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Handling of uncertainty in medical data using machine learning and probability theory techniques: A review of 30 years (1991-2020)

Roohallah Alizadehsani, Mohamad Roshanzamir, Sadiq Hussain, Abbas Khosravi, Afsaneh Koohestani, Mohammad Hossein Zangooei, Moloud Abdar, Adham Beykikhoshk, Afshin Shoeibi, Assef Zare, Maryam Panahiazar, Saeid Nahavandi, Dipti Srinivasan, Amir F. Atiya, U. Rajendra Acharya

arXiv:2008.10114v1cs.AI

TL;DR

Uncertainty in medical data and models remains a less-explored issue, and the review describes limited knowledge for addressing healthcare uncertainty. The paper reviews uncertainty quantification in medical science, identifying uncertainty across data and models and methods including Bayesian inference, fuzzy systems, Monte Carlo simulation, rough classification, Dempster–Shafer theory, and imprecise probability. The review finds that classical machine-learning and probability-theory methods have been widely used, while deep-learning techniques are becoming more popular among researchers.

  • Problem

    Uncertainty in medical data and models remains a less-explored issue, and the review describes limited knowledge for addressing healthcare uncertainty.

    Source: §1 · p. 2

  • Method

    The paper reviews uncertainty quantification in medical science, identifying uncertainty across data and models and methods including Bayesian inference, fuzzy systems, Monte Carlo simulation, rough classification, Dempster–Shafer theory, and imprecise probability.

    Source: §1 · p. 2

  • Results

    The review finds that classical machine-learning and probability-theory methods have been widely used, while deep-learning techniques are becoming more popular among researchers.

    Source: §1 · p. 2, §5 · p. 22

  • Takeaways & Limitations

    The review concludes that deep-learning methods may be employed to handle uncertainty in medical data, with high performance reported for noisy-signal arrhythmia classification.

    Source: §5 · p. 22

    The review identifies unresolved challenges in computational cost and dimensionality, method and result validation, patient-specific inputs, and choosing model complexity.

    Source: §4 · p. 21

Abstract

from arXiv · show

Understanding data and reaching valid conclusions are of paramount importance in the present era of big data. Machine learning and probability theory methods have widespread application for this purpose in different fields. One critically important yet less explored aspect is how data and model uncertainties are captured and analyzed. Proper quantification of uncertainty provides valuable information for optimal decision making. This paper reviewed related studies conducted in the last 30 years (from 1991 to 2020) in handling uncertainties in medical data using probability theory and machine learning techniques. Medical data is more prone to uncertainty due to the presence of noise in the data. So, it is very important to have clean medical data without any noise to get accurate diagnosis. The sources of noise in the medical data need to be known to address this issue. Based on the medical data obtained by the physician, diagnosis of disease, and treatment plan are prescribed. Hence, the uncertainty is growing in healthcare and there is limited knowledge to address these problems. We have little knowledge about the optimal treatment methods as there are many sources of uncertainty in medical science. Our findings indicate that there are few challenges to be addressed in handling the uncertainty in medical raw data and new models. In this work, we have summarized various methods employed to overcome this problem. Nowadays, application of novel deep learning techniques to deal such uncertainties have significantly increased.

1. Introduction

Medical data uncertainty complicates decision-making, while the review addresses limited knowledge about how to quantify and handle uncertainty in healthcare. It distinguishes uncertainty arising from noisy data from uncertainty in model structure or parameters.

1. Introduction

  • Medical data uncertainty, including missing values and noise, makes decision-making difficult.The paper relates machine-learning performance to both the selected algorithm and the nature of the data.Source: §1 · p. 2
  • Data uncertainty can arise from measurement imprecision, while model uncertainty concerns structure or parameter choices.The paper also calls model uncertainty epistemic uncertainty.Source: §1 · p. 2
  • The review surveys uncertainty quantification in medical science and identifies Bayesian inference, fuzzy systems, Monte Carlo simulation, rough classification, Dempster–Shafer theory, and imprecise probability as commonly applied methods.It reports that uncertainty is a common challenge across different raw data and models.Source: §1 · p. 2

2. Search Criteria

The review searches for medical-science studies published from January 1991 through May 2020, then screens and supplements the initial results. Its final corpus contains 165 papers.

