A new test for trait mean and variance detects unreported loci for blood-pressure variation.

Variability in quantitative traits has clinical, ecological, and evolutionary significance. Most genetic variants identified for complex quantitative traits have only a detectable effect on the mean of trait. We have developed the mean-variance test (MVtest) to simultaneously model the mean and log-variance of a quantitative trait as functions of genotypes and covariates by using estimating equations. The advantages of MVtest include the facts that it can detect effect modification, that multiple testing can follow conventional thresholds, that it is robust to non-normal outcomes, and that association statistics can be meta-analyzed. In simulations, we show control of type I error of MVtest over several alternatives. We identified 51 and 37 previously unreported associations for effects on blood-pressure variance and mean, respectively, in the UK Biobank. Transcriptome-wide association studies revealed 633 significant unique gene associations with blood-pressure mean variance. MVtest is broadly applicable to studies of complex quantitative traits and provides an important opportunity to detect novel loci.

Variable selection in high dimensions for discrete-outcome individualized treatment rules: Reducing severity of depression symptoms.

Despite growing interest in estimating individualized treatment rules, little attention has been given the binary outcome setting. Estimation is challenging with nonlinear link functions, especially when variable selection is needed. We use a new computational approach to solve a recently proposed doubly robust regularized estimating equation to accomplish this difficult task in a case study of depression treatment. We demonstrate an application of this new approach in combination with a weighted and penalized estimating equation to this challenging binary outcome setting. We demonstrate the double robustness of the method and its effectiveness for variable selection. The work is motivated by and applied to an analysis of treatment for unipolar depression using a population of patients treated at Kaiser Permanente Washington.

Detecting sparse microbial association signals adaptively from longitudinal microbiome data based on generalized estimating equations.

The association between the compositions of microbial communities and various host phenotypes is an important research topic. Microbiome association research addresses multiple domains, such as human disease and diet. Statistical methods for testing microbiome-phenotype associations have been studied recently to determine their ability to assess longitudinal microbiome data. However, existing methods fail to detect sparse association signals in longitudinal microbiome data. In this paper, we developed a novel method, namely aGEEMIHC, which is a data-driven adaptive microbiome higher criticism analysis based on generalized estimating equations to detect sparse microbial association signals from longitudinal microbiome data. aGEEMiHC adopts generalized estimating equations framework that fully considers the correlation among different observations from the same subject in longitudinal data. To be robust to diverse correlation structures for longitudinal data, aGEEMiHC integrates multiple microbiome higher criticism analyses based on generalized estimating equations with different working correlation structures. Extensive simulation experiments demonstrate that aGEEMiHC can control the type I error correctly and achieve superior performance according to a statistical power comparison. We also applied it to longitudinal microbiome data with various types of host phenotypes to demonstrate the stability of our method. aGEEMiHC is also utilized for real longitudinal microbiome data, and we found a significant association between the gut microbiome and Crohn's disease. In addition, our method ranks the significant factors associated with the host phenotype to provide potential biomarkers.

A parameter-free deep embedded clustering method for single-cell RNA-seq data.

Clustering analysis is widely used in single-cell ribonucleic acid (RNA)-sequencing (scRNA-seq) data to discover cell heterogeneity and cell states. While many clustering methods have been developed for scRNA-seq analysis, most of these methods require to provide the number of clusters. However, it is not easy to know the exact number of cell types in advance, and experienced determination is not always reliable. Here, we have developed ADClust, an automatic deep embedding clustering method for scRNA-seq data, which can accurately cluster cells without requiring a predefined number of clusters. Specifically, ADClust first obtains low-dimensional representation through pre-trained autoencoder and uses the representations to cluster cells into initial micro-clusters. The clusters are then compared in between by a statistical test, and similar micro-clusters are merged into larger clusters. According to the clustering, cell representations are updated so that each cell will be pulled toward centers of its assigned cluster and similar clusters, while cells are separated to keep distances between clusters. This is accomplished through jointly optimizing the carefully designed clustering and autoencoder loss functions. This merging process continues until convergence. ADClust was tested on 11 real scRNA-seq datasets and was shown to outperform existing methods in terms of both clustering performance and the accuracy on the number of the determined clusters. More importantly, our model provides high speed and scalability for large datasets.

