Applications of AHP
Applying the Analytic Hierarchy Process to Health
Decision Making: Deriving Priority Weights
Tom´as Arag´on, MD, DrPH
Principal Investigator, Cal PREPARE,. CIDER UC Berkeley School of Public Health Health Officer, City & County of San Francisco
San Francisco Department of Public Health Blogger at http://medepi.com
Ferenc Dalnoki-Veress, PhD
Scientist-in-Residence & Adjunct Professor James Martin Center for Nonproliferation Studies
Monterey Institute of International Studies
Applications of AHP Outline
1 Introduction and Background
2 Analytic Hierarchy Process
Applications of AHP Quote
“Not everything that counts can be counted and
not everything that can be counted, counts”
Applications of AHP Acknowledgements
Lisa Goldberg, MPP, MPH, DrPH (c), Graduate Student, Johns Hopkins Bloomberg School of Public Health
Ferenc Dalnoki-Veress, PhD, Lead Investigator, Monterey Institute of International Studies, James Martin Center for Non-proliferation Studies
Applications of AHP What process do we/you use to . . .
Make decisions? Set priorities? Allocate resources? Prioritize budgets? Resolve conflict? Achieve consensus?
Applications of AHP How do we commonly set priorities?
Informal methods
Organizational traditions Leadership preferences Politics and advocacy Categorical funding Personal interests
“Formal” methods
Conduct a needs assessment Define “core” services
Conduct economic evaluations (CBA, CBA)
Applications of AHP Challenges to setting health priorities
Our understanding of complex health and social systems is limited Qualitative attributes (values, ethics, and equity) are difficult to combine with quantitative attributes (e.g., burden of disease) Inclusion of diverse stakeholders with competing interests and values Goals, criteria, or alternatives are not always well specified
Timely decisions must be made with limited evidence Ideal analyses are rarely complete, timely, or feasible Decision-making process may not be transparent
Our understanding of prioritization methods may be limited Criteria may have different measurement scales or no scale at all
Applications of AHP
The analytic hierarchy process will help us . . .
Make decisions Set priorities Allocate resources Achieve consensus Resolve conflicts Improve communications Justify and defend decisions
Applications of AHP Analytic hierarchy process in 4 steps
1 Define the goal
2 Select, organize, and weight criteria 3 Apply criteria to alternatives and rank 4 Conduct sensitivity analysis
Applications of AHP
Applications of AHP Analytic hierarchy process
Applications of AHP
Derive criteria weights using pairwise comparisons
Pairs to compare Criterion A vs. Criterion B Criterion A vs. Criterion C Criterion B vs. Criterion C Measurments 1 Nominal categories 2 Ordinal categories 3 Interval scale 4 Ratio scale*
Applications of AHP
The fundamental scale for pairwise comparisons
Table: The fundamental scale
Intensity Definition
1 Equal importance
3 Moderate importance
5 Strong importance
7 Very strong (or demonstrated) importance
9 Extreme importance
Applications of AHP
Apply the fundamental scale for pairwise comparisons
Which criterion is more important? How much more important?
Figure: Pairwise comparisons of Criteria A, B, and C using the fundamental scale
Applications of AHP Create comparison matrix
Which criterion is more important? How much more important?
Criterion A Criterion B Criterion C
Criterion A 1
Criterion B 1
Applications of AHP
Complete comparison matrix with integer ratios
Which criterion is more important? How much more important?
Criterion A Criterion B Criterion C
Criterion A 1 5
Criterion B 1
Applications of AHP
Complete comparison matrix with reciprocal ratios
Which criterion is more important? How much more important?
Criterion A Criterion B Criterion C
Criterion A 1 5 1/3
Criterion B 1/5 1 1/7
Applications of AHP Derive criteria priority weights
To derive the criteria priority weights we solve for the normalized right eigenvector of the comparison matrix (free software available)
Table: Criteria priority weights Criterion (j) Priority Weight (pj)
A 0.2790
B 0.0719
C 0.6491
Total 1.0000
(In)consistency ratio 0.0624
The consistency ratio is the amount of “inconsistency” in the judgements. A CR < 0.10 is considered acceptable.
Applications of AHP
Example 1: Establishing health priorities (see tutorial)
Now consider a local health department (LHD) that is committed to becoming a high performance, learning organization through robust strategic effectiveness, performance management, and quality and equity improvement. They have adopted AHP to improve their decision making, priority setting, and resource allocation. The planning unit has developed a priority setting tool to assist in prioritizing health programs so that they align with the agency’s strategic directions.
Applications of AHP Example 1: Establishing health priorities
AHP for Prioritizing Health Programs (Adapted from Mitton, 2011, PMID 21756357)
Applications of AHP Example 1: Establishing health priorities
The executive team completed a session where they defined and approved the criteria. Each executive had been provided with a criteria scoring tool. They had been instructed to use their experience, expert judgement, and understanding of existing evidence to score the criteria based on pairwise comparisons. If they judged two criteria to be equal in importance that pair would be get an intensity score of 1. If not, they would use the
fundamental scale to express how much more important one criteria is compared to another.