2. Search Criteria

  • The search used Google Scholar and covered papers published from 1 January 1991 to 31 May 2020.The search terms combined medical science with Bayesian inference, fuzzy systems, Monte Carlo simulation, rough classification, Dempster–Shafer theory, or imprecise probability.Source: §2 · p. 3
  • The review investigated 165 papers: 91 selected high-quality papers plus 74 additional papers found through reference lists.The initial search identified about 324 English-language papers; papers deemed not to have significant impact were removed before the 91-paper selection.Source: §2 · p. 3
  • The review reports that research on handling uncertainty in medical data received more attention in recent years.Figure 3 presents the publication trend across the review period.Source: §2 · p. 3, Figure 3 · p. 4

3. Uncertainty Handling Algorithms in Medical Science

The review identifies six commonly used approaches for handling uncertainty in medical science.

3. Uncertainty Handling Algorithms in Medical Science

  • Bayesian inference, fuzzy systems, Monte Carlo simulation, rough classification, Dempster–Shafer theory, and imprecise probability are identified as common approaches.Source: §3 · p. 4, Figure 4 · p. 4

3.1. Bayesian inference (BI)

Bayesian inference updates disease hypotheses using evidence and prior probabilities, and the review describes its medical applications alongside Bayesian deep-learning approaches. In Bayesian neural networks, weights are represented by distributions rather than fixed values.

3.1. Bayesian inference (BI)

  • Bayesian inference is described as using Bayes’ theorem to update a hypothesis probability when additional evidence is available.The section frames the inference as a repeated process that can yield a likely diagnosis from patient symptoms.Source: §3.1 · pp. 4–5

3.1.1. Related work based on bayesian inference

  • The cited passages describe Bayesian studies estimating HIV prevalence from screening data, modeling HIV dynamics and virologic responses, designing medical-diagnosis expert systems, and applying Bayesian methods to distributed medical data and expenditure prediction.Source: §3.1.1 · pp. 5–6

3.1.2. Related works based on Bayesian Deep Learning

  • Bayesian neural networks learn parameters of random variables instead of deterministic weights, with backpropagation used to learn those parameters.The figure contrasts this distribution-based representation with fixed weights in classical backpropagation.Source: §3.1.2 · p. 7, Figure 5 · p. 7
  • Kendall et al. report about 3% improved segmentation performance after modeling uncertainty with Monte Carlo dropout at test time.The improvement was especially significant on the small dataset (Kendall et al. 2015).Source: §3.1.2 · p. 7
  • Bayesian deep learning combines deep learning’s perception capabilities with Bayesian reasoning for higher-level inference tasks.Wang and Yeung (2016) proposed a general framework and applied it to recommender or control systems.Source: §3.1.2 · p. 7
  • Bayesian deep-learning research also combines aleatoric and epistemic uncertainty and uses uncertainty decomposition for decision-making.Kendall and Gal (2017) formulated a loss function robust to data uncertainty; Depeweg et al. (2018) used decomposition to define a risk-sensitive reinforcement-learning criterion.Source: §3.1.2 · pp. 7–8

3.2. Fuzzy Logic

This section describes fuzzy logic and ANFIS as approaches to represent uncertainty, then surveys medical applications of ANFIS. ANFIS combines fuzzy inference with neural-network learning through a layered system of rules and parameters.

