Post-hoc Methods Research Articles

Coalitional Bayesian autoencoders: Towards explainable unsupervised deep learning with applications to condition monitoring under covariate shift

This paper aims to improve the explainability of autoencoder (AE) predictions by proposing two novel explanation methods based on the mean and epistemic uncertainty of log-likelihood estimates, which naturally arise from the probabilistic formulation of the AE, the Bayesian autoencoder (BAE). These formulations contrast the conventional post-hoc explanation methods for AEs, which incur additional modelling effort and implementations. We further extend the methods for sensor-based explanations, aggregating the explanations at the sensor level instead of the lower feature level.To evaluate the performance of explanation methods quantitatively, we test them on condition monitoring applications. Due to the lack of a common assessment of explanation methods, especially under covariate shift, we propose three evaluation metrics: (1) the G-mean of Spearman drift coefficients, (2) the G-mean of sensitivity-specificity of explanation ranking and (3) a sensor explanation quality index (SEQI) which combines the first two metrics, capturing the explanations’ abilities to measure the degree of monotonicity and to rank the sensors.Surprisingly, we observe that the explanations of BAE’s predictions suffer from high correlation resulting in misleading explanations. This new observation cautions against trusting these explanations without further understanding of when they may fail. To alleviate this, a “Coalitional BAE” is proposed, inspired by agent-based system theory. The Coalitional BAE models each sensor independently and eliminates the correlation in explanations. Our comprehensive experiments on publicly available condition monitoring datasets demonstrate significant improvements of the Coalitional BAEs over the baseline Centralised AEs on the proposed metrics, visualised through critical difference diagrams.

Explainable artificial intelligence (XAI) post-hoc explainability methods: risks and limitations in non-discrimination law

Organizations are increasingly employing complex black-box machine learning models in high-stakes decision-making. A popular approach to addressing the problem of opacity of black-box machine learning models is the use of post-hoc explainability methods. These methods approximate the logic of underlying machine learning models with the aim of explaining their internal workings, so that human examiners can understand them. In turn, it has been alluded that the insights from post-hoc explainability methods can be used to help regulate black-box machine learning. This article examines the validity of these claims. By examining whether the insights derived from post-hoc explainability methods in post-model deployment can prima facie meet legal definitions in European (read European Union) non-discrimination law, we argue that machine learning post-hoc explanation methods cannot guarantee the insights they generate.Ultimately, we argue that the use of post-hoc explanatory methods is useful in many cases, but that these methods have limitations that prohibit reliance as the sole mechanism to guarantee fairness of model outcomes in high-stakes decision-making. By way of an ancillary function, the inadequacy of European Non-Discrimination Law for algorithmic decision-making is demonstrated too.

On the interpretability of machine learning methods in crash frequency modeling and crash modification factor development

Machine learning (ML) model interpretability has attracted much attention recently given the promising performance of ML methods in crash frequency studies. Extracting accurate relationship between risk factors and crash frequency is important for understanding the causal effects of risk factors and developing safety countermeasures. However, there is no study that comprehensively summarizes ML model interpretation methods and provides guidance for safety researchers and practitioners. This research aims to fill this gap. Model-based and post-hoc ML interpretation methods are critically evaluated and compared to study their suitability in crash frequency modeling. These methods include classification and regression tree (CART), multivariate adaptive regression splines (MARS), Local Interpretable Model-agnostic Explanations (LIME), Local Sensitivity Analysis (LSA), Partial Dependence Plots (PDP), Global Sensitivity Analysis (GSA), and SHapley Additive exPlanations (SHAP). Model-based interpretation methods cannot reveal the detailed interaction relationships among risk factors. LIME can only be used to analyze the effects of a risk factor at the prediction level. LSA and PDP assume that different risk factors are independently distributed. Both GSA and SHAP can account for the potential correlation among risk factors. However, only SHAP can visualize the detailed relationships between crash outcomes and risk factors. This study also demonstrates the potential and benefits of using ML and SHAP to derive Crash Modification Factors (CMF). Finally, it is emphasized that statistical and ML models may not directly differentiate causation from correlation. Understanding the differences between them is critical for developing reliable safety countermeasures.

