Representation and analysis of medical decision problems with influence diagrams.

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 127761, ’Probabilistic Modeling for Decision Support in Integrated Operations,’ by Martin Giese, University of Oslo, and Reidar B. Bratvold, SPE, University of Stavanger, prepared for the 2010 SPE Intelligent Energy Conference and Exhibition, Utrecht, Netherlands, 23-25 March. The paper has not been peer reviewed. A system was designed to assist operational decisions on the basis of real-time sensor readings in a typical scenario: While drilling close to the transition to a high-pressure formation, gas influx is observed. The technology used Bayesian networks and influence diagrams (IDs) to apply the method of decision analysis. The resulting ID was tested with a simulation. Introduction An assumption of integrated operations is that all information provided by the technology will help to make better decisions faster. But for this to happen, information must be presented in an accessible, useful, and decision-relevant format. Decision-analysis tools provide decision makers with logical and consistent recommendations based on the available data. This decision-analysis method was applied to a real case, representative of a typical scenario in drilling operations. The tool enabled good decisions consistently. However, effort is required and challenges exist in the modeling process along with problems regarding the way decision making is treated in the industry. Modeling and Solving A decision tree provides a graphical illustration of all the uncertainties, decisions, and payoffs associated with a decision situation. Although application of decision trees is intuitive for simple problems, the method loses its appeal for complex decisions. A symmetric decision tree grows exponentially with the number of variables in the decision domain, which often makes its use impractical. For complex decisions, the ID can provide a level of insight and transparency that cannot be achieved with the equivalent decision tree. The ID is a compact graphical-model representation for reasoning under uncertainty and was developed to assist structuring and analysis of complex decisions. The ID has two advantages—structuring and probabilistic evaluation. The structuring provides a graphical representation of the inter-relationships among the decision-basis elements (i.e., alternatives, information, and preferences), while the evaluation appraises the resulting decision structure and provides an assessment of its expected utility given the quantified decision basis. The representational framework of an ID captures the probabilistic relationships among decisions (alternatives), key uncertainties (information), and utilities (values or preferences). The ID model comprises four types of nodes. Decision nodes specify a set of alternatives. Chance nodes represent the key uncertainties in the decision domain. Deterministic nodes represent either constants or intermediate calculations. Value nodes represent the criteria used to make the decisions.

TWO ALGORITHMS THAT LEARN DNF BY DISCOVERING RELEVANT FEATURES

Chapter 5 - Decision Analysis Fundamentals

Warning and evacuation are among the most effective ways for saving human lives and properties from landslide dam hazards. A new warning decision model for landslide dam break is developed using Influence Diagrams to minimize the total losses. An Influence Diagram is a simple visual representation of a decision problem. It analyzes the qualitative (causal) relationships between the variables via a logic diagram and determines the quantitative relationships via conditional probability and Bayes’ theorem. The model is applied for the warning decision-making of the 2008 Tangjiashan landslide dam. The new model unifies the dam failure probability, evacuation, life loss, and flood damage in an Influence Diagram. Besides, a warning criterion is proposed for efficient decision-making. The model is more advanced than the decision tree since the inter-relationships of influence factors are qualitatively analyzed with causality connections and quantitatively analyzed with conditional probabilities. It is more efficient than a dynamic decision-making model (DYDEM) as it can directly calculate the three types of flood loss (i.e., evacuation cost, flood damage, and monetized life loss) and the expected total loss. Moreover, the probabilities of the influence factors leading to known results can be obtained through inversion analysis based on Bayesian theory. The new warning decision model offers an efficient way to save lives from landslide dam breaking and avoid unnecessary expenses from premature warning and evacuation.

