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Session 6
Design and Analysis for
Operations Research
William A. Reinke, Ph.D.
Professor
Department of International Health
Johns Hopkins University
School of Hygiene and Public Health
Unique Features of Operations
Research
• Multiple Factors Affect Results
• Many Factors Not Subject to Control
• Places Emphasis on Analysis of Variation
More Than its Control Through Study
Design
Healthy Status
- Mortality
- Morbidity
- Disability
Health Needs
- Population
- Problems
- Demand
Service Functions
&
Programs
Health Resources
- Human
- Physical
- Financial
Service Capacity
- Provider Competence
- Service Support
Forms of Health Systems
Research
• Prescriptive
– Explicit Mathematical Model
– Associated Quantitative Data
• Descriptive
– Indicators Regarding Factors Subject to
Manipulation
– Indicators Regarding Population Groups for
Targeted Services
Potential Outcomes
Thousands of Cases
Diarrhea Treated (D)
160
140
D + 2.5V = A
120
150 Deaths Averted (A)
100
100
80
60
50
40
20
0
0
10
20
30
Thousands Vaccinated (V)
40
Linear Programming Model
160
120
D + 2.5V = A
0.5D+0.6V ≤ 50
0.3D+1.5V ≤ 45
100
150 Deaths Averted (A)
Thousands of Cases
Diarrhea Treated (D)
140
50 workers
80
60
40
150
$45,000 Budget
Deaths Averted
20
117
0
10
20
30
40
Thousands Vaccinated (V)
Unit of Analysis
Compared to
Unit of Observation
• Unit of Analysis
– Cases of Diarrhea in Past Two Weeks
– Prevalence Approximately 20% in Children
Under 5
– Children Approximately 16% in Population
• Unit of Observation
– Household
– Approximately 5 Persons per Household
Sample Calculation
Based on
Measure of Interest
Use of Oral Rehydration
Expected to be About 50%
Precision Required + 5%
n =
=
=
4 p( 1 − p )
D 2
(4 )(.5 )(.5 )
(.0 5 ) 2
400
400
= 1 2 ,5 0 0 P e r s o n s
(.2 )(.1 6 )
1 2 ,5 0 0
= 2 ,5 0 0 H o u s e h o ld s
5
Needs Assessment
WHO
Health Needs
- Population
- Problems
- Demand
Entire Population in Defined Area
Selected Target Groups
Specific High Risk Traits
Service Users
WHAT
Biological Need
Consumer Wants
Willingness to Pay
Effective Demand
HOW EXPRESSED
Attitudes and Beliefs
Behavior
Resources and Services
Health Resources
Service Coverage
Human
Physical
Financial
Technical Quality
Provider Knowledge
and Skills
Availability of Service Support
Appropriate Application
of Competence
Client Satisfaction
Perceived Benefit
Perceived Cost and
Inconvenience
Service Functions
&
Programs
Service Capacity
Provider Competence
Service Support
Outcomes
Effectiveness
- Benefits Level
-Cost: Affordability
Health Status
-Mortality
-Morbidity
-Disability
Cost-effectiveness
-Tangible
-Intangible
Equity
-Distribution of Benefit
Service Functions
&
Programs
Healthy
Quality of Life Determination
H
Impaired
A
B
C
H preferred to A
Indifferent between
H&B
C Preferred to H
0
3
6
9
12
Conclusion: A Year of Impaired Life is Equivalent
to 0.8 Year of Healthy Life
Framework for Standard Gamble
Impaired
?
P=?
Relieved
100
Death
0
Relationships Among Specified
Variables
Independent Variables
Experimental Interventions
Dependent Variables
Result of Interest
Intervening Variables
Additional Factors Present
that Could Affect Outcome
Effects of Confounding
No
Confounding
Persons
Prevalence(%) Cases
% with
M
F
M
F
M
F Conditions
Smokers
30
30
15
21 60
40%
Non-Smokers 70
70
7
21 Diff.
50
70
20
10
Confounding
Smokers
40
20
30
20
14 57
36%
Overcoming
Confounding
Non-Smokers 60
80
6
Smokers
50
25
50
24 Diff.
21
35 60
40%
Non-Smokers 50
50
5
15 Diff.
20
Smoking
Condition
Sex
Effects of Interaction
Proportional Smokers
Sample
Non-Smokers
Persons
M
F
40
20
60
80
Prevalence (%)
M
F
Cases
M
F
16 16
12
% with
Conditions
53
33% diff.
16 20
20
40 60
50-10=40 70+10=80
10+10=20 30-10=20
Equal
Sample
Smokers
50
50
40% Diff.
Non-Smokers 50
50
10
Smoking
Condition
Sex
10 20
Common Techniques of
Operations Research
• Linear Programming
• Inventory Models
• Queuing Models
Economic Order Quantity
Qo
=
2U
C
Ch
r
1000
800
Annual Cost
Total Cost
600
Holding cost
400
200
U = 800
Cr = 50
Ch = 2
Replenishment Cost
0
50
150
250
350
450
550
Order Quantity (Q)
650
750
Traditional Techniques of
Statistical Analysis
• Univariate Analyses
–
–
–
–
Frequency Distributions
Average
Standard Deviations
Proportions, Rates and Ratios
• Bivariate Analyses
– t-tests
– X2 Analyses
• Multivariate Analyses
–
–
–
–
Analysis of Variance (ANOVA)
Multiple Linear Regression
Logistic Regression
Discriminant Analysis