Geo Data Institute, University of Southampton

Geo Data Institute, University of Southampton

A K Shahani, GeoData Institute

& School of Mathematics,

University of Southampton, UK

Paper presented at the 32nd Annual Meeting of the European Working Group on Operational Research Applied to Health Services,

Wroclaw, Poland

Making Good Decisions for: Planning and Managing Health Services &

Preventing, Detecting, and Treating Diseases


Making Good Decisions for: Planning and Managing Health Services &

Preventing, Detecting, and Treating Diseases Main Message

Collaborative work + Good databases +

Appropriate statistical analysis including classifications + Detailed stochastic mathematical models +

Easy to use computer programs for the models + Evaluation of a range of scenarios =

High quality information for making good decisions

Example of Collaboration: Screening for Breast Cancer

University of Southampton UK Department of Health

• General research on inspection of systems &screening for detection

of disease

• Research on growthand detection of breast

cancer

• Information needed fordecisions about a national

policy for screening for breast cancer

•Discussions with Prof Jackson and Dr Shahani

• Development and testing of

particular models and scenarios

• Results given to UK Department of Health

• Decision about national policy made by UK DoH

Example of Collaboration: Critical Care Capacities

University of Southampton Southampton General Hospital

• General research on classification of patients &

flow of patients

• Information needed fordecisions about number of

intensive care beds

•Discussions with Dr Shahani• Development and testing of particular models

and scenarios • Results given to Southampton General Hospital

• Decision made about numberof intensive care beds

• Funding for critical care modelling work at local, regional and national

levels

•Results given to various health authorities •Decisions made

Example of Collaboration: Control of Trachoma University of Southampton

• General research on detection and treatment of diseases

• Professor Ward’s interest in Trachoma

• Development of pilot models for evaluating strategies for control of Trachoma

• International Team: Southampton modellers + USA and UK Trachoma experts funded by Edna McConnell Clark Foundation

• • Detailed data analysis and modelling work • Models and scenario analyses delivered to Edna McConnell Clark Foundation

Collaborations: Developments at University of Southampton

• Health modelling work developed by the Operational Research (OR) Group in Mathematics Department from about 1975.

• Options on modelling for Health Services and for the care of people with particular diseases arranged in MSc OR course.

• Collaborative work with various health organisations• Projects for MSc students, PhD students, Research Assistants. • Consulting work.

• Collaborative health modelling work is now an important part of of the work of Southampton University.

Necessary Conditions for Successful Collaborations

•Data analysis,modelling, and computing

expertise

• Good Communications with health professionals

• Appreciation of the need for detailed stochastic models

• Good Communications with modellers

• Appropriate data

Modellers Health Professionals

• Collaborative work on developing, testing, validating and implementing the necessary detailed stochastic models

Example of a Poor Model for Number of Beds

• Annual Number of Patients to be admitted = 1350• Average Length of Stay (LOS) = 3.677 Days• Required bed days = 3.677 x 1350 = 4963.95• With 85% bed occupancy, Beds Required = 4963.95/ (0.85 x 365) = 16.

• 16 beds could be a good estimate. OR

• Typically it would be a substantial under-estimate because variability in LOS is not taken into account.

• Decisions based on this sort of model can be described as Poor practice


Dangers of Using Averages Only

20 small marbles. Average diameter = 1.646 cm 20 large marbles. Average diameter = 2.533 cm Average diameter of all 40 marbles = 2.089 cm

Estimated volume of 20 small marbles = 20 {/6 (1.646)3} = 47 cm 3

Actual volume of 20 small marbles = 47 cm 3 O.K.

20 large marbles: Estimated and actual volume = 170 cm 3 O.K.

20 small + 20 large marbles: Estimated volume = 191 cm 3

actual volume = 47 + 170 = 217 cm 3 ???? Under-estimate!!!Estimated length of line of 40 marbles = actual length = 83.56cmO.K.


Variability: Insight Through a Simple Analysis

INPUT X SYSTEM OUTPUT Y= f(x)

• E(x) = Deterministic approximation: E(Y) = f()

• Expansion of f(x) about gives Y = f() + (x- ) f ´( ) + (x- )2 f ( ) ´´/2 + ……..

E(Y) = f() + Variance (x) f ´´ ( )/2 + ……..


• Use of averages only is dangerous when there is substantial variability and non-linearity. Patient flows, disease processes, health care, and use of capacities involve substantial variability and non-linearity.

•Seriousness of bottlenecks will be under-estimated

•Resources required will be under-estimated

•There will be false expectations about service levels that will be provided

Use of Averages Only

Nature of the Necessary Models

• Sufficiently detailed• Often based on individual patient flows with the help of classification of the patients

• Complexity, variability, uncertainty, and use of resources are taken properly into account.

• Example: Markov models are often not appropriate

• Careful testing and validation of the models

• Easy to use computer programs for the models

Arrival of Individual patient. Patient type. Care Unit needed

Admission rules for Care Units

Required capacities available?

Send elsewhere

No Yes

Admit Treat Discharge

Health Services Models Capture Patient Flows and Use of Resources

Evaluate scenarios for organisation of services, patient arrivals, capacities, admissions, etc.


