# IctNeo SYSTEM FOR JAUNDICE MANAGEMENT

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4 310 Problemas complejos de decisión: C. Bielza et al. Rev.R.Acad.Cienc.Exact.Fís.Nat. (Esp), 1998; 92 o duplicated nodes forclarity Figure 2. Final D for our problem. to obtain from experts, tables with so many entries and how to store and manage so much information. For example, consider the node "injuries due to hyperbilirubinemia" (HY), see Figure 2. The initial versions of the D did not containthe node "hyperbilirubinemia", and the predecessors of node BY were: ah the bilirubin concentrations, "pathology seriousness", and the newbom age at the third stage (when a higher level of bilirubin may exist), see Figure 3 a). Therefore, we should assign = 1152 numbers to obtain the probability distribution for node HY. sumptions, the only assignments required to derive the others are those of the conditional probabilities ofx given that ah causes but one are absent, needing a number of assignments that is linear inthe number of causes instead of exponential, as in the general case. n our case, by adding node "hyperbilirubinemia", we can define a causal relation between bilirubin levels and the presence or not of their alteration. Since with the other variables -"pathology seriousness" and the newbom age at the third stage-, is not possible this causal relation, the diagram is the oneshown in Figure 3 b). Now, we need only to assign 10 values for node "hyperbilirubinemia" plus = 72 for node HY, for a total of 82 values. Our medical problem had 50 chance nodes, obtaining, with OR-gate modelisations, a reduction of 70% inthe number of assignments required. To face this problem, we used generalized noisy OR-gates (2, 11), which are based on a model ofcausal nature, with sorne causes P'"'' P k acting to produce effect X, ah the causes and the effect having valuesabsent and present with various grades of intensity. After having checked their asa) b) Figure 3. Node injuries due to hyperbilirubinemia a) before and b) after OR-gate modelisations. Number in parentheses indicates the cardinal of the domain.

5 Problemas complejos de decisión: C.Bielza et al. Rev.R.Acad.Cienc.Exact.Fís.Nat. (Esp), 1998; Utilities The only issue left to complete the D is the preferences elicitation. We have shown aboye the value node in that D (see Figure 2) representing the (expected) utilities depending on their predecessors. Some of these predecessors have been explained in priorsections, but the process to get al1 of them fol1ows, as typical1y, a structured scheme: (1) to construct an objectives hierarchy along with the corresponding attributes and their scales; and (2) to derive the functional forrn of the multi-attribute utility function consistent with various sets of independence assumptions about the risk attitudes investigated (6). This function col1ects the influence of each subobjective on the overal1 objective. As a result, we obtained the hierarchy shown in Figure 4 with 6 lowest-evel objectives. Highlight X 4 ' conceming the stay at hospital which arises from the risk of infections, contagions, etc. and the preferences of parents measured by the inconvenience of visiting the baby every day (X) if he is at hospital, and the interruption of parent-infant bonding (X 3 ). For al1 attributes except for X!' ad hoc constructed scales were introduced. Observe now how al1 X/s are represented in the D (Figure 2) as factors that value the process, illustrating that not only therapeutic actions are important but also their suitability to the patient situation. The utility function was derived as multiplicative on (X!' Y 1 =(X 2, X 3 ), X 4, Y 2 =(Xs' X 6» with additive decompositions for (X 2, X 3 ) and (Xs' X 6 ). The assignment of component utility functions and scaling constants was carried out with the aid of Logical Decisions (8), but allowing imprecise assignments, as a way of sensitivity analysis, see (5) for a detailed explanation. Global Vvell-being of the nevvbom Direct effecis ntangible effecis NeVvbom-mother gap njuries Y2 Y 4 Economical Social Emotional Risk of being Duetothe Duetothe cost cost cost admitted treatrnent hyperbilirub. Xl X 2 X 3 X 4 X s X 6 Figure 4. An objectives hierarchy for our problem 3. EVDENCE PROPAGATON The evaluation of an D is typical1y carried out via Shachter's algorithrn (13), but it works for relatively smal1 problems. As we have seen, our jaundice problem has a big size: 50 chance nodes, 5 decision nodes and 144 arcs connecting some ofthem, plus 112 no~forgetting arcs. t amounts to requiring memory positions to storage the probability distributions (90458) plus the utility function (5400). Typical1y, the need for storage space grows enorrnously during the solution process, due to node inheritances at chance node removal and arc reversal operations. For instance, when removing a chance node e which precedes the value node v, v inherits the predecessors of e (if any) becoming new predecessors of v, provided that they were not before. Since the storage requirements for the utility function grow exponential1y in the number of variablesthat influence on it, this situation can lead to require more memory space than that available in any personal computer. A first way to overcome this problem is to find the opti~ mal sequence of variable reductions and arc removals, that which involves the minimum computational effort. But this is a NP-hard problem and, therefore, we can only pick a good sequence via some heuristic, like Kong's greedy heuristic (7). We have worked on this, see (1), improvingthe existent heuristics, obtaining e.g., a required storage space divided atmost by two with respect to Kong's heurístico Also, we have provided other computational savings by computing the expected utilities when a chance node is removed, only whenever this implies a saving in the storage space with respect to the previous diagram. Otherwise, we postpone it until it is necessary, i.e., at the moment of a decision node removal. But this is not enough for big problems. Our D requires a maximum storage capacity (for the operation which introduces the highest increase) of 1.66 x storage positions, being the average size of the problem 1.79 x storage positions. Therefore, the evaluation process becomes unmanageable.