Toward Explainable Artificial Intelligence for Early Anticipation of Traffic Accidents

Traffic accident anticipation is a vital function of Automated Driving Systems (ADS) in providing a safety-guaranteed driving experience. An accident anticipation model aims to predict accidents promptly and accurately before they occur. Existing Artificial Intelligence (AI) models of accident anticipation lack a human-interpretable explanation of their decision making. Although these models perform well, they remain a black-box to the ADS users who find it to difficult to trust them. To this end, this paper presents a gated recurrent unit (GRU) network that learns spatio-temporal relational features for the early anticipation of traffic accidents from dashcam video data. A post-hoc attention mechanism named Grad-CAM (Gradient-weighted Class Activation Map) is integrated into the network to generate saliency maps as the visual explanation of the accident anticipation decision. An eye tracker captures human eye fixation points for generating human attention maps. The explainability of network-generated saliency maps is evaluated in comparison to human attention maps. Qualitative and quantitative results on a public crash data set confirm that the proposed explainable network can anticipate an accident on average 4.57 s before it occurs, with 94.02% average precision. Various post-hoc attention-based XAI methods are then evaluated and compared. This confirms that the Grad-CAM chosen by this study can generate high-quality, human-interpretable saliency maps (with 1.23 Normalized Scanpath Saliency) for explaining the crash anticipation decision. Importantly, results confirm that the proposed AI model, with a human-inspired design, can outperform humans in accident anticipation.

Interpretation and Classification of Arrhythmia Using Deep Convolutional Network

Electrocardiogram signal analysis can be time-consuming, tedious, and error-prone. Therefore, automated analysis is need of time that will assist clinicians in detecting cardiac abnormalities accurately and efficiently. Recently, deep learning models have shown unprecedented progress and strong arrhythmia classification capabilities, but their deployment in the medical sector is constrained due to their “black-box” nature. This paper proposes a robust explainability method to assist in explaining the underlying decision-making process in deep neural networks (DNN) and help provide feedback on biases that would benefit in improving DNN models. To achieve these objectives, initially, a deep learning model is trained on the MIT-BIH Arrhythmia Database and their classification performance is evaluated. The classification findings are then interpreted using the post-hoc explanation methods such as the SHapley Additive exPlanations (SHAP), Local Interpretable Model-Agnostic Explanations (LIME) and Gradient-weighted Class Activation Mapping (Grad-CAM) that interpret the decision rationale. As these methods are initially proposed for image applications therefore a new masking approach is proposed to cater these post-hoc explainability methods for ECG time-series data. After evaluating these methods for ECG arrhythmia classification, several drawbacks are drawn such as they fail to locate a feature’s importance if there are multiple occurrences of the same feature in a signal and also, SHAP and LIME perform random perturbations that sometimes produce unreliable explanations. Therefore, to overcome the drawbacks associated with these post-hoc explainability methods on time-series data, a novel K-GradCam method is proposed. The proposed K-GradCam method ensemble the benefits of these gradient based and perturbation based approaches and has demonstrated advantages over SHAP, Grad-CAM and LIME in terms of interpreting the models’ decisions. To compare the the proposed technique with post-hoc explainability methods quantitatively, the confidence index of the proposed method is evaluated using dice loss. The proposed method shares 71% similarity with SHAP and 81% similarity with Grad-CAM methods; however, it shares the benefits of both methods and is computationally faster than SHAP and LIME.

The Robustness of Counterfactual Explanations Over Time

Counterfactual explanations are a prominent example of post-hoc interpretability methods in the explainable Artificial Intelligence (AI) research domain. Differently from other explanation methods, they offer the possibility to have recourse against unfavourable outcomes computed by machine learning models. However, in this paper we show that retraining machine learning models over time may invalidate the counterfactual explanations of their outcomes. We provide a formal definition of this phenomenon and we introduce a method, namely counterfactual data augmentation, to help improving the robustness of counterfactual explanations over time. We test our method in an empirical study where we simulate different model retraining scenarios. Our results show that counterfactual data augmentation improves the robustness of counterfactual explanations over time, therefore contributing to their use in real-world machine learning applications.

A Survey on Attention Mechanisms for Medical Applications: are we Moving Toward Better Algorithms?

