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1 Dr. Shahram Yazdani Multi ‑ Criteria Decision Making.

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1 1 Dr. Shahram Yazdani Multi ‑ Criteria Decision Making

2 Dr Shahram Yazdani 2 The Nature of Decision-Making in Healthcare System Process is interactive - involves group of persons Multiple criteria (objectives/attributes) Interaction among criteria/objectives Need for a standard process - need for consistency and continuity Time dependent: both short- and long-term

3 Dr Shahram Yazdani 3 Multi ‑ Criteria Decision Making Ben Franklin over 200 years ago recognized the presence of multiple attributes in everyday decisions and suggested a workable solution Major development in theory and practice since 1970

4 Dr Shahram Yazdani 4  Optimizing  Satisficing  Elimination-by-aspects  Incrementalism  Mixed scanning  Analytic Hierarchy Process Decision-Making Strategies

5 Dr Shahram Yazdani 5  Select the alternative that gives the best overall value  Identify criteria to judge alternatives  Can be expressed in mathematical terms and implemented using computer programs  Difficult to solve when model involves qualitative criteria  Optimization of “Utility Super Function” Decision-Making Strategies : Optimization

6 Dr Shahram Yazdani 6  Recognizes that “utility super functions” are difficult to formulate and In most cases one doesn’t want optimality Sequence in which alternatives are identified and considered; usually governed by heuristics)  Understand decision process (flow) (Sequence in which alternatives are identified and considered; usually governed by heuristics)  Decision maker is therefore part of the multi-objective problem  Select the first alternative that is good enough with respect to some minimal criteria  Cutoff level of constraints  Simon: satisficing or finding solutions that are good enough e.g. Goal Programming  Keen: viewed requirement of assigning weights or priorities to be problematic. Noninferior sets. Decision-Making Strategies : Satisficing

7 Dr Shahram Yazdani 7  Elimination of all alternatives that fail with respect to one aspect, then consider another aspect …  An aspect is like a constraint involving one or more criteria  Order of aspects can strongly influence results  An alternative that superior in many aspects may be eliminated Decision-Making Strategies : Elimination-by-Aspects

8 Dr Shahram Yazdani 8  Compare alternative courses of action to the current course of action  Look for alternatives that can overcome shortcomings of the current course of action  A decision that results in incremental improvement Decision Making Strategies: Incrementalism Decision Making Strategies: Incrementalism

9 Dr Shahram Yazdani 9  Scanning: Collection, processing, evaluating and weighing of information  Importance of decision determines the degree of scanning and choice  Each alternative is briefly considered  Reject alternatives for which strong objections are detected Decision Making Strategies: Mixed Scanning Decision Making Strategies: Mixed Scanning

10 Dr Shahram Yazdani 10  Decomposes the overall decision objective into a hierarchic structure of criteria, subcriteria, and alternatives  Pairwise comparison matrix for criteria, subcriteria and alternatives  Matrices are mathematically processed to calculate relative weights of criteria and sub criteria  Relative weights are used to arrive at a score for each alternative Decision Making Strategies: Analytic Hierarchy Process

11 Dr Shahram Yazdani 11  Dominance rule  Select the alternative that is better than other alternative(s) on at least one attribute and not worse on other attributes  Lexicographic rule  Starts with the most important attribute and selects the attribute that ranks highest on that attribute  If two or more are tied, proceed to the next important attribute  Maximizing number of attributes with greater attractiveness rule  Classify each alternative as better, equal or worse on each attribute  Select the alternative with the greater number of favorable attributes Decision Making : Other Strategies

12 Dr Shahram Yazdani 12  Conjunctive decision making  Compare all attributes of one alternative against all criteria  Reject the alternatives that do not meet the criteria  Additive linear rule  Start with a set of predetermined weights of each alternative on each attribute (A)  Allocate weights against the attributes (B)  Multiply (A) by (B) to determine the score for each alternative  Select the alternative having the highest score Decision Making Strategies: Other Strategies Decision Making Strategies: Other Strategies

13 Dr Shahram Yazdani 13 Political Approaches Actions and decisions result from bargaining among players To predict decision, find out:  who the players are  what are the players’ interests or stands?  what are the players’ relative influence?  How does the combined dynamics of the above affect the decisions

14 Dr Shahram Yazdani 14 Anarchic Theory of Decision-Making Decision-making in organizations are random and disjointed e.g. Lindblom: “muddling-through” concept of decision theory; avoid comprehensive analysis and concentrate on marginal gains An organization is a collection of:  choices looking for problems  issues and feelings waiting for decision situations  solutions looking for issues they apply to; or  decision makers looking for work  so-called organized anarchy.

