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Design and Analysis for

Operations ResearchWilliam A. Reinke, Ph.D.

Professor

Department of International Health

Johns Hopkins University

School of Hygiene and Public Health

Session 6



Unique Features of Operations

Research

• Multiple Factors Affect Results

• Many Factors Not Subject to Control

• Places Emphasis on Analysis of VariationMore 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 forTargeted Services



0

20

40

60

80

100

120

140

160

0 10 20 30 40

50

100

150 Deaths Averted (A)

Potential Outcomes

Thousands Vaccinated (V)

T h o u s a n

d s o f C a s e s

D i a r r h e a

T r e a t e d

( D )

D + 2.5V = A



150 Deaths Averted (A)

Linear Programming Model

Thousands Vaccinated (V)

T h o u s a n d s o f C a

s e s

D i a r r h e

a T r e a t e d

( D )

D + 2.5V = A0.5D+0.6V ≤ 50

0.3D+1.5V ≤

45

50 workers

$45,000 Budget Deaths Averted

150

117

0

20

40

60

80

100

120

140

160

10 20 30 40



Unit of Analysis

Compared to

Unit of Observation

• Unit of Analysis

– Cases of Diarrhea in Past Two Weeks

– Prevalence Approximately 20% in ChildrenUnder 5

– Children Approximately 16% in Population• Unit of Observation

– Household

– Approximately 5 Persons per Household



Sample CalculationBased on

Measure of InterestUse of Oral Rehydration

Expected to be About 50%Precision Required + 5%

n p p

D

4 1

2

( )

=( 4 ) ( . 5 ) ( . 5 )

( . 0 5 )

= 4 0 0

4 0 0

( . 2 ) ( . 1 6 ) 1 2 , 5 0 0 P e r s o n s

1 2 , 5 0 0

5 2 , 5 0 0 H o u s e h o l d s

2



Needs Assessment

Health Needs- Population

- Problems

- Demand

WHOEntire Population in Defined Area

Selected Target Groups

Specific High Risk TraitsService Users

WHATBiological Need

Consumer Wants

Willingness to Pay

Effective Demand

HOW EXPRESSED

Attitudes and BeliefsBehavior



Resources and Services

Service CoverageTechnical QualityProvider Knowledge

and SkillsAvailability of Service Support

Appropriate Application

of Competence

Client SatisfactionPerceived Benefit

Perceived Cost and

Inconvenience

Service Functions&

Programs

Health Resources

HumanPhysical

Financial

Service Capacity

Provider Competence

Service Support



Outcomes

Effectiveness- Benefits Level

-Cost: Affordability

Cost-effectiveness-Tangible

-Intangible

Equity-Distribution of Benefit

Health Status-Mortality

-Morbidity

-Disability

Service Functions

&

Programs



Quality of Life Determination

H preferred to A

Indifferent betweenH & B

C Preferred to H

0 6 9 123Conclusion: A Year of Impaired Life is Equivalent

to 0.8 Year of Healthy Life

H e a l t h y

I m p a i r e

d

H

A

B

C



Framework for Standard Gamble

Impaired

?

Relieved100

Death0

P = ?



Relationships Among Specified

Variables

Independent VariablesExperimental Interventions

Intervening VariablesAdditional Factors Present

that Could Affect Outcome

Dependent VariablesResult of Interest



Effects of Confounding

PersonsM F Prevalence(%) M F CasesM F % withConditions

No

Confounding

Smokers

Non-Smokers

30 30

70 70

50 70

10 30

15 21

7 21

60

40%

Diff.

20

Confounding Smokers

Non-Smokers

40 20

60 80

20 14

6 24

57

36%Diff.

21

Overcoming

Confounding

Smokers

Non-Smokers

50 50

50

50

25 35

5 15

60

40%

Diff.

20

Smoking

Sex

Condition



Effects of Interaction

Condition

Persons

M F

Prevalence (%)

M F

Cases

M F

% with

Conditions

Proportional

Sample

Smokers

Non-Smokers

40 20

60 80

50-10=40 70+10=80

10+10=20 30-10=20

16 16

12 16

53

33% diff.

20

Equal

Sample

Smokers

Non-Smokers

50 50

50 50

20 40

10 10

60

40% Diff.

20

Smoking

Sex



Common Techniques of

Operations Research

• Linear Programming

• Inventory Models

• Queuing Models

Economic Order Quantity



0

200

400

600

800

1000

50 150 250 350 450 550 650 750

Holding cost

Replenishment Cost

Total Cost

Order Quantity (Q)

Economic Order Quantity

o r

h

QC

C

2

U

A n n u

a l C o s t

U = 800

Cr = 50

Ch = 2

Traditional Techniques of



Traditional Techniques ofStatistical 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

design and analysis for operations research

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