Applications of AHP Example 1: Establishing health priorities
Dr. Juan Nieve is a public health officer and believes that Health Impact is the most important criterion. He has no strong feelings on the other criteria and considers them equal. His scoring tool results are displayed in Figure.
Applications of AHP Example 1: Establishing health priorities
Dr. Juan Nieve
Dr. Juan Nieve is a public health officer and believes that Health Impact is the most important criterion. He has no strong feelings on the other criteria and considers them equal. His scoring tool results are displayed in previous Figure.
Dr. Donald Trumpini
In contrast, Mr. Donald Trumpini is a finance officer and he stays up-to-date on the anticipated fiscal impacts of health care reform. He recommends that programs that generate revenue should be weighted moderately higher to ensure a financially sustainable health system. (His score sheet is not shown.)
Applications of AHP Example 1: Establishing health priorities
Dr. Juan Nieve’s comparison matrix
HA SA OI FI
Health Impact (HI) 1 5 3 7
Strategic Alignment (SA) 1/5 1 1 1
Organizational Impact (OI) 1/3 1 1 1
Financial Impact (FI) 1/7 1 1 1
Dr. Donald Trumpini comparison matrix
HA SA OI FI
Health Impact (HI) 1 1 1 1/3
Strategic Alignment (SA) 1 1 1 1/3
Organizational Impact (OI) 1 1 1 1/5
Financial Impact (FI) 3 3 5 1
Applications of AHP Example 1: Establishing health priorities
Aggregating Individual Priority (AIP) weights
Table: Criteria priority weights, including normalized geometric mean
Nieve Trumpini Aggregated
Criterion (j) Weights Weights Weights
p1j p2j p0j Health Impact 0.6125 0.1581 0.3676 Strategic Alignment 0.1253 0.1581 0.1663 Organizational Impact 0.1454 0.1401 0.1686 Financial Impact 0.1167 0.5437 0.2976 Total 1.0000 1.0000 1.0000 (In)consistency ratio 0.0259 0.0123
Applications of AHP Example 1: Establishing health priorities
An alternative approach is aggregating individual judgment (AIJ) weights. In the AIJ method we aggregate the comparison matrices first then derive the criteria priority weights.
Aggregating Individual Judgment (AIJ) weights
HA SA OI FI
Health Impact (HI) 1.00 2.24 1.73 1.53
Strategic Alignment (SA) 0.45 1.00 1.00 0.58
Organizational Impact (OI) 0.58 1.00 1.00 0.45
Financial Impact (FI) 0.65 1.73 2.24 1.00
Applications of AHP Example 1: Establishing health priorities
Table: Comparison of aggregated priority weights using the AIP and AIJ methods
AIP AIJ
Arithmetic Geometric Geometric
Criterion Mean Mean Mean
Health Impact 0.3853 0.3676 0.3678
Strategic Alignment 0.1417 0.1663 0.1661
Organizational Impact 0.1428 0.1686 0.1683
Financial Impact 0.3302 0.2976 0.2978
Applications of AHP Example 2: Selecting a high school
Applications of AHP
Example 2: Selecting a high school: Luis vs. Mami vs. Papi
Applications of AHP
Example 3: UCLA Hazard Risk Assessment (HRA) Instrument
In general, expected impact of an adverse event:
E [Impact] = (Risk of Event) × (Impact of Event) = P (Haz)P (Exp | Haz)P (Ev | Exp) × Impact Risk management
Avoid risk;
Mitigate risk (eliminate/minimize risks); Transfer risk (buy insurance, outsource); Consequence management
Detect early and control (monitor and control)
Applications of AHP
Applications of AHP
Why are multi-criteria decision making methods not used?
Lack of familiarity with decision sciences
Lack of understanding of computers or mathematics Concerns about losing control over decision-making
Applications of AHP Concluding thoughts
Decision making, priority setting, or resource allocation requires ranking and selection of alternatives. To achieve this we must develop and weight criteria that are applied to these alternatives. Using the analytic hierarchy process (AHP), criteria can be
weighted by conducting pairwise comparisons of each criterion with respect to importance, likelihood, preference, or other factor of interest. AHP allows us to combine our interpretations of evidence (from data, testimony, etc.) with qualitative attributes such as preference or other “intangibles.” This fact alone makes AHP incredibly powerful and practical. At worse, AHP improves our decision making. Finally, AHP can be used as a research tool to measure decision making, learning, interpretation and much more.
Applications of AHP Bibliography
1 Decision Sciences page at Med Epi blog
(http://medepi.com). Register to receive email updates.
2 Decision by Objectives: How to Convince Others that You are
Right, by Ernest H. Forman
Permalink: http://amzn.com/9810241429
Also available for free PDF download from http://mdm.gwu. edu/profforman/DecisionByObjectives/default.html
3 Decision Making for Leaders: The Analytic Hierarchy Process
for Decisions in a Complex World, New Edition 2001 (Analytic Hierarchy Process Series, Vol. 2), by Thomas L. Saaty