15 Dr Shahram Yazdani 15 Major categories of MCDM methods A normative approach the disregards decision maker Statement of decision maker’s preference prior to analysis Interactive responses between analyst and decision maker Generation of noninferior (nondominated) solutions that decision maker selects from.

16 Dr Shahram Yazdani 16 Multiple Criteria Decision Making Multiple Objective Decision Making  MODM: used primarily for designing Multiple Attribute Decision Making  MADM: used primarily for choosing an alternative

17 17 Dr. Shahram Yazdani Multiple ‑ Objective Decision Making

18 Dr Shahram Yazdani 18 Multi ‑ Objective Decision Making Some decisions involve more than one objective. Utility theory provides a methodology that allows a subjective tradeoff among valued attributes.

19 Dr Shahram Yazdani 19 Approach is demonstrated with a decision table:

20 Dr Shahram Yazdani 20 EV(Alternative j) The expected effectiveness of each decision alternative is the weighted average of the probabilities with the utilities as weights. EV(A j ) =  i=1,n U i p ij j=1,…m

21 Dr Shahram Yazdani 21 Relative Utilities 1. Every objective must has a utility value 2. The most important objective has the highest utility value 3. The utility value of achieving 2 objectives is the sum of the individual utility values

22 Dr Shahram Yazdani 22 Advantages of Methodology 1. Clearly shows interrelationships among objectives and alternatives 2. Allows non-quantifiable objectives

23 Dr Shahram Yazdani 23 Problems 1. Difficult to get consistent utilities, meaningful probabilities, realistic objectives and feasible alternatives 2. Must generate new utilities in every situation for every individual or group

24 24 Dr. Shahram Yazdani Multiple Attribute Decision Making

25 Dr Shahram Yazdani 25 Nature of alternatives Nature of Criteria/ objective Concordance analysis AHP Regime Method Evamix Method ELECTRE continuous discrete quantitative Qualitative/ mixed Multi-attribute utility theory Weighted summation Ideal point method Linear programming Goal programming

26 Dr Shahram Yazdani 26 Generic process for MCDM Identify objectives Weight Criteria/ attributes Rank alternatives Choose alternative Identify alternatives Develop Criteria/ attributes

27 Dr Shahram Yazdani 27 MADM Matrix X1X1 X2X2 X3X3 XnXn A1A1 A2A2 A3A3 AmAm Alternatives Attributes

28 Dr Shahram Yazdani 28 Give Numerical Values to Attributes of Each Alternative Consider simple measures in simple quantitative attributes Consider decision tree analysis in complex quantitative attributes Consider pair wise comparison in qualitative attributes

29 Dr Shahram Yazdani 29 MADM Matrix X1X1 X2X2 X3X3 XnXn A1A1 v 11 v 12 v 13 v 1n A2A2 v 21 v 22 v 23 v 2n A3A3 v 31 v 32 v 33 v 3n AmAm v m1 v m2 v m3 v mn Alternatives Attributes v ij is the specific value of attribute X j for alternative A i

30 Dr Shahram Yazdani 30 Standardizing the attribute values 1. Normalization 2. Linear 3. Fuzzy j r ij = v ij – min v ij max v ij – min v ij j j j r ij = max v ij – v ij max v ij – min v ij j j For positive attributes Where more is better For negative attributes Where less is better

31 Dr Shahram Yazdani 31 Standardized attributes X1X1 X2X2 X3X3 XnXn A1A1 r 11 r 12 r 13 r 1n A2A2 r 21 r 22 r 23 r 2n A3A3 r 31 r 32 r 33 r 3n AmAm r m1 r m2 r m3 r mn Alternatives Attributes r ij is the standardized value of attribute X j for alternative A i

