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Paulo Lisboa , Terence Etchells, Ian Jarman Ana Sofia Fernandes Elia Biganzoli

Generic non-linear models of prognostic outcome. Paulo Lisboa , Terence Etchells, Ian Jarman Ana Sofia Fernandes Elia Biganzoli. Outline. Data from an observational longitudinal cohort study in oncology Risk stratification for time-to-event data

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Paulo Lisboa , Terence Etchells, Ian Jarman Ana Sofia Fernandes Elia Biganzoli

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  1. Generic non-linear models of prognostic outcome Paulo Lisboa, Terence Etchells, Ian Jarman Ana Sofia Fernandes Elia Biganzoli

  2. Outline • Data from an observational longitudinal cohort study in oncology • Risk stratification for time-to-event data • Integrated interface showing domain-specific visualization of the database • Multi-centre validation

  3. Breast tumours - clinical indicators Recruitment criteria: TNM (<=2, <=1, 0), Path. size<= 5cm Modelling cohort recruited during (n=917) 1983-89 Validation cohort (n= 931) 1990-93

  4. Cox regression

  5. Cox regression

  6. Cox regression

  7. Cox regression Prognostic index βi X1 X2 … tk

  8. Nottingham Prognostic Index (NPI) NPI= 0.2*Path. Size (cm)+ Histological Grade (1:3)+ N stage (1:3)

  9. Partial Logistic Artificial Neural Network X1 X2 … tk 1 1 Prognostic index wij vjk

  10. Partial Logistic Artificial Neural Network Attributes Time Value Event indicator X . . . . . . X 0.5 0 1 J X . . . . . . X 1.5 0 1 J X . . . . . . X 2.5 0 1 J X . . . . . . X 3.5 1 1 J Example:A patient who survives 3 years and dies during year 4

  11. Bayesian regularisation framework 1 1 X1 X2 … tk

  12. Automatic Relevance Determination (ARD) X1 X2 … tk 1 1 Path size Clinical stage nodes Histological type Nodes ratio Age ER status

  13. Automatic Relevance Determination Bayesian regularization framework for ARD Setting the regularization parameters Model selection

  14. Automatic Relevance Determination Bayesian regularization framework for ARD Setting the regularization parameters Model selection

  15. The evidence approximation αm 1 1

  16. Marginalisation a Σ 1 1

  17. Cox regression, breast cancer mortality: Christie 1983-89 1 2 3 4 Cox regression prognostic indexes arising in a 60 months study of LRG

  18. PLANN-ARD, breast cancer mortality: Christie 1983-89 1 2 3 4

  19. Hazard function, breast cancer mortality: Christie 1983-89 Operable patients

  20. 1990-93 1983-89

  21. High risk cohort

  22. High risk cohort

  23. Competing risks • Model time to first event • More than one risk – • e.g. intra-breast recurrence cf. distant metastasis • Case series from the Istituto dei Tumori, Milan (n=2,010) • (Veronesi et al. (1995) ) • Recruitment criterion QUART: conservative surgery

  24. Competing risks • Classification into mutually exclusive and complete classes a1 y1=h1 + a2 y2 =h2 + a3 y3=1- h1 -h2 +

  25. Cause-specific hazards DM IBTR Cumulative hazard Time

  26. Conditional cause-specific hazard IBTR Distant metastasis Hazard rate 4.3 cm ← 0.2 cm Years Years 4.3 cm ← 0.2 cm Tumour size Tumour size

  27. Conditional cause-specific hazard IBTR Distant metastasis Hazard rate Hazard rate 78 yrs ← 18 yrs 78 yrs ← 18 yrs Years Age Years Age Years Years 15 ← 0 15 ← 0 Nodes involved Nodes involved

  28. Ocular melanoma

  29. Double blind evaluation Ocular melanoma

  30. Double blind evaluation Ocular melanoma Cox regression PLSP PLANN-ARD

  31. Individual Survival Distributions 88 82 1 2 3 … 60

  32. Decision trees Rules PLANN-ARD

  33. www.adjuvantonline.com

  34. The Learned Intermediary Doctrine • The  learned intermediary doctrine says that product manufacturers owe no duty to warn consumers about the risks of consuming their products because the manufacturers can rely on the prescribing physician to do so. Law of Torts

  35. Rule extraction • Decompositional methods • Rules are derived for each hidden node • These rules are then composed together using the logic of the output node • Boolean logic derived in this way may contradict the real-valued network outputs x1 y x2 1 1

  36. Rule extraction Axis parallel boxes to fit smooth decision surfaces

  37. Multi-linear functions and scalar logic • Tsukimoto showed that the logic from a MLP with output • can be optimally resolved by approximating in [0,1] y as a function of the form • where or TSUKIMOTO, H., “Extracting rules from trained neural networks”, IEEE Transactions on Neural Networks, vol. 11, no. 2, pp. 377-389, March 2000. T.A. Etchells

  38. Multi-linear functions and scalar logic • e.g. for a 2 input network • where the parameters are to be determined. • The parameters are evaluated by substituting the values 0 or 1 for each variable. T.A. Etchells

  39. Rule extractionData in class are BLUE and data out of class are RED T.A. Etchells

  40. The Decision Surface T.A. Etchells

  41. Search in Orthogonal Directions T.A. Etchells

  42. Search in Orthogonal Directions T.A. Etchells

  43. Create Rule Box from the search T.A. Etchells

  44. Sensitivity and Specificity T.A. Etchells

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