Conversion of a colorectal cancer guideline into clinical decision trees with assessment of validity

Motivation and Objectives Neuroblastoma (NB) is the most common pediatric solid tumor characterized by clinical and molecular risk factors. The mortality is about fifty percent and this makes exploration of new and more effective risk factors for improving stratification mandatory. Hypoxia is a condition of low oxygen tension occurring in poorly vascularized areas of the tumor associated with poor prognosis. We had previously defined a robust gene expression signature measuring the hypoxic component of NB tumors (NB-hypo) that is a novel, independent risk factor (Fardin et al., 2010). Integrating classical risk factors with NB-hypo could improve the stratification of NB patients. We wanted to develop a prognostic classifier of NB patients’ outcome blending existing knowledge on clinical and molecular risk factors with the prognostic NB-hypo signature. Furthermore, we were interested in the decision tree classifier that outputs explicit rules easily translated into the clinical setting. Methods A total of 182 NB patients were enrolled on the bases of availability of gene expression profile by Affymetrix GeneChip HG-U133plus2.0, clinical and molecular information. NB tumor stage was defined according to the International NB Staging System (INSS). Age at diagnosis was dichotomized as greater or equal than 1 year and less than one year. MYCN status was amplified or normal. Good and poor outcome were defined as the patient’s status alive or dead 5 years after diagnosis respectively. The risk group was assigned according to the International Neuroblastoma Risk Group (INRG) Consensus Pretreatment Classification Schema. The 182 NB patients cohort was clustered in High and low hypoxia by k-means analysis of the 62 probsets constituting the NB-hypo signature previously described to measure tumor hypoxia (Fardin et al., 2009). We utilized the k-means algorithm implemented in the WEKA software (Hall et al., 2009) setting up number of clusters to 2, 500 iterations, preserving instances order and using Manhattan distance. The classification was performed by induction of decision trees. We utilized the Weka J48 implementation of the popular C4.5 algorithm (Kotsiantis, 2007; Murthy, 1998) and we set up the following options: pruning parameter was 0.25, pruning method was sub-tree raising and minimum number of instances per leaf was 2. Each leaf of the decision tree classifier identifies a non overlapping group of patients and each decision node identifies a branch which splits the dataset. We utilized Fisher’s exact test to measure the statistical significance of groups and branches. Fisher’s test was utilized in the context of decision trees to design a top-down approach to prune out non statistically significant branches (Liu et al., 2010). For each leaf we counted the number of correctly classified (named n) and the number of incorrectly classified instances (named m). We considered the marginal totals y and ¬y which represent poor and good outcome patients respectively. We designed a 2x2 contingency table of the two possible outcomes (Good or Poor) against the number of instances included in a give leaf and the remaining instances. Application of the Fisher exact test to this table generates a p value giving the probability of observing 2x2 table, or more extreme tables, knowing the marginal totals (y, ¬y) and assuming independency among the patients in a specific leaf and those in other leaves. Results and Discussion Patients were stratified in good and poor outcome on the bases of the following risk factors: Age at diagnosis, INSS stage, MYCN status and NB-hypo. The algorithm generated a decision tree classifier composed by 3 decision nodes and 7 leaves covering 87% of non overlapping good outcome patients and 100% of non overlapping poor outcome patients. Each path from the root to a leaf utilizes some, but not all, considered risk factors. Interestingly NB-hypo was included in the decision node that stratified stage 3 tumors demonstrating its