32 Dr Shahram Yazdani 32 Weight of each attribute X1X1 X2X2 X3X3 XnXn A1A1 r 11 r 12 r 13 r 1n A2A2 r 21 r 22 r 23 r 2n A3A3 r 31 r 32 r 33 r 3n AmAm r m1 r m2 r m3 r mn Alternatives W1W1 W2W2 W3W3 WnWn

33 Dr Shahram Yazdani 33 Weighting methods for attributes Fixed Point Scoring Paired Comparisons Judgment Analysis

34 Dr Shahram Yazdani 34 Fixed Point Scoring Attribute 1 Attribute 2 Attribute 3 Attribute n Give to each attribute a weight (<1) that sum up in 1 W1 W2 W3 Wn 1

35 Dr Shahram Yazdani 35 Paired Comparisons of Attributes Importance

36 Dr Shahram Yazdani 36 Paired Comparisons X4X3X2X1 X4 X3 X2 X1 attributes n×n AHP matrix

37 Dr Shahram Yazdani 37 Paired Comparisons Equally Important Slightly More Important Moderately More Important Very More Important Bipolar Scale for positive attributes Slightly Less Important Moderately Less Important Very Less Important

38 Dr Shahram Yazdani 38 Paired Comparisons X4X3X2X1 X4 X3 X2 X1 attributes Perform Pairwise Comparison

39 Dr Shahram Yazdani 39 Paired Comparisons X4X3X2X1 X4 X3 X2 X1 attributes Perform Pairwise Comparison Using reciprocals

40 Dr Shahram Yazdani 40 Paired Comparisons X4X3X2X1 X4 X3 X2 X1 attributes Totals Sum the columns

41 Dr Shahram Yazdani 41 Paired Comparisons X4X3X2X1 X4 X3 X2 X1 attributes Totals Normalize the values in each column

42 Dr Shahram Yazdani 42 Paired Comparisons X4X3X2X1 X4 X3 X2 X1 attributesSum Totals Calculate sum of normalized values for Each row

43 Dr Shahram Yazdani 43 Paired Comparisons X4X3X2X1 X4 X3 X2 X1 attributesSum Totals Calculate the Average (weight) for Each Row Average (W)

44 Dr Shahram Yazdani 44 Analytical hierarchic process

45 Dr Shahram Yazdani 45 Analytical hierarchic process Information is decomposed into a hierarchy of alternatives and criteria Information is then synthesized to determine relative ranking of alternatives Both qualitative and quantitative information can be compared using informed judgements to derive weights and priorities

46 Dr Shahram Yazdani 46 Analytical hierarchic process Classifying attributes in a hierarchic model No end branch should contain more than 10 (preferably 8) attribute Begin cross sectional weighting at root side of three and progress to the end branch side of three At each level if the number of items are less than 6 (preferably 4) use fixed point scoring otherwise use paired comparison through AHP matrix Combine cross sectional weights into hierarchical weights which must sum up to 1 for end branches

47 Dr Shahram Yazdani 47 Hierarchic Organization of Attributes

48 Dr Shahram Yazdani 48 End Branch Attributes

49 Dr Shahram Yazdani 49 w1w2w3 w11w12w13w14w31w32 w321w322w323w141w142w143w111w112 Determine simple weight of attributes

50 Dr Shahram Yazdani 50 w1w2w3 w11w12w13w14w31w32 w321w322w323w141w142w143w111w Determine simple weight of attributes

51 Dr Shahram Yazdani 51 w1 w2w3 w11 w12w13w14w31w32 w321w322w323w141w142w143 w111 w112 Wf1Wf1  Determine final weight of attributes

52 Dr Shahram Yazdani 52 w1 w2w3 w11w12 w13 w14w31w32 w321w322w323w141w142w143w111w112  Wf4Wf4 Determine final weight of attributes

53 Dr Shahram Yazdani 53 w1w2w3 w11w12w13w14w31w32 w321w322w323w141w142w143w111w112 Wf1Wf1Wf2Wf2 Wf3Wf3 Wf5Wf5 Wf4Wf4 Wf6Wf6 Wf8Wf8 Wf7Wf7Wf9Wf9W f 10W f 11  Wfi = 1 Wfi = 1 i=1  11 Determine final weight of attributes

54 Dr Shahram Yazdani 54 Application areas  strategic planning  resource allocation  source selection, program selection  business policy  etc., etc., etc.. AHP software (ExpertChoice)  computations  sensitivity analysis  graphs, tables Group AHP Analytical hierarchic process