Glomerular Filtration Rate Estimation Using ß2-Microglobulin and ß-Trace Protein in Adults With Solid Tumors: A Prospective Cross-Sectional Study.

RATIONALE & OBJECTIVE: ß2-Microglobulin (B2M) and ß-trace protein (BTP) are novel endogenous filtration markers that may improve the accuracy of estimated glomerular filtration rate (eGFR) beyond creatinine and cystatin C (eGFRcr-cys), but they have not been assessed in patients with cancer. STUDY DESIGN: Cross-sectional analysis. SETTING & PARTICIPANTS: Prospective cohort of 1,200 patients with active solid tumors recruited between April 2015 and September 2017. EXPOSURE: CKD-EPI equations without race combining B2M and/or BTP with creatinine with or without cystatin C (2-, 3-, or 4-marker panel eGFR). OUTCOME: Performance of equations compared with eGFRcr-cys and non-GFR determinants of serum B2M and BTP (SB2M, and SBTP, respectively). Measured GFR (mGFR) was determined using the plasma clearance of chromium-51 labeled ethylenediamine tetraacetic acid (51Cr-EDTA). ANALYTICAL APPROACH: Bias was defined as the median of the differences between mGFR and eGFR, and 1-P30 was defined as the percentage of estimates that differed by more than 30% from the mGFR (1-P30). Linear regression was used to assess association of clinical and laboratory variables with SB2M, and SBTP after adjustment for mGFR. RESULTS: Mean age and mGFR were 58.8±13.2 SD years and 78.4±21.7 SD mL/min/1.73m2, respectively. Performance of the 3-marker and 4-marker panel equations was better than eGFRcr-cys (lesser bias and 1-P30). Performance of 2-marker panel equations was as good as eGFRcr-cys (lesser bias and similar 1-P30). SB2M and SBTP were not strongly influenced by cancer site. LIMITATIONS: Participants may have had better clinical performance status than the general population of patients with solid tumors. CONCLUSIONS: B2M and BTP can improve the accuracy of eGFR and may be useful as confirmatory tests in patients with solid tumors, either by inclusion in a multimarker panel equation with creatinine and cystatin C, or by substituting for cystatin C in combination with creatinine. PLAIN-LANGUAGE SUMMARY: The most accurate method to assess estimate kidney function is estimated glomerular filtration rate (eGFR) using creatinine and cystatin C (eGFRcr-cys). We studied whether using ß2-microglobulin (B2M) and/or ß-trace protein (BTP) with creatinine with or without cystatin C (2-, 3-, or 4-marker panel eGFR) might be useful in patients with active solid tumors. The performance of the 3-marker and 4-marker panel equations was better than eGFRcr-cys. Performance of 2-marker panel equations was as good as eGFRcr-cys. We conclude that B2M and BTP can improve the accuracy of eGFR and may be useful as a confirmatory test in patients with solid tumors either by inclusion in multimarker panel equation with creatinine and cystatin C or by substituting for cystatin C in combination with creatinine.

Estimating regional and national cancer incidence in Uganda: a retrospective population-based study, 2013-2017.

BACKGROUND: Cancer is becoming a major health problem in Uganda. Cancer control requires accurate estimates of the cancer burden for planning and monitoring of the cancer control strategies. However, cancer estimates and trends for Uganda are mainly based on one population-based cancer registry (PBCR), located in Kampala, the capital city, due to a lack of PBCRs in other regions. This study aimed at estimating cancer incidence among the geographical regions and providing national estimates of cancer incidence in Uganda. METHODS: A retrospective study, using a catchment population approach, was conducted from June 2019 to February 2020. The study registered all newly diagnosed cancer cases, in the period of 2013 to 2017, among three geographical regions: Central, Western and Eastern regions. Utilizing regions as strata, stratified random sampling was used to select the study populations. Cases were coded according to the International Classification of Diseases for Oncology (ICD-0-03). Data was analysed using CanReg5 and Microsoft Excel. RESULTS: 11598 cases (5157 males and 6441 females) were recorded. The overall national age-standardized incidence rates (ASIR) were 82.9 and 87.4 per 100,000 people in males and females respectively. The regional ASIRs were: 125.4 per 100,000 in males and 134.6 per 100,000 in females in central region; 58.2 per 100,000 in males and 56.5 per 100,000 in females in Western region; and 46.5 per 100,000 in males and 53.7 per 100,000 in females in Eastern region. Overall, the most common cancers in males over the study period were cancers of the prostate, oesophagus, Kaposi's sarcoma, stomach and liver. In females, the most frequent cancers were: cervix, breast, oesophagus, Kaposi's sarcoma and stomach. CONCLUSION: The overall cancer incidence rates from this study are different from the documented national estimates for Uganda. This emphasises the need to enhance the current methodologies for describing the country's cancer burden. Studies like this one are critical in enhancing the cancer surveillance system by estimating regional and national cancer incidence and allowing for the planning and monitoring of evidence-based cancer control strategies at all levels.