The increasing popularity of attention mechanisms in deep learning algorithms for computer vision and natural language processing made these models attractive to other research domains. In healthcare, there is a strong need for tools that may improve the routines of the clinicians and the patients. Naturally, the use of attention-based algorithms for medical applications occurred smoothly. However, being healthcare a domain that depends on high-stake decisions, the scientific community must ponder if these high-performing algorithms fit the needs of medical applications. With this motto, this paper extensively reviews the use of attention mechanisms in machine learning methods (including Transformers) for several medical applications based on the types of tasks that may integrate several works pipelines of the medical domain. This work distinguishes itself from its predecessors by proposing a critical analysis of the claims and potentialities of attention mechanisms presented in the literature through an experimental case study on medical image classification with three different use cases. These experiments focus on the integrating process of attention mechanisms into established deep learning architectures, the analysis of their predictive power, and a visual assessment of their saliency maps generated by post-hoc explanation methods. This paper concludes with a critical analysis of the claims and potentialities presented in the literature about attention mechanisms and proposes future research lines in medical applications that may benefit from these frameworks.

Distribution-Aware Counterfactual Explanation by Mixed-Integer Linear Optimization

Post-hoc explanation methods for machine learning models have been widely used to support decision-making. One of the popular methods is Counterfactual Explanation (CE), also known as Actionable Recourse, which provides a user with a perturbation vector of features that alters the prediction result. Given a perturbation vector, a user can interpret it as an "action" for obtaining one's desired decision result. In practice, however, showing only a perturbation vector is often insufficient for users to execute the action. The reason is that if there is an asymmetric interaction among features, such as causality, the total cost of the action is expected to depend on the order of changing features. Therefore, practical CE methods are required to provide an appropriate order of changing features in addition to a perturbation vector. For this purpose, we propose a new framework called Ordered Counterfactual Explanation (OrdCE). We introduce a new objective function that evaluates a pair of an action and an order based on feature interaction. To extract an optimal pair, we propose a mixed-integer linear optimization approach with our objective function. Numerical experiments on real datasets demonstrated the effectiveness of our OrdCE in comparison with unordered CE methods.

Empirical observation of negligible fairness–accuracy trade-offs in machine learning for public policy

Growing use of machine learning in policy and social impact settings have raised concerns for fairness implications, especially for racial minorities. These concerns have generated considerable interest among machine learning and artificial intelligence researchers, who have developed new methods and established theoretical bounds for improving fairness, focusing on the source data, regularization and model training, or post-hoc adjustments to model scores. However, little work has studied the practical trade-offs between fairness and accuracy in real-world settings to understand how these bounds and methods translate into policy choices and impact on society. Our empirical study fills this gap by investigating the impact of mitigating disparities on accuracy, focusing on the common context of using machine learning to inform benefit allocation in resource-constrained programs across education, mental health, criminal justice, and housing safety. Here we describe applied work in which we find fairness-accuracy trade-offs to be negligible in practice. In each setting studied, explicitly focusing on achieving equity and using our proposed post-hoc disparity mitigation methods, fairness was substantially improved without sacrificing accuracy. This observation was robust across policy contexts studied, scale of resources available for intervention, time, and relative size of the protected groups. These empirical results challenge a commonly held assumption that reducing disparities either requires accepting an appreciable drop in accuracy or the development of novel, complex methods, making reducing disparities in these applications more practical.

Polyphenol Rich Sugarcane Extract Reduces Body Weight in C57/BL6J Mice Fed a High Fat, High Carbohydrate Diet

Background: Energy-dense diets have been implicated as a driving force in the global obesity crisis. Sucrose derived from sugar cane (Saccharum officinarum) is a carbohydrate source at the centre of this discussion. However, sugar cane is a complex plant containing a wide variety of phytochemicals that may have anti-obesity properties. The objective of this study was to assess if polyphenols extracted from sugar cane were capable of mitigating the progression of diet-induced obesity. Methods: Forty-five male, six-week-old C57BL/6J mice were divided into groups of 15 and fed a high-fat, high-carbohydrate diet supplemented with 0%, 2% or 4% polyphenol-rich sugarcane extract (PRSE) for twelve weeks. Body weight, food intake, water intake and faecal content were measured in addition to dual energy x-ray absorptiometry (DEXA) of the mice. Gene expression was also assessed for a range of key metabolic pathways in both blood and tissue samples in order to determine PRSE’s potential mechanisms of action. Data was analysed using ANOVA and post-hoc statistical methods. Results: Mice fed 4% PRSE were found to have a significantly lower overall bodyweight and adipose tissue accumulation compared to control (0%). This finding was supported by a reduced plasma leptin concentration and an increased excretion of carbohydrates. Upregulated gene transcriptions of adiponectin, PPARγ, PPARα, UCP2 and fatty acid synthase mRNAs were also observed. Conclusions: These results indicate that reduced carbohydrate absorption is the primary mechanism leading to the reduction of body weight in mice fed a high-fat, high-carbohydrate diet. This is predominately supported by the detection of increased carbohydrate concentration in the faeces of mice that lost weight. Other potential mechanisms, such as feed intake and energy expenditure, did not show significant differences between groups and are less likely to be involved.

