The effect of assuming independence in applying Bayes' Theorem to risk estimation and classification in diagnosis

Russek, Estelle; Kronmal, Richard A.; Fisher, Lloyd D.

doi:10.1016/0010-4809(83)90040-x

Cited by 46 publications

(26 citation statements)

References 8 publications

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“…Other authors have verified by Monte Carlo simulation that "choosing a simple method of discrimination is often beneficial even if the underlying model assumptions are wrong" (Flury, Schmid, & Narayanan (1994) for quadratic discriminant functions; Russek, Kronmal, & Fisher (1983) for the Bayesian classifier vs. multivariate Gaussian models). In general, the amount of structure that can be induced for a domain will be limited by both the available sample and the learner's representational power.…”

Section: When Will the Bayesian Classifier Outperform Other Learners?mentioning

confidence: 99%

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1997

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Abstract. The simple Bayesian classifier is known to be optimal when attributes are independent given the class, but the question of whether other sufficient conditions for its optimality exist has so far not been explored. Empirical results showing that it performs surprisingly well in many domains containing clear attribute dependences suggest that the answer to this question may be positive. This article shows that, although the Bayesian classifier's probability estimates are only optimal under quadratic loss if the independence assumption holds, the classifier itself can be optimal under zero-one loss (misclassification rate) even when this assumption is violated by a wide margin. The region of quadratic-loss optimality of the Bayesian classifier is in fact a second-order infinitesimal fraction of the region of zero-one optimality. This implies that the Bayesian classifier has a much greater range of applicability than previously thought. For example, in this article it is shown to be optimal for learning conjunctions and disjunctions, even though they violate the independence assumption. Further, studies in artificial domains show that it will often outperform more powerful classifiers for common training set sizes and numbers of attributes, even if its bias is a priori much less appropriate to the domain. This article's results also imply that detecting attribute dependence is not necessarily the best way to extend the Bayesian classifier, and this is also verified empirically.

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Section: When Will the Bayesian Classifier Outperform Other Learners?mentioning

confidence: 99%

Untitled

1997

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“…In this context, the non-independence of the tests is critical, äs the actual values of performance chäracteristics (sensitivity, specificity, predictive value) can diverge from those obtained by combinatorial calculätions that ignore the possible between-test correlätions (1)(2)(3)(4)(5)(6)(7)(8).…”

Section: Introductionmentioning

confidence: 99%

“…The predictive value has also been derived from the experimental datä using simplified procedures based on semiempirical formulae (7,8). Mathematical models have been described äs well, to predict the misclassifications resulting from test correlation (2,5).…”

Section: Introductionmentioning

confidence: 99%

Performance Assessment of Coupled Tests: The Effects of Statistical Non-Independence

Chiecchio

Malvano²,

Giglioli³

et al. 1994

CCLM

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l Summary: Limited to two-test associations (series and parallel schemes), the effects of Statistical non-independence ! were studied through a mathematical approach and an experimentally-based evaluation. Both procedures were applied to results for total hormones and free fractipns in euthyroid and dysthyroid subjects. Assuming independence, the sensitivity of combiHed tests was found to increase in parallel coupling, and to decrease, symmetrically, in series coupling, depending critically on the degree of between-test correlation and on the value of single test sensitivity (the opposite modifications obviously occur for specificity). A more complicated Situation resulted for the predictive valüe of test associations, where a prediction based on a mathematical model was found not to be generally valid; in this case, calculätions using the correct values of conditional probabilities of coupled tests seemingly remain the safest procedure.

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“…This does not mean that syndromes may not exist for diagnoses. Also, Bayes’ theorem seems to be robust against violations to the prerequisite of conditional independence [3, 4, 5]. …”

Section: Methodsmentioning

confidence: 99%

Clinical Experience with a Decision Support Computer Program Using Bayes’ Theorem to Diagnose Chest Pain Patients

Aase¹

1999

Cardiology

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A decision support computer program (DSP) was used by the emergency room physician as a diagnostic tool on patients admitted with acute chest pain to guide the referral of these patients either to the Coronary Care Unit (CCU) or general ward. The DSP used Bayes’ theorem on 38 anamnestic and clinical variables to classify patients into one of nine diagnoses. During a six months trial period 32 physicians used the DSP to diagnose 493 patients admitted with acute chest pain. The physicians referred the patients to CCU or general ward based on their clinical judgements, the ECG findings and the diagnostic estimates given by the DSP. The program correctly diagnosed 150 (84%) of 178 patients with acute myocardial infarction and 63 of 112 patients with unstable angina. However, acute ischemic heart disease (acute myocardial infarction or unstable angina) was correctly classified by the DSP for 259 (89%) of 290 patients. By using the DSP, the number of patients unnecessarily referred to CCU was reduced from 35% to 19% and the number of patients in need of CCU observation misallocated to general ward was reduced from 13% to 10%. Thus, use of the DSP in the emergency room on easily available anamnestic and clinical variables may improve referrals to the CCU, optimize therapy and resource use.

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The effect of assuming independence in applying Bayes' Theorem to risk estimation and classification in diagnosis

Cited by 46 publications

References 8 publications

Untitled

Untitled

Performance Assessment of Coupled Tests: The Effects of Statistical Non-Independence

Clinical Experience with a Decision Support Computer Program Using Bayes’ Theorem to Diagnose Chest Pain Patients

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