6 312 Problemas complejos de decisión: C. Bielza et al. Rev.R.Acad.Cienc.Exact.Fís.Nat. (Esp), 1998; 92 As we said aboye, the system manages closed cases, from which there is some information available, Le., the outcomes of most random variables are known (maybe ex" cept for some hemoglobin measures not taken). This knowledge can be used via the technique of evidence propagation (3). The D is updated based on these new observations reflecting then the new state ofknowledge by changing the probability of observed variables together with the D structure. Consider, e.g., the operation of chance-to-chance evidence propagation. Figure 5 will illustrate the ideas. Suppose X = X is known. We will now add this information reducing the uncertainty content on the problem '.... ).. ~\ ' ". '.".'... \ 8/:/ 08 P(EX) P(AX) X az 0.9 Figure S. Chance-to-chance evidence propagation. The evidence X is first absorbed on X just by the table lookup of the observed outcome. This has effect on successors and predecessors of X, as follows. First, a forward evidence propagation to its successors E, F, G takes place, which is to discard situations of X taking values different thanthe observed x!' reducing in turn thesize of the probability distributions of these three variables. For example,the distribution for E changes from P(Ex) to P(EX = X)' as shown in Figure 5 by the non-shaded zone of the table, deleting then the arc (X, E). Second, a backward evidence propagation to its predecessors A, B takes place. For that, we first reverse the arcs between X and its predecessors by ap" plication of Bayes' rule, these becorning successors ofx as in the previous case. Therefore, arcs (X, A) and (X, B) are elirninated and X too. The computational burden alleviation is obvious since we reduce the sizes of probability tables and we elirninate node X and the arcs from and onto X. There are sirnilar operations to propagate evidence with other kind of nodes. Should the value node be a successor of an observed node, the storage requirements for the utility function would be reduced. These ideas have perrnitted us to solve our jaundice problem. For each patient, we have a historical record with his data, and those of his mother and familiar environment. This evidence is known before making the first decision and do not take into account any medical valuation, thus keeping the uncertainty on all the aspects related to the medical valuation of the problem. As a result, it produces important implications on the system operation. The conventional evaluation of an D provides at each decision node, atable with the optimal alternative for each possible combination of outcomes ofthe value node predecessors at that moment. Once the system has generated all these tables, we only must look for that combination that coincides with the patient under consideration. Hence,the D is evaluated only once and we perforro on these tables as many lookups as cases studied. Nevertheless, the evaluation oran D by instantiation of evidence on some nodes amounts to solving it for each par" ticular patient once this evidence has been propagatedand has updatedthe D. Consequently, we mustevaluate as many Ds as different cases studied. Decision tables will have a smaller size because they do not contain any reference to the instantiated variables. Our requirements have decreased now with this approach: storage positions, with a maximum storage capacity and an average size of 5.35 x 10 9 and 7.48 x 10 8 storage positions, respectively. 4. MPLEMENTATlON ctneo is implemented in C++ under Windows-95. Figure 6 shows ctneo general architecture. ctneo includes its own grammar to describe the D, th-