Homogeneity pursuit and variable selection in regression models for multivariate abundance data.

When building regression models for multivariate abundance data in ecology, it is important to allow for the fact that the species are correlated with each other. Moreover, there is often evidence species exhibit some degree of homogeneity in their responses to each environmental predictor, and that most species are informed by only a subset of predictors. We propose a generalized estimating equation (GEE) approach for simultaneous homogeneity pursuit (ie, grouping species with similar coefficient values while allowing differing groups for different covariates) and variable selection in regression models for multivariate abundance data. Using GEEs allows us to straightforwardly account for between-response correlations through a (reduced-rank) working correlation matrix. We augment the GEE with both adaptive fused lasso- and adaptive lasso-type penalties, which aim to cluster the species-specific coefficients within each covariate and encourage differing levels of sparsity across the covariates, respectively. Numerical studies demonstrate the strong finite sample performance of the proposed method relative to several existing approaches for modeling multivariate abundance data. Applying the proposed method to presence-absence records collected along the Great Barrier Reef in Australia reveals both a substantial degree of homogeneity and sparsity in species-environmental relationships. We show this leads to a more parsimonious model for understanding the environmental drivers of seabed biodiversity, and results in stronger out-of-sample predictive performance relative to methods that do not accommodate such features.

Longitudinal varying coefficient single-index model with censored covariates.

It is of interest to health policy research to estimate the population-averaged longitudinal medical cost trajectory from initial cancer diagnosis to death, and understand how the trajectory curve is affected by patient characteristics. This research question leads to a number of statistical challenges because the longitudinal cost data are often non-normally distributed with skewness, zero-inflation, and heteroscedasticity. The trajectory is nonlinear, and its length and shape depend on survival, which are subject to censoring. Modeling the association between multiple patient characteristics and nonlinear cost trajectory curves of varying lengths should take into consideration parsimony, flexibility, and interpretation. We propose a novel longitudinal varying coefficient single-index model. Multiple patient characteristics are summarized in a single-index, representing a patient's overall propensity for healthcare use. The effects of this index on various segments of the cost trajectory depend on both time and survival, which is flexibly modeled by a bivariate varying coefficient function. The model is estimated by generalized estimating equations with an extended marginal mean structure to accommodate censored survival time as a covariate. We established the pointwise confidence interval of the varying coefficient and a test for the covariate effect. The numerical performance was extensively studied in simulations. We applied the proposed methodology to medical cost data of prostate cancer patients from the Surveillance, Epidemiology, and End Results-Medicare-Linked Database.

Soft classification and regression analysis of audiometric phenotypes of age-related hearing loss.

Age-related hearing loss has a complex etiology. Researchers have made efforts to classify relevant audiometric phenotypes, aiming to enhance medical interventions and improve hearing health. We leveraged existing pattern analyses of age-related hearing loss and implemented the phenotype classification via quadratic discriminant analysis (QDA). We herein propose a method for analyzing the exposure effects on the soft classification probabilities of the phenotypes via estimating equations. Under reasonable assumptions, the estimating equations are unbiased and lead to consistent estimators. The resulting estimator had good finite sample performances in simulation studies. As an illustrative example, we applied our proposed methods to assess the association between a dietary intake pattern, assessed as adherence scores for the dietary approaches to stop hypertension diet calculated using validated food-frequency questionnaires, and audiometric phenotypes (older-normal, metabolic, sensory, and metabolic plus sensory), determined based on data obtained in the Nurses' Health Study II Conservation of Hearing Study, the Audiology Assessment Arm. Our findings suggested that participants with a more healthful dietary pattern were less likely to develop the metabolic plus sensory phenotype of age-related hearing loss.