usefulness in NB patients’ stratification. The leaves classifying good outcome patients had the very low error of 2% indicating a good performance of the algorithm in predicting this class. In contrast, the classification of poor outcome patients produced the leaf with the highest error of 13%. This leaf includes stage 4 tumors that are traditionally difficult to stratify by any known risk factor. To test statistical significance of the splits performed by the algorithm and the groups of patients, we utilized the Fisher’s exact test with a confidence set at 95%. The results showed that the groups obtained at each split were statistically significant. Furthermore, analysis of single groups of patients identified by leaves demonstrated that some, but no all reached the significance threshold. The significant leaves included the NB-hypo among the utilized risk factors. These results further strengthen the value of NB-hypo in predicting patients’ outcome. Lack of significance was often associated with a rather low number of patients in the leaf. This is a limitation of the divide-and-conquer approach of the algorithm, applied to relatively small patients’ cohorts, that recurrently splits the dataset. We then assessed the concordance of the predictions with INRG risk assessment. High Risk patients were correctly included in the leaves classifying poor outcome patients and Low Risk patients mapped correctly in the good outcome leaves. Interestingly, NB-hypo generated a leaf identifying a new group of poor outcome patients, sharing the high NB-hypo, whose characteristic fell into both High and Intermediate Risk. We collected and analyzed the results of 1000 10-fold cross validations and we observed that most classifiers had 7 leaves and only 5 out of 10^4 deviated from this pattern. The recurrence of 7 leaves demonstrated the high stability of the decision tree classifier that we generated. Analysis of the pruning parameters revealed optimal performance in the range of 0.1-0.3 in line with what used in this study. The path to reach each leaf can be easily transposed into a “if…than…” rule that, in turn provides an easy readout of the classifier, precious for translating the classification into the clinical setting. In conclusion, we demonstrated that the decision tree algorithm C4.5 can derive explicit rules for NB patients stratification if classical risk factors are blended with the NB hypo signature. These rules are statistically significant and quite stable and suitable to be conveyed to the clinic to design new therapies perhaps taking hypoxia into consideration as a potential target. Acknowledgements The work was supported by the Fondazione Italiana per la Lotta al Neuroblastoma, the Associazione Italiana per la Ricerca sul Cancro, the Società Italiana Glicogenosi, the Fondazione Umberto Veronesi and the Ministero della Salute Italiano. Davide Cangelosi and Fabiola Blengio are recipients of a fellowship from the Fondazione Italiana per la Lotta al Neuroblastoma. References Fardin P, Barla A, Mosci S, Rosasco L, Verri A, Varesio L. (2009) The l1-l2 regularization framework unmasks the hypoxia signature hidden in the transcriptome of a set of heterogeneous neuroblastoma cell lines. BMC Genomics, 10:474. doi:10.1186/1471-2164-10-474 Fardin P, Barla A, Mosci S, Rosasco L, Verri A, et al. (2010) A biology-driven approach identifies the hypoxia gene signature as a predictor of the outcome of neuroblastoma patients, Journal of Molecular Cancer 9:1. 185. doi:10.1186/1476-4598-9-185 Hall M, Eibe F, Holmes G, Pfahringer B, Reutemann P, Witten IH. (2009) The WEKA Data Mining Software: An Update: SIGKDD Explorations. doi: 10.1145/1656274.1656278 Kotsiantis S.B. (2007) Supervised Machine Learning: A Review of Classification Techniques. Informatica 31:249-268. Liu W, Chawla S, Cieslak D, Chawla N. (2010) A Robust Decision Tree Algorithm for Imbalanced Data Sets. In: SDM. 766-777. Murthy S.K. (1998) Automatic Construction of Decision Trees from Data: A Multi-Disciplinary Survey, Data Mining Knowledge Discovery 2:4. 345-389. doi: 10.1023/A:1009744630224