3.2. Fuzzy Logic

  • Fuzzy processing converts crisp inputs into membership functions, applies fuzzy rules, then maps fuzzy outputs back to standard outputs.Fuzzy sets represent objects with degrees of membership determined by a membership function.Source: §3.2 · p. 8

3.2.1. ANFIS

  • ANFIS combines fuzzy logic and neural-network learning in a five-layer Takagi–Sugeno system whose rules approximate nonlinear functions.Its adaptive layers use premise and consequent parameters, and the final layer sums incoming signals to produce the output.Source: §3.2.1 · pp. 8, 10

3.2.2. Related Works based on ANFIS

  • Medical ANFIS applications include missing-value handling, kidney-damage timeframe prediction, and rheumatoid arthritis classification, with 91.25% and 95% accuracy reported for left- and right-hand signals.The cited rheumatoid-arthritis model combined ANFIS with MUSIC; a separate model predicted GFR variations over long future timeframes.Source: §3.2.2 · p. 10
  • Other reviewed work reports feature selection as important for reducing time and increasing accuracy, while interval type-2 fuzzy logic is applied to noisy, high-dimensional medical data.A wavelet-transform and interval type-2 fuzzy-logic method was described as a potential clinical decision-support system.Source: §3.2.2 · p. 10

3.3. Monte Carlo simulation

The section presents Monte Carlo simulation as repeated random sampling for estimating unknown quantities and modelling risk. It describes integration estimates and their uncertainty, then gives examples of medical applications.

3.3. Monte Carlo simulation

  • Monte Carlo simulation uses repeated random sampling to estimate unknown parameters and model risk when many random variables are involved.The review characterizes the method as using random-number generation to address deterministic problems.Source: §3.3 · p. 11, §3.3.1 · p. 12

3.3.1. Monte Carlo method

  • Monte Carlo integration estimates an expectation by averaging sampled values h(Xi); under the stated finite-expectation condition, the estimate converges to I as N increases.The passage states the condition E|h(x)| < ∞ for convergence.Source: Basic Principle Monte Carlo Integration · p. 12

3.3.2. RELATED WORKS BASED ON MONTE CARLO SIMULATION (MCS)

  • The review describes medical uses including CT breast-imaging scatter simulation and GPU-accelerated dose calculation, with GPU simulations reported as faster than CPU simulations without significant accuracy differences.The dose-calculation package was tested on phantoms and realistic patients.Source: §3.3.2 · pp. 12–13

3.4. Rough set theory (RST)

Rough set theory represents uncertain or inconsistent knowledge using classifications and approximations of sets. The section defines its core relations and surveys medical applications.

3.4. Rough set theory (RST)

  • Rough set theory organizes knowledge through classification of relational databases, then mines knowledge by approximating targets and classifying equivalence relations.The review describes RST as a mathematical tool for uncertain and inconsistent knowledge.Source: §3.4 · p. 14

3.4.1. Formal Definition

  • Objects matching on every attribute in B belong to the same indiscernibility class, which supports upper and lower approximations of a target set.The boundary region represents uncertainty: a larger boundary corresponds to a higher degree of uncertainty.Source: §3.4.1 · p. 14

3.4.2. Related Works based on RST

  • Medical applications include rough-set sub-health classification and tumor classification, while a modified variable-precision model produced smaller rule sets and better feature reduction for inconsistent or noisy records at higher computational effort.The tumor-classification approach used neighborhood rough sets and probabilistic neural networks for gene reduction.Source: §3.4.2 · p. 15

3.5. Dempster–Shafer theory (DST)

Dempster–Shafer theory represents uncertainty with belief masses over possible outcomes and combines evidence from multiple sources. The review outlines its probability bounds, combination rule, computational cost, and medical applications.

3.5. Dempster–Shafer theory (DST)

  • Dempster–Shafer theory assigns belief mass to subsets of possible states, representing ignorance and integrating evidence beyond single-event probabilities.Belief and plausibility provide lower and upper bounds on a probability interval.Source: §3.5 · p. 16, §3.5.1 · p. 16

3.5.2. Dempster's rule of combination

  • Dempster’s rule combines two mass assignments into a joint mass, with k estimating the conflict between the mass sets.The review notes that computation may involve 2^n sets, while adding evidence can reduce the uncertainty interval.Source: §3.5.2 · p. 17

3.5.3. Related Works based on DST

  • Medical applications include DST-based image processing for imprecision and partial-volume effects, fuzzy-DST diagnostic reasoning, and fusion of breast-cancer classifiers from two data sources.The breast-cancer classifier fusion was reported to yield better results in automatic detection.Source: §3.5.3 · pp. 17–18

3.6. Imprecise probability

Imprecise probability generalizes traditional probability by using lower and upper probabilities to quantify aleatory and epistemic uncertainty. The section outlines its definitions and reviews medical applications.