55 Dr Shahram Yazdani 55 Weight of each attribute X1X1 X2X2 X3X3 XnXn A1A1 r 11 r 12 r 13 r 1n A2A2 r 21 r 22 r 23 r 2n A3A3 r 31 r 32 r 33 r 3n AmAm r m1 r m2 r m3 r mn Alternatives W1W1 W2W2 W3W3 WnWn

56 Dr Shahram Yazdani 56 Weighted value of attributes for alternatives X1X1 X2X2 X3X3 XnXn A1A1 R 11 R 12 R 13 R 1n A2A2 R 21 R 22 R 23 R 2n A3A3 R 31 R 32 R 33 R 3n AmAm R m1 R m2 R m3 r mn Alternatives Attributes R ij = r ij × W j

57 Dr Shahram Yazdani 57 Scoring Alternatives: Weighted summation X1X1 X2X2 X3X3 XnXn Score A1A1 R 11 R 12 R 13 R 1n S1S1 A2A2 R 21 R 22 R 23 R 2n S2S2 A3A3 R 31 R 32 R 33 R 3n S3S3 AmAm R m1 R m2 R m3 r mn SmSm Alternatives Attributes Si = Σ R ij J=1 n Si = Σ r ij× w j J=1 n

58 58 Dr. Shahram Yazdani Judgement Analysis through Virtual Portfolios

59 Dr Shahram Yazdani 59 Judgement analysis through virtual portfolios Choosing the right people Defining objectives and options Determining ranking attributes Defining ranking attributes Scaling ranking attributes Constructing random virtual portfolios Ranking or scoring virtual portfolios by panel performing stepwise regression analysis Finding independent attributes and their weight (regression coefficient) Formulating ranking equation Assessing the validity and reliability of equation on a separate set of portfolios

60 Dr Shahram Yazdani 60 Attribute 1 Attribute 2 Attribute 3 Attribute 4 Attribute 5 Attribute 6 Attribute 7 Level 1Level 2Level 3Level 4Level 5 S11S12S13S14S15 S21S22S23S24S25 S31S32S33S34S35 S41S42S43S44S45 S51S52S53S54S55 S61S62S63S64S65 S71S72S73S74S75

61 Dr Shahram Yazdani 61 Attribute 1 Attribute 2 Attribute 3 Attribute 4 Attribute 5 Attribute 6 Attribute 7 Level 1Level 2Level 3Level 4Level 5 S11S12S13S14S15 S21S22S23S24S25 S31S32S33S34S35 S41S42S43S44S45 S51S52S53S54S55 S61S62S63S64S65 S71S72S73S74S75 S11 S25 S32 S54 S61 S74 Random Virtual Portfolio 1 Random Virtual Portfolio 1

62 Dr Shahram Yazdani 62 Ranking of virtual portfolios Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 1 Random Virtual Portfolio 10 Random Virtual Portfolio

63 Dr Shahram Yazdani 63 Perform Stepwise Regression Analysis Portfolios Rank = iAiiAi Where Ai = i th Attribute  i = Regression Coefficient ( weight) of i th Attribute Results in the minimal set of independent attributes contributing in the judgment of stakeholders about the topic

64 Dr Shahram Yazdani 64 Problem: Diagnosis of malignant tumors of breast Positive Biopsy rate is 10%-31% for cancer Total cost of percutaneous large core biopsy of a breast nodule is $1000 The total cost of excisional biopsy of a breast lump is between $3000 and $4500

65 Dr Shahram Yazdani 65 Alternatives Magnetic Resonance Imaging Mammography Ultrasonography Positron Emission Tomography

66 Dr Shahram Yazdani 66 Attributes Sensitivity (SE) Specificity (SP) Positive Predictive Value (PPV) Negative Predictive Value (NPV) Complexity of Interaction with Patients (CIP)  Includes time spent, degree of discomfort, Invasiveness Complexity of Interaction with Doctors (CID)  Includes Time spent, Level of necessary training and experience, Complexity of protocol Cost (C)

67 Dr Shahram Yazdani 67 SESPPPVNPVCIPCIDC MRI Mammography Ultrasonography PET

68 Dr Shahram Yazdani 68 Thank You ! Any Question ?


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