Psycho-Behavioural Segmentation in Food and Nutrition: A Systematic Scoping Review of the Literature.

Inadequate dietary intakes are a key modifiable risk factor to reduce the risk of developing non-communicable diseases. To encourage healthy eating and behaviour change, innovative public health interventions are required. Social marketing, in particular segmentation, can be used to understand and target specific population groups. However, segmentation often uses demographic factors, ignoring the reasons behind why people behave the way they do. This review aims to explore the food and nutrition related research that has utilised psycho-behavioural segmentation. Six databases from were searched in June 2020. Inclusion criteria were: published 2010 onwards, segmentation by psycho-behavioural variables, outcome related to food or nutrition, and healthy adult population over 18 years. 30 studies were included; most were quantitative (n = 28) and all studies used post-hoc segmentation methods, with the tools used to segment the population varying. None of the segments generated were targeted in future research. Psycho-behavioural factors are key in understanding people’s behaviour. However, when used in post-hoc segmentation, do not allow for effective targeting as there is no prior understanding of behaviours that need to change within each segment. In future, we should move towards hybrid segmentation to assist with the design of interventions that target behaviours such as healthy eating.

Ordered Counterfactual Explanation by Mixed-Integer Linear Optimization

Post-hoc explanation methods for machine learning models have been widely used to support decision-making. One of the popular methods is Counterfactual Explanation (CE), also known as Actionable Recourse, which provides a user with a perturbation vector of features that alters the prediction result. Given a perturbation vector, a user can interpret it as an "action" for obtaining one's desired decision result. In practice, however, showing only a perturbation vector is often insufficient for users to execute the action. The reason is that if there is an asymmetric interaction among features, such as causality, the total cost of the action is expected to depend on the order of changing features. Therefore, practical CE methods are required to provide an appropriate order of changing features in addition to a perturbation vector. For this purpose, we propose a new framework called Ordered Counterfactual Explanation (OrdCE). We introduce a new objective function that evaluates a pair of an action and an order based on feature interaction. To extract an optimal pair, we propose a mixed-integer linear optimization approach with our objective function. Numerical experiments on real datasets demonstrated the effectiveness of our OrdCE in comparison with unordered CE methods.

Bayes-TrEx: a Bayesian Sampling Approach to Model Transparency by Example

Post-hoc explanation methods are gaining popularity for interpreting, understanding, and debugging neural networks. Most analyses using such methods explain decisions in response to inputs drawn from the test set. However, the test set may have few examples that trigger some model behaviors, such as high-confidence failures or ambiguous classifications. To address these challenges, we introduce a flexible model inspection framework: Bayes-TrEx. Given a data distribution, Bayes-TrEx finds in-distribution examples which trigger a specified prediction confidence. We demonstrate several use cases of Bayes-TrEx, including revealing highly confident (mis)classifications, visualizing class boundaries via ambiguous examples, understanding novel-class extrapolation behavior, and exposing neural network overconfidence. We use Bayes-TrEx to study classifiers trained on CLEVR, MNIST, and Fashion-MNIST, and we show that this framework enables more flexible holistic model analysis than just inspecting the test set. Code and supplemental material are available at https://github.com/serenabooth/Bayes-TrEx.

Interpretable Graph Capsule Networks for Object Recognition

Capsule Networks, as alternatives to Convolutional Neural Networks, have been proposed to recognize objects from images. The current literature demonstrates many advantages of CapsNets over CNNs. However, how to create explanations for individual classifications of CapsNets has not been well explored. The widely used saliency methods are mainly proposed for explaining CNN-based classifications; they create saliency map explanations by combining activation values and the corresponding gradients, e.g., Grad-CAM. These saliency methods require a specific architecture of the underlying classifiers and cannot be trivially applied to CapsNets due to the iterative routing mechanism therein. To overcome the lack of interpretability, we can either propose new post-hoc interpretation methods for CapsNets or modifying the model to have build-in explanations. In this work, we explore the latter. Specifically, we propose interpretable Graph Capsule Networks (GraCapsNets), where we replace the routing part with a multi-head attention-based Graph Pooling approach. In the proposed model, individual classification explanations can be created effectively and efficiently. Our model also demonstrates some unexpected benefits, even though it replaces the fundamental part of CapsNets. Our GraCapsNets achieve better classification performance with fewer parameters and better adversarial robustness, when compared to CapsNets. Besides, GraCapsNets also keep other advantages of CapsNets, namely, disentangled representations and affine transformation robustness.

