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“Victor Babes” UNIVERSITY OF MEDICINE AND PHARMACY TIMISOARA DEPARTMENT OF MEDICAL INFORMATICS AND BIOPHYSICS Medical Informatics Division www.medinfo.umft.ro/dim 2004 / 2005 COURSE 12 MEDICAL DECISION SUPPORT (II) 4. ELEMENTS OF LOGICS 4.1. GENERAL NOTIONS • a) SENTENCE – expressing ideas about different objects or events features or causes – TYPES: cognitive, interogative, imperative... – TRUTH VALUE : • True (T), False (F), Uncertain (?) • b) LOGIC FORMS : – notion, sentence, inference – logic form of a declarative affirmative sentence: S is P (S=subject, P=predicate) • c) PRINCIPLES OF LOGICS – identity principle – non-contradiction principle – excluded tertiary principle – sufficient rationale principle • d) CATEGORICAL SENTENCES: – Universal - affirmative/negative • All S are P. None S is P. – Particular - affirmative, negative • Some S are P. Some S are not P. 4.2. COMPOSED SENTENCES • Applying an operator on one or two simple sentences (unary or binary operators) • Truth value of composed sentences: • Negation p 1 0 (not) ~p 0 1 • Conjunction (p q) (and) q p 1 0 1 1 0 0 0 0 • Disjunction (p q) (or) q p 1 0 1 1 1 0 1 0 • Implication (p q) (if…then...) q p 1 0 1 1 0 0 1 1 • Exclusive q p disjunction 1 (or…or...) XOR0 1 1 0 0 0 1 • Equivalence (p q) (if and only if) 1 1 0 0 0 1 q p 1 0 4.3. LOGICAL INFERENCE • Structure: premises (2 sen) conclusion • Modus ponens (p q) p q • Modus tollens (p q) ~q ~p • Sillogism (p q) (q r) (p r) 4.4. Ex: PROLOG LANGUAGE domains person, activity = symbol predicates likes (person, activity) clauses likes (ellen, tennis) likes (tom, baseball) likes (bill, X) if likes (tom, X) RUN: goal: likes (bill, baseball) TRUE 5. HEURISTIC METHODS: EXPERT SYSTEMS 5.1. SCHEME 5.2. COMPONENTS • a) COGNITIVE SYSTEM –KNOWLEDGE BASE: 3 levels • FACTUAL • CONCEPTUAL • (meta-knowledge) • b) REASONING SYSTEM (inference machine) • c) COMMUNICATION SYSTEM (user interface) • d) EXPLANATORY SYSTEM • [ e) Meta-resolutive system – to check if results are valid and reasoning is adequate) ] 5.3. COGNITIVE SYSTEM AND KNOWLEDGE BASE • Medical knowledge extraction: – general knowledge – knowledge from clinical experience • Medical knowledge formalization • KB may be extended • Self-completion (PROLOG language – appropriate for “Artificial Intelligence) • May be used either for decision support or for educational purposes) • 5.4. REASONING SYSTEM – leading position - drives the dialogue – may accept statistical procedures • 5.5. EXPLANATORY SYSTEM • shows the reasoning ‘trace’ – educational purposes • 5.6. COMMUNICATION SYSTEM – natural language use 5.7. MEDICAL Expert Systems • • • • • • • • MYCIN - bacterial infections PUFF - pulmonary deseases HEADMED - neuro-psychiatry CASNET - ophtalmology VM -’ventilator monitor’ INTERNIST - internal medicine TROPICAID - tropical diseases Domain-independent E.S. 6. CLASSIFICATION QUALITY ASSESSMENT a) Classification table Classifier T+ TD+ N11 N12 R1 Real D- N 21 N22 R2 C 1 C2 N b) PARAMETERS • • • • true positive = TP = N11 false negative = FN = N12 false positive = FP = N21 true negative = TN = N22 • sensitivity = p(T+/D+) = N11 / R1 – (capacity to detect the diseased) • specificity = p(T-/D-) = N22 / R2 – (capacity to reject the non-diseased) • positive predicitve value ppv = p(D+/T+) = N11 / C1 • negative predictive value npv = p(D-/T-) = N22 / C2 Global indicators • accuracy = (N11 + N22) / N • classification error rate = (N12 + N21) / N Threshold value d) ROC Curve SN = f(1 – SP) Receiver – Operator Characteristic SN si SP vary inversly proportional c) Example • A study was carried on a population of 3000 individuals. 500 of them had virosis during last year. Our computer program was able to detect 480 of them, but gave the same diagnosis to another 50 persons. Compute: • number of false positives and false negatives • sensitivity and specificity • accuracy and classification error rate • positive and negative predictive rate End