Trajectories of fear of cancer recurrence and its influence factors: A longitudinal study on Chinese newly diagnosed cancer patients.

OBJECTIVE: The fear of cancer recurrence (FCR) is an ongoing and common psychological problem faced by cancer patients. The objective of this study was to explore the variation trend of FCR and its influencing factors in Chinese newly diagnosed cancer patients from admission to 2 months after discharge. Demographic and tumor characteristics, as well as experiential avoidance (EA), were used as predictors. METHOD: A longitudinal design and a consecutive sampling method were used to select 266 newly diagnosed cancer patients admitted to a tertiary cancer hospital in China from July to December 2022. Measurements of FCR and EA were obtained at admission (T1), 1 month after discharge (T2), and 2 months post-discharge (T3). Generalized estimating equations were used to identify factors associated with FCR for longitudinal data analysis. RESULTS: A total of 266 participants completed the follow-up. Both FCR and EA scores of patients with newly diagnosed cancer showed a significant trend of first increasing and then decreasing at baseline and follow-up (p < 0.001). The junior secondary and less education level, rural residence, advanced tumor and high EA level were risk factors for higher FCR. CONCLUSIONS: Our findings suggest that the FCR levels of most newly diagnosed cancer patients in China are different at the three time points and affected by different factors, with the highest level at 1 month after discharge. These results have significant implications for future identifying populations in need of targeted intervention based on their FCR trajectories.

How estimating nuisance parameters can reduce the variance (with consistent variance estimation).

We often estimate a parameter of interest ψ $$ \psi $$ when the identifying conditions involve a finite-dimensional nuisance parameter θ ∈ ℝ d $$ \theta \in {\mathbb{R}} $$ . Examples from causal inference are inverse probability weighting, marginal structural models and structural nested models, which all lead to unbiased estimating equations. This article presents a consistent sandwich estimator for the variance of estimators ψ ^ $$ \hat{\psi} $$ that solve unbiased estimating equations including θ $$ \theta $$ which is also estimated by solving unbiased estimating equations. This article presents four additional results for settings where θ ^ $$ \hat{\theta} $$ solves (partial) score equations and ψ $$ \psi $$ does not depend on θ $$ \theta $$ . This includes many causal inference settings where θ $$ \theta $$ describes the treatment probabilities, missing data settings where θ $$ \theta $$ describes the missingness probabilities, and measurement error settings where θ $$ \theta $$ describes the error distribution. These four additional results are: (1) Counter-intuitively, the asymptotic variance of ψ ^ $$ \hat{\psi} $$ is typically smaller when θ $$ \theta $$ is estimated. (2) If estimating θ $$ \theta $$ is ignored, the sandwich estimator for the variance of ψ ^ $$ \hat{\psi} $$ is conservative. (3) A consistent sandwich estimator for the variance of ψ ^ $$ \hat{\psi} $$ . (4) If ψ ^ $$ \hat{\psi} $$ with the true θ $$ \theta $$ plugged in is efficient, the asymptotic variance of ψ ^ $$ \hat{\psi} $$ does not depend on whether θ $$ \theta $$ is estimated. To illustrate we use observational data to calculate confidence intervals for (1) the effect of cazavi versus colistin on bacterial infections and (2) how the effect of antiretroviral treatment depends on its initiation time in HIV-infected patients.

Cox regression with linked data.

Record linkage is increasingly used, especially in medical studies, to combine data from different databases that refer to the same entities. The linked data can bring analysts novel and valuable knowledge that is impossible to obtain from a single database. However, linkage errors are usually unavoidable, regardless of record linkage methods, and ignoring these errors may lead to biased estimates. While different methods have been developed to deal with the linkage errors in the generalized linear model, there is not much interest on Cox regression model, although this is one of the most important statistical models in clinical and epidemiological research. In this work, we propose an adjusted estimating equation for secondary Cox regression analysis, where linked data have been prepared by a third-party operator, and no information on matching variables is available to the analyst. Through a Monte Carlo simulation study, the proposed method is shown to lead to substantial bias reductions in the estimation of the parameters of the Cox model caused by false links. An asymptotically unbiased variance estimator for the adjusted estimators of Cox regression coefficients is also proposed. Finally, the proposed method is applied to a linked database from the Brest stroke registry in France.

Estimating average treatment effects for clustered RCTs with recruitment bias.