On-field test and data calibration of a low-cost sensor for fine particles exposure assessment

BackgroundAccurate individual exposure assessment is crucial for evaluating the health effects of particulate matter (PM). Various portable monitors built upon low-cost optical sensors have emerged. However, the main challenge for their application is to guarantee accuracy of measurements. ObjectiveTo assess the performance of a newly developed PM sensor, and to develop methods for post-hoc data calibration to optimize its data quality. MethodWe conducted a series of laboratory experiments and field evaluations to quantify the reproducibility within Plantower PM sensors 7003 (PMS 7003) and the consistency between sensors and two established PM2.5 measurement methods [tapered element oscillating microbalances (TEOM) and gravimetric method (GM)]. Post-hoc data calibration methods for sensors were based on a multiple linear regression model (MLRM) and a random forest model (RFM). Ratios of raw and calibrated readings over the data of reference methods were calculated to examine the improvement after calibration. ResultsStrong correlations (≥0.82) and relatively small relative standard deviations (16–21%) between sensors were found during the laboratory and the field sampling. Compared with the reference methods, moderate to strong coefficients of determination (0.56–0.83) were observed; however, significant deviations were presented. After calibration, the ratios of PMS measurements over that of two reference methods both became convergent. ConclusionsOur study validated low-cost optical PM sensors under a wide range of PM2.5 concentrations (8–167 μg/m3). Our findings indicated potential applicability of PM sensors in PM2.5 exposure assessment, and confirmed a need of calibration. Linear calibration methods may be sufficient for ambient monitoring using TEOM as a reference, while nonlinear calibration methods may be more appropriate for indoor monitoring using GM as a reference.

LASSO Regularization within the LocalGLMnet Architecture

Deep learning models have been very successful in the application of machine learning methods, often out-performing classical statistical models such as linear regression models or generalized linear models. On the other hand, deep learning models are often criticized for not being explainable nor allowing for variable selection. There are two different ways of dealing with this problem, either we use post-hoc model interpretability methods or we design specific deep learning architectures that allow for (more) easy interpretation and explanation. This paper builds on our previous work on the LocalGLMnet architecture that gives an interpretable deep learning architecture. In the present paper, we show how group LASSO regularization (and other regularization schemes) can be implemented within the LocalGLMnet architecture so that we receive feature sparsity for variable selection. We benchmark our approach with the recently developed LassoNet of Lemhadri et al.

Artificial Intelligence in economic decision making: how to assure a trust?

Motivation: The decisions made by modern ‘black box’ artificial intelligence models are not understandable and therefore people do not trust them. This limits down the potential power of usage of Artificial Intelligence. Aim: The idea of this text is to show the different initiatives in different countries how AI, especially black box AI, can be made transparent and trustworthy and what kind of regulations will be implemented or discussed to be implemented. We also show up how a commonly used development process within Machine Learning can be enriched to fulfil the requirements e.g. of the Ethics guidelines for trustworthy AI of the High-Level Expert Group of the European Union. We support our discussion with a proposition of empirical tools providing interpretability. Results: The full potential of AI or products using AI can only be raised if the decision of AI models are transparent and trustworthy. Regulations which are followed over the whole life cycle of AI models, algorithms or the products they using these are therefore necessary as well as understandability or explainability of the decisions these models and algorithms made. Initiatives on every level of stakeholders started, e.g. international level on the European Union, country level, USA, China etc. as well on a company level. The post-hoc local interpretability methods could and should be implemented by economic decision makers to provide compliance with the regulations.