This paper provides a survey on probabilistic decision graphs for modeling and solving decision problems under uncertainty. We give an introduction to influence diagrams, which is a popular framework for representing and solving sequential decision problems with a single decision maker. As the methods for solving influence diagrams can scale rather badly in the length of the decision sequence, we present a couple of approaches for calculating approximate solutions. The modeling scope of the influence diagram is limited to so-called symmetric decision problems. This limitation has motivated the development of alternative representation languages, which enlarge the class of decision problems that can be modeled efficiently. We present some of these alternative frameworks and demonstrate their expressibility using several examples. Finally, we provide a list of software systems that implement the frameworks described in the paper.

Graphical representations have played a central role in decision analysis. Although decision trees remain popular, more general graphical languages can be used to encode relationships among variables of a decision basis. Influence diagrams, introduced in the late 1970s, provide a general graphical representation for decision analysis. We publish, in this first of two volumes of a special issue of Decision Analysis, the original manuscript on influence diagrams, along with a retrospective by the authors. We also include two new articles focusing respectively on the use of graphical models for group coordination challenges and on handling the unintended side effects of interventions.

Dynamic decision making without expected utility: An operational approach

Building an influence diagram in a knowledge-based decision system

Decision Model for Acute Appendicitis Treatment With Decision Tree Technology—A Modification of the Alvarado Scoring System

We develop new graphical representations for the problem of sequential decision making in partially observable multiagent environments, as formalized by interactive partially observable Markov decision processes (I-POMDPs). The graphical models called interactive influence diagrams (I-IDs) and their dynamic counterparts, interactive dynamic influence diagrams (I-DIDs), seek to explicitly model the structure that is often present in real-world problems by decomposing the situation into chance and decision variables, and the dependencies between the variables. I-DIDs generalize DIDs, which may be viewed as graphical representations of POMDPs, to multiagent settings in the same way that I-POMDPs generalize POMDPs. I-DIDs may be used to compute the policy of an agent given its belief as the agent acts and observes in a setting that is populated by other interacting agents. Using several examples, we show how I-IDs and I-DIDs may be applied and demonstrate their usefulness. We also show how the models may be solved using the standard algorithms that are applicable to DIDs. Solving I-DIDs exactly involves knowing the solutions of possible models of the other agents. The space of models grows exponentially with the number of time steps. We present a method of solving I-DIDs approximately by limiting the number of other agents’ candidate models at each time step to a constant. We do this by clustering models that are likely to be behaviorally equivalent and selecting a representative set from the clusters. We discuss the error bound of the approximation technique and demonstrate its empirical performance.

We investigate the problem of learning Boolean functions with a short DNF representation using decision trees as a concept description language. Unfortunately, Boolean concepts with a short description may not have a small decision tree representation when the tests at the nodes are limited to the primitive attributes. This representational shortcoming may be overcome by using Boolean features at the decision nodes. We present two new methods that adaptively introduce relevant features while learning a decision tree from examples. We show empirically that these methods outperform a standard decision tree algorithm for learning small random DNF functions when the examples are drawn at random from the uniform distribution.

AimsThis study aimed to clarify the different topographical distribution of tau pathology between progressive supranuclear palsy (PSP) and corticobasal degeneration (CBD) and establish a machine learning‐based decision tree classifier.MethodsParaffin‐embedded sections of the temporal cortex, motor cortex, caudate nucleus, globus pallidus, subthalamic nucleus, substantia nigra, red nucleus, and midbrain tectum from 1020 PSP and 199 CBD cases were assessed by phospho‐tau immunohistochemistry. The severity of tau lesions (i.e., neurofibrillary tangle, coiled body, tufted astrocyte or astrocytic plaque, and tau threads) was semi‐quantitatively scored in each region. Hierarchical cluster analysis was performed using tau pathology scores. A decision tree classifier was made with tau pathology scores using 914 cases. Cross‐validation was done using 305 cases. An additional ten cases were used for a validation study.ResultsCluster analysis displayed two distinct clusters; the first cluster included only CBD, and the other cluster included all PSP and six CBD cases. We built a decision tree, which used only seven decision nodes. The scores of tau threads in the caudate nucleus were the most decisive factor for predicting CBD. In a cross‐validation, 302 out of 305 cases were correctly diagnosed. In the pilot validation study, three investigators made a correct diagnosis in all cases using the decision tree.ConclusionRegardless of the morphology of astrocytic tau lesions, semi‐quantitative tau pathology scores in select brain regions are sufficient to distinguish PSP and CBD. The decision tree simplifies neuropathologic differential diagnosis of PSP and CBD.

Multistage decision making is either under certainty or uncertainty data conditions. Expected monetary values’ perfect information and monetary loss or gain at each stage of decision making are the research topics of a constrained decision making under risk. In the multistage decision making process, one stage’s decision interferes with the subsequent stage’s decision. In this paper, a simple study on decision making for creating Avionic infrastructure within the Odisha region is emphasized by using the mathematical logic tool on a case study problem. In this case study, the first stage D1 has two options, either construct or not construct new airports with utilizing the budgeted allot money. Each option’s outcome probability, conditional value and expected outcome value are determined by applying arithmetic and logical calculations to next two stages D2 and D3. The expected value and percentage of returns are mentioned in the decision trees designed in Section 3. The nodes of the decision tree are stages or chance nodes and the arc lines’ labels are mentioned from the appropriate expressions written in the decision tree and chance nodes table mentioned in Section 4.