8 314 Problemas complejos de decisión: C. Bielza et al. Rev.R.Acad.Cienc.Exact.Fís.Nat. (Esp), 1998; 92 r Fecha ngreso {12/01/1997] "", 1, l::~... ["'-Fecha ngreso (14/01/1997) o, l.iw;:j j... Nombre-madre: 1M! del Carmen x ApelJidos~madle: Pérez Sanchez xxxxxxxxxxx rprueba ABO y Rh ~ ~ Grupo-Hijo Grupo-Madre ~ ~ 11':1 ractór~h-j,liio. 1: i~~ill~jj l~ ~ ~l roclo-rh-madre. : U Reanimación ~ Raza: Baio Medio Alto muvalto de Ulilidad < Coste Social Asiática o Sudamericana Negra Gitana ~ ~ Riesgo /ngreso HiperBrb Nulo Bajo Medio mujlalto Figura 7. User interface of ctneo. find out which are the relevant factors to apply the different therapies. The matter in question is to draw conclusions from the whole set of the system proposals with regard to ah possible user profiles. 4. To include pathology diagnosis by looking at the final updated probabilities of the diagram. 5. To have the possibility of dealing with missing patient information and/or unspecified distributions. 6. To include a constructor of (imprecise) utility functions to be used in other different hospitals. n short, we hope ctneo will become an important aid for doctors, both for intems and residents, who will be able to evaluate the implications relative to changes of protocol of neonatal jaundice in newboms, and will have in tum a better understanding of the jaundice problem. REFERENCES 1. Bielza, c., Gómez, M., Ríos-nsua, S. & Fdez del Pozo, J.A. (1999) Structural, Elicitation and Computational ssues Faced when Solving Complex Decision Making Prob1ems with nfluence Diagrams, Computers & Operations Research, to appear. 2. Díez, EJ. (1993) Parameter Adjustment in Bayes Networks. The Generalized Noisy OR-Gate, in D. Heckerrnan and A. Mamdani (eds.), Uncert. in Artif. ntell.: Proc. of the 9th Confer , Morgan Kaufmann, San Mateo, CA. 3. Ezawa, K.J. (1998) Evidence Propagation and Value of Evidence on nfluence Diagrams, Oper. Res., 46, 1, 73" Gartner, L.M. (1995) Neonatal Jaundice, Pedo in Review, 16, Gómez, M., Ríos-nsua, S., Bielza, C. & Fdez del Pozo, J.A. (1999) Multi-attribute Uti1ity Analysis in the ctneo System, in Y.Y. Haimes and R. Steuer (eds), XV-th nt. Con! on Multiple Criteria Decision Making, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin (to appear). ACKNOWLEDGMENTS 6. Keeney, R.L. & Raiffa, H. (1976) Decisions with Multiple Objectives. Preferences and Value Tradeoffs, Wiley. Research supported by DGESC project PB and PS project 97/ We wish to thank doctor D. Blanco who helped us in our visits to hospital. 7. Kong, A. (1986) Multivariate Belief Functions and Graphical Models, PhD. Diss., Dept. of Statistics, Harvard Univ., Cambridge, Mass.

9 Problemas complejos de decisión: C. Bielza et al. Rev.R.Acad.Cienc.Exact.Fís.Nat. (Esp), 1998; Logical Decisions for Windows 95 (1998) Multimeasure Decision Analysis Software, Golden, CO. 9. Merkhofer, M.W. (1987) Quantifying ludgmental Uncertainty: Methodo1ogy, Experiences,and nsights, EEE Trans. on Sys., Man and Cyber. SMC 17, Newman, T.B. & Maisels, M.l. (1992) Evaluation and Treatment of laundice in the Term nfant: A Kinder, Gentler Approach, Pediatrics, 89, (with discussion). 11. Pear1, l. (1988) Probabilistic Reasoning in ntelligent Systems, Morgan Kaufmann. 12. Ríos-nsua, S., Bielza, C., Gómez, M., Fdez del Pozo, l.a., Sánchez, M. & Caballero, S. (1998) An ntelligent Decision System for laundice Management in Newbom Babies, in El. Girón (ed.), Applied Decision Analysis, , Kluwer. 13. Shachter, R.D. (1986)Eva1uating nfluence Diagrarns, Opero Res., 34,

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