Post-hoc explanation of black-box classifiers using confident itemsets

Black-box Artificial Intelligence (AI) methods, e.g. deep neural networks, have been widely utilized to build predictive models that can extract complex relationships in a dataset and make predictions for new unseen data records. However, it is difficult to trust decisions made by such methods since their inner working and decision logic is hidden from the user. Explainable Artificial Intelligence (XAI) refers to systems that try to explain how a black-box AI model produces its outcomes. Post-hoc XAI methods approximate the behavior of a black-box by extracting relationships between feature values and the predictions. Perturbation-based and decision set methods are among commonly used post-hoc XAI systems. The former explanators rely on random perturbations of data records to build local or global linear models that explain individual predictions or the whole model. The latter explanators use those feature values that appear more frequently to construct a set of decision rules that produces the same outcomes as the target black-box. However, these two classes of XAI methods have some limitations. Random perturbations do not take into account the distribution of feature values in different subspaces, leading to misleading approximations. Decision sets only pay attention to frequent feature values and miss many important correlations between features and class labels that appear less frequently but accurately represent decision boundaries of the model. In this paper, we address the above challenges by proposing an explanation method named Confident Itemsets Explanation (CIE). We introduce confident itemsets, a set of feature values that are highly correlated to a specific class label. CIE utilizes confident itemsets to discretize the whole decision space of a model to smaller subspaces. Extracting important correlations between the features and the outcomes of the classifier in different subspaces, CIE produces instance-wise and class-wise explanations that accurately approximate the behavior of the target black-box. Conducting a set of experiments on various black-box classifiers, and different tabular and textual data classification tasks, we show that our CIE method performs better than the previous perturbation-based and rule-based explanators in terms of the descriptive accuracy (an improvement of 9.3%) and interpretability (an improvement of 8.8%) of the explanations. Subjective evaluations demonstrate that the users find the explanations of CIE more understandable and interpretable than those of the other comparison methods.

Automatic detection of tuberculosis related abnormalities in Chest X-ray images using hierarchical feature extraction scheme

Machine learning techniques have been widely used for abnormality detection in medical images. Chest X-ray images (CXR) are among the non-invasive diagnostic tools used to detect various disease pathologies. The ambiguous anatomical structure of soft tissues is one of the major challenges for segregating normal and abnormal images. The main objective of this study is to mimic the expert radiologist’s interpretation procedure in computer-aided diagnosis (CAD) systems. We propose an automatic technique for detection of abnormal CXR images containing one or more pathologies like pleural effusion, infiltration, fibrosis, hila enlargement, dense consolidation, etc. due to tuberculosis (TB). The proposed abnormality detection technique is based on the hierarchical feature extraction scheme in which the features are used in two-level of hierarchy to categorize healthy and unhealthy groups. In level one the handcrafted geometrical features like shape, size, eccentricity, perimeter, etc. and in level 2 traditional first order statistical feature along with texture features like energy, entropy, contrast, correlation, etc. are extracted from segmented lung-fields. Further, a supervised classification approach is employed on the extracted features to detect normal and abnormal CXR images. The performance of the algorithm is validated on a total of 800 CXR images from two public datasets, namely the Montgomery set and Shenzhen set. The obtained results (accuracy = 95.60 ± 5.07% and area under curve (AUC) = 0.95 ± 0.06 for Montgomery collection, and accuracy = 99.40 ± 1.05% and AUC = 0.99 ± 0.01 for Shenzhen collection) shows the promising performance of the proposed technique for TB detection compared to the existing state of the art approaches. Further, the obtained results are statistically validated using Friedman post-hoc multiple comparison methods, which confirms the significance of the proposed method.

The Effects of Initial Procalcitonin Levels on Mortality Rates in Geriatric Patients Undergoing Surgery

IntroductionThe aim of the current study is to investigate the relationship between mortality rate in geriatric patients undergoing surgery with preoperative serum levels of procalcitonin, C-reactive protein, and erythrocyte sedimentation rate.MethodsThis was a single-center retrospective study, including three groups with 101 patients, who are older than 65 years of age. A retrospective investigation was carried out from the laboratory information system for all groups from January to December 2018. Group 1 included patients who had surgery and then mortality within 30 days after surgery. Group 2 included hospitalized patients who had surgery and no mortality within 30 days after surgery. Group 3 included outpatient patients, who had suspicion for a bacterial infection and then no surgery or no mortality within 30 days.ResultsWhen three group comparisons were made for procalcitonin, C-reactive protein, and erythrocyte sedimentation rate values, the p-value of one-way analysis of variance (ANOVA) was higher than 0.05 for procalcitonin and lower than 0.05 for C-reactive protein and erythrocyte sedimentation rate, suggesting that one or more groups were significantly different. When post-hoc multiple comparison methods were applied, there were statistically significant differences between Groups 1 and 3 for C-reactive protein and erythrocyte sedimentation rate.ConclusionsProcalcitonin levels do not predict mortality following surgery. C-reactive protein and erythrocyte sedimentation rate are more useful biomarkers predicting mortality in geriatric patients undergoing surgery.