In clustered randomized controlled trials (RCTs), sample recruitment is often conducted after cluster randomization. This timing can lead to recruitment bias if access to the intervention affects the composition of study-eligible cluster entrants and study consenters. This article develops a potential outcomes framework in such settings that yields a causal estimand that pertains to the always-recruited in either research condition. A consistent inverse probability weighting (IPW) estimator is developed using data on recruits only, and a generalized estimating equations approach is used to obtain robust clustered SE estimators that adjust for estimation error in the IPW weights. A simple data collection strategy is discussed to improve the predictive accuracy of the logit propensity score models. Simulations show that the IPW estimator achieves nominal confidence interval coverage under the assumed identification conditions. An empirical application demonstrates the methods using data from an RCT testing the effects of a behavioral health intervention in schools. An R program for estimation is available for download.

Online causal inference with application to near real-time post-market vaccine safety surveillance.

Streaming data routinely generated by social networks, mobile or web applications, e-commerce, and electronic health records present new opportunities to monitor the impact of an intervention on an outcome via causal inference methods. However, most existing causal inference methods have been focused on and applied to static data, that is, a fixed data set in which observations are pooled and stored before performing statistical analysis. There is thus a pressing need to turn static causal inference into online causal learning to support near real-time monitoring of treatment effects. In this paper, we present a framework for online estimation and inference of treatment effects that can incorporate new information as it becomes available without revisiting prior observations. We show that, under mild regularity conditions, the proposed online estimator is asymptotically equivalent to the offline oracle estimator obtained by pooling all data. Our proposal is motivated by the need for near real-time vaccine effectiveness and safety monitoring, and our proposed method is applied to a case study on COVID-19 vaccine safety surveillance.

Covariate-adjusted generalized pairwise comparisons in small samples.

Semiparametric probabilistic index models allow for the comparison of two groups of observations, whilst adjusting for covariates, thereby fitting nicely within the framework of generalized pairwise comparisons (GPC). As with most regression approaches in this setting, the limited amount of data results in invalid inference as the asymptotic normality assumption is not met. In addition, separation issues might arise when considering small samples. In this article, we show that the parameters of the probabilistic index model can be estimated using generalized estimating equations, for which adjustments exist that lead to estimators of the sandwich variance-covariance matrix with improved finite sample properties and that can deal with bias due to separation. In this way, appropriate inference can be performed as is shown through extensive simulation studies. The known relationships between the probabilistic index and other GPC statistics allow to also provide valid inference for example, the net treatment benefit or the success odds.

Accommodating misclassification effects on optimizing dynamic treatment regimes with Q-learning.

Research on dynamic treatment regimes has enticed extensive interest. Many methods have been proposed in the literature, which, however, are vulnerable to the presence of misclassification in covariates. In particular, although Q-learning has received considerable attention, its applicability to data with misclassified covariates is unclear. In this article, we investigate how ignoring misclassification in binary covariates can impact the determination of optimal decision rules in randomized treatment settings, and demonstrate its deleterious effects on Q-learning through empirical studies. We present two correction methods to address misclassification effects on Q-learning. Numerical studies reveal that misclassification in covariates induces non-negligible estimation bias and that the correction methods successfully ameliorate bias in parameter estimation.

Designing individually randomized group treatment trials with repeated outcome measurements using generalized estimating equations.

Individually randomized group treatment (IRGT) trials, in which the clustering of outcome is induced by group-based treatment delivery, are increasingly popular in public health research. IRGT trials frequently incorporate longitudinal measurements, of which the proper sample size calculations should account for correlation structures reflecting both the treatment-induced clustering and repeated outcome measurements. Given the relatively sparse literature on designing longitudinal IRGT trials, we propose sample size procedures for continuous and binary outcomes based on the generalized estimating equations approach, employing the block exchangeable correlation structures with different correlation parameters for the treatment arm and for the control arm, and surveying five marginal mean models with different assumptions of time effect: no-time constant treatment effect, linear-time constant treatment effect, categorical-time constant treatment effect, linear time by treatment interaction, and categorical time by treatment interaction. Closed-form sample size formulas are derived for continuous outcomes, which depends on the eigenvalues of the correlation matrices; detailed numerical sample size procedures are proposed for binary outcomes. Through simulations, we demonstrate that the empirical power agrees well with the predicted power, for as few as eight groups formed in the treatment arm, when data are analyzed using the matrix-adjusted estimating equations for the correlation parameters with a bias-corrected sandwich variance estimator.

