchers have used weighted quantile sum (WQS) regression to estimate the effect of multiple exposures in a manner that identifies the important (etiologically relevant) components in the mixture. However, complications arise when an experimental apparatus detects concentrations for each chemical with a different detection limit. Current strategies to account for values below the detection limit (BDL) in WQS include single imputation or placing the BDL values into the first quantile of the weighted index (BDLQ1), which do not fully capture the uncertainty in the data when estimating mixture effects. In response, we integrated WQS regression into the multiple imputation framework (MI-WQS). In a simulation study, we compared the BDLQ1 approach to MI-WQS when using either a Bayesian imputation or bootstrapping imputation approach over a range of BDL values. We examined the ability of each method to estimate the mixture's overall effect and to identify important chemicals. The results showed that as the number of BDL values increased, the accuracy, precision, model fit, and power declined for all imputation approaches. When chemical values were missing at 10%, 33%, or 50%, the MI approaches generally performed better than single imputation and BDLQ1. In the extreme case of 80% of all the chemical values were missing, the BDLQ1 approach was superior in some examined metrics.

Imputation of attributes in networked data using Bayesian autocorrelation regression models

Misspecification in network autocorrelation models poses a challenge for parameter estimation, which is amplified by missing data. Model misspecification has been a focus of recent work in the statistics literature and new robust procedures have been developed, in particular cutting feedback. This paper shows how this helps in a misspecified network autocorrelation model. Where model misspecification is mild and the traits are fully observed, Bayesian imputation is routine. In settings with high missingness, Bayesian inference can fail, but a closely related cut model is robust. We illustrate this on a data set of graduate students using a Facebook-like messaging app.

A model-based imputation procedure for multilevel regression models with random coefficients, interaction effects, and nonlinear terms.

Despite the broad appeal of missing data handling approaches that assume a missing at random (MAR) mechanism (e.g., multiple imputation and maximum likelihood estimation), some very common analysis models in the behavioral science literature are known to cause bias-inducing problems for these approaches. Regression models with incomplete interactive or polynomial effects are a particularly important example because they are among the most common analyses in behavioral science research applications. In the context of single-level regression, fully Bayesian (model-based) imputation approaches have shown great promise with these popular analysis models. The purpose of this article is to extend model-based imputation to multilevel models with up to 3 levels, including functionality for mixtures of categorical and continuous variables. Computer simulation results suggest that this new approach can be quite effective when applied to multilevel models with random coefficients and interaction effects. In most scenarios that we examined, imputation-based parameter estimates were quite accurate and tracked closely with those of the complete data. The new procedure is available in the Blimp software application for macOS, Windows, and Linux, and the article includes a data analysis example illustrating its use. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

A Bayesian Processor of Uncertainty for Precipitation Forecasting Using Multiple Predictors and Censoring

Abstract A Bayesian processor of uncertainty for numerical precipitation forecasts is presented. The predictive density is estimated on the basis of normalized variates, the use of censored distributions, and the implementation of a parameter-parsimonious and computationally efficient processor that is applicable in operational settings. The structure of the processor is sufficiently generic to handle mixed binary-continuous random processes such as intermittent rainfall (and similarly ephemeral river flows), and an arbitrary number of predictors. First, predictors and observations, the parent data sample, are mapped into standard Gaussian variates, obtaining a nonparametric approximately multivariate normal distribution (MVND) that is considered censored for days with no precipitation. To convert the Gaussian binary-continuous multivariate precipitation process into a continuous one, the parent sample is augmented into the negative range through Bayesian imputation by Gibbs sampling, recovering the true, a priori unknown variance–covariance structure of the full uncensored sample. The dependency among marginal distributions of observations and predictions is hereby assumed multivariate normal, for which closed-form expressions of conditional densities exist. These are then mapped back into the variable space of provenience to yield the predictive density. The processor is applied to a well-monitored study area in Switzerland. Standard forecast performance evaluation and verification metrics are employed to set the approach into perspective against Bayesian model averaging (BMA).