3.6. Imprecise probability

  • Imprecise probability replaces a single probability with lower and upper bounds to quantify both epistemic and aleatory uncertainty.The review names coherent lower prevision, possibility theory, de Finetti's subjective probability, and Dempster-Shafer evidence theory as representations.Source: §3.6 · p. 19

3.6.1. Definitions

  • The interval width measures lack of perfect information, while lower and upper probabilities reflect evidence for and against an event and have gamble-based subjective interpretations.The supplied definitions also distinguish precise probability, where the bounds coincide, from complete lack of knowledge, where the lower bound is 0 and the upper bound is 1.Source: §3.6.1 · p. 19

3.6.2. Related Works on Imprecise Probability

  • Medical applications include noisy-data classification with creedal decision trees, imprecise-probability analysis of medicinal plants, and contextual modelling of medical-data imprecision.The review reports that creedal decision trees outperformed single-tree and ensemble methods in noisy environments; Kwiatkowska et al. integrated multidimensional, fuzzy-logic, and semiotic approaches.Source: §3.6.2 · pp. 19–20, Table 6 · p. 20

4. Discussion

The discussion compares uncertainty-handling methods, describes robustness to noisy medical data, and identifies computational, validation, and patient-specific modelling challenges.

Methods and trade-offs

  • Bayesian inference is the most widely used medical-field method among those discussed, while fuzzy systems rank second and Monte Carlo simulation is also widely used.Bayesian inference addresses both data and model uncertainty and incorporates prior knowledge, but is computationally intensive; Monte Carlo simulation is flexible but costly and approximate.Source: Figure 8 · p. 20, §4 · p. 21
  • Other uncertainty methods, including Bayesian information criterion, Laplace and variational approximations, exact sampling, and expectation propagation, are reported as little used.Source: §4 · p. 21

Challenges

  • Key challenges include dimensionality and computational cost, validating methods and results, adapting inputs to patient settings, and selecting model complexity.More complex models can reduce output uncertainty while increasing input uncertainty because more inputs must be examined patient-specifically; some inputs are unmeasurable or costly to measure.Source: §4 · p. 21

Noisy medical data

  • Higher-order statistics/spectra and deep learning are reported as more robust to noise, with bispectra and cumulants used to capture subtle biomedical-signal changes.The review favors higher-order statistics over second-order correlations for signals that are nonstationary, nonlinear, and non-Gaussian.Source: §4 · p. 22
  • Deep neural networks can generalize from noisy training data, and studies report high arrhythmia-classification performance on noisy ECG signals.The review notes successful learning under arbitrary amounts of noise on other datasets and proposes exploring deep learning for noisy medical data.Source: §4 · p. 22

5. Conclusions and Future works

The review concludes that uncertainty is intrinsic to medical decisions and that both classical methods and probability theory have been widely used to address it. Deep learning is gaining popularity, including for noisy signals, while the authors emphasize clinicians' role in responding to uncertainty.

5. Conclusions and Future works

  • The review characterizes medical decisions and outcomes as subject to multiple sources of uncertainty.Source: §5 · p. 22
  • The authors argue that useful uncertainty-handling methods in healthcare should start with physicians, who need a clearer understanding of uncertainty in their work.They caution that clinicians commonly downplay uncertainty and that medical decision-making is intricate.Source: §5 · p. 22
  • The authors state that uncertainty quantification is needed for early disease detection, time savings, and accurate diagnosis.Source: §5 · p. 22
  • Classical machine-learning and probability-theory methods have been significantly used for uncertainty classification, while deep learning is becoming popular and has achieved high arrhythmia-classification performance on noisy signals.The cited studies include Acharya et al. 2017, Oh et al. 2018, and Oh et al. 2019; the authors propose exploring deep learning for medical-data uncertainty.Source: §5 · p. 22

Data availability; Declaration of interests; Funding

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