Multiply robust generalized estimating equations for cluster randomized trials with missing outcomes.

Generalized estimating equations (GEEs) provide a useful framework for estimating marginal regression parameters based on data from cluster randomized trials (CRTs), but they can result in inaccurate parameter estimates when some outcomes are informatively missing. Existing techniques to handle missing outcomes in CRTs rely on correct specification of a propensity score model, a covariate-conditional mean outcome model, or require at least one of these two models to be correct, which can be challenging in practice. In this article, we develop new weighted GEEs to simultaneously estimate the marginal mean, scale, and correlation parameters in CRTs with missing outcomes, allowing for multiple propensity score models and multiple covariate-conditional mean models to be specified. The resulting estimators are consistent provided that any one of these models is correct. An iterative algorithm is provided for implementing this more robust estimator and practical considerations for specifying multiple models are discussed. We evaluate the performance of the proposed method through Monte Carlo simulations and apply the proposed multiply robust estimator to analyze the Botswana Combination Prevention Project, a large HIV prevention CRT designed to evaluate whether a combination of HIV-prevention measures can reduce HIV incidence.

τ $$ \tau $$ -Inflated beta regression model for censored recurrent events.

This research introduces a multivariate τ $$ \tau $$ -inflated beta regression ( τ $$ \tau $$ -IBR) modeling approach for the analysis of censored recurrent event data that is particularly useful when there is a mixture of (a) individuals who are generally less susceptible to recurrent events and (b) heterogeneity in duration of event-free periods amongst those who experience events. The modeling approach is applied to a restructured version of the recurrent event data that consists of censored longitudinal times-to-first-event in τ $$ \tau $$ length follow-up windows that potentially overlap. Multiple imputation (MI) and expectation-solution (ES) approaches appropriate for censored data are developed as part of the model fitting process. A suite of useful analysis outputs are provided from the τ $$ \tau $$ -IBR model that include parameter estimates to help interpret the (a) and (b) mixture of event times in the data, estimates of mean τ $$ \tau $$ -restricted event-free duration in a τ $$ \tau $$ -length follow-up window based on a patient's covariate profile, and heat maps of raw τ $$ \tau $$ -restricted event-free durations observed in the data with censored observations augmented via averages across MI datasets. Simulations indicate good statistical performance of the proposed τ $$ \tau $$ -IBR approach to modeling censored recurrent event data. An example is given based on the Azithromycin for Prevention of COPD Exacerbations Trial.

PrEP Uptake and Methamphetamine Use Patterns in a 4-Year U.S. National Prospective Cohort Study of Sexual and Gender Minority People, 2017-2022.

Methamphetamine use is on the rise among sexual and gender minority people who have sex with men (SGMSM), escalating their HIV risk. Despite pre-exposure prophylaxis (PrEP) being an effective biomedical HIV prevention tool, its uptake in relation to methamphetamine use patterns in SGMSM has not been studied. In a U.S. cohort study from 2017 to 2022, 6,253 HIV-negative SGMSM indicated for but not using PrEP were followed for four years. Methamphetamine use was categorized (i.e., newly initiated, persistently used, never used, used but quit), and PrEP uptake assessed using generalized estimating equation (GEE), adjusted for attrition. Participants had a median age of 29, with 51.9% White, 11.1% Black, 24.5% Latinx, and 12.5% other races/ethnicities. Over the four years, PrEP use increased from 16.3 to 27.2%. GEE models identified risk factors including housing instability and food insecurity. In contrast, older age, health insurance, clinical indications, and prior PrEP use increased uptake. Notably, Latinx participants were more likely to use PrEP than Whites. Regarding methamphetamine use, those who newly initiated it were more likely to use PrEP compared to non-users. However, those who quit methamphetamine and those who persistently used it had PrEP usage rates comparable to those of non-users. Though PrEP uptake increased, it remained low in SGMSM. Methamphetamine use was associated with PrEP uptake. Healthcare providers should assess methamphetamine use for harm reduction. Prioritizing younger, uninsured SGMSM and addressing basic needs can enhance PrEP uptake and reduce HIV vulnerabilities.