What will be effects of increasing capacities

from

eleven Level 3 beds in 2002-2003

to

eleven Level 3 beds and three Level 2 beds in 2003-2004?

Example: Critical Care Beds in a UK hospital


Total 660 patients in 2002-2003

Patient Classification Analysis: PORT program

414 Level 3 patients 246 Level 2 patients

323Emergency

Patients

199Emergency

Patients

91ElectivePatients

47ElectivePatients


Lengths of Stay of Classified Patients

All Lvl 3Emrg

Lvl 3Elec

Lvl 2Emrg

Lvl 2Elec

No. of patients 660 323 91 199 47

Mean LOS 5.81 7.07 4.41 5.30 2.05

Minimum LOS 0.01 0.07 0.21 0.01 0.03

Maximum LOS 78.60 45.94 29.98 78.60 10.92

5% LOS 0.29 0.37 0.77 0.24 0.39

95% LOS 23.85 27.80 15.15 21.74 6.44

• Large variability in lengths of stay. Avoid using averages only for planning and managing CCU.

Distributions of Lengths of Stay

• Level 3 Emergency Patients

Arrival Profiles of Patients

• Arrival profiles by month, day, and hour of the classified were used. Examples shown are monthly and daily arrival profiles of Level 3 emergency patients

Data and Model Results for 2002-2003

Level 2 Level 3 Total

Data Model Data Model Data ModelEmergency Admissions

95% Limits199 198 323 321 522 519

500-567Elective Admissions

95% Limits47 46 91 89 138 135

128-157Total Admissions

95% Limits244 246 414 410 660 654

636-703Deferrals

95% Limits ---- ---- ----- ---- 56? 61

52-82 Transfers

95% Limits---- ---- ----- ---- 178 156

134-208Bed Occupancy

95% Limits ---- ---- ----- ---- 95% 95%

93-99%


Data and Model Predictions for 2002-2003

There is a good match

between

model predictions

and

2002-2003 data

Scenarios for Effects of Increased Capacities

• 2002-2003 case-mix and lengths of stay (LOS)

• Additional 50 Level 2 patients and 2002-2003 LOS

• Additional 50 Level 2 patients and changed LOS

Level 2 Patients

Level 3 Patients

All Patients

Emergency 308 433 741

Elective 56 91 138

Total 364 524 888

Case-mix with 50 additional Level 2 patients


Changes in 2002-2003 Lengths of Stay

02-03

MeanValuesStd.Dev

IncrsMean

1Std. Dev

IncrsMean

2Std. Dev

Level 2Emergency

5.31 12.06 6.00 13.20 7.00 15.40

Level 2 Elective

1.98 2.47 2.50 4.00 2.50 4.00

Level 3Emergency

7.14 15.00 8.00 17.60 9.00 19.80

Level 3Elective

4.38 7.24 5.00 8.00 5.00 8.00


Scenarios for Predictions of Effects of Increased Capacities

Case -Mix of Patients LOS

Scenario 1 2002-2003 2002-2003

Scenario 2 02-03 + 50 Additional Level 2 2002-2003

Scenario 3 2002-2003 Increase 1

Scenario 4 02-03 + 50 Additional Level 2 Increase 1

Scenario 5 2002-2003 Increase 2

Scenario 6 02-03 + 50 Additional Level 2 Increase 2

• Critical Care Unit Capacities: 14 beds and 12 nurses

CCU_SIM Predictions and 2003-2004 data

Model Model Model Model Model Model Data

Scn 1 Scn 2 Scn 3 Scn 4 Scn 5 Scn 6 03– 04

Lvl 2 Emrg

239 269 224 249 212 231 253

Lvl 2 Elec

46 56 47 56 47 55 55

Lvl 3 Emrg 366 363 332 327 305 300 294

Lvl 3 Elec 91 91 93 91 92 91 82

Total Adm 742 779 696 723 656 677 684

Deferrals 2921.1%

3423.1%

4129.3%

4832.7%

5237.4%

5839.7%

4935.8%

Transfers 9613.7%

10614.4%

14020.1%

16021.7%

18326.1%

20828.2%

19526.2%

Bed Occ 84% 85% 88% 90% 91% 93% 94%


Hospital Capacities: Critical Care Units. A&E + MAU. Hospital Care units. Hospital (existing or new) as a whole.

Outpatient Clinics: Orthopaedics, Depressive illness, ENT, Eye, Skin.

Waiting Lists: Inpatients and Outpatients.

Regional Capacities: Cleft lip and Palate, Coronary, Dental.

Service Organisation: Maternity Care. Critical Care

“Whole System”: Primary Care, Acute Hospital, Post-Acute Care.

Forecasts of daily emergency admissions for all hospitals in England. Met Office project

Some Southampton Health Services Models


Health Care Modelling

•Description of community or patient groups.

e.g. age, sex, risk groups

•Disease history or patient progress

•Interventions e.g. screening, vaccination, treatment, socio-

economic actions

•Resources needed or planned

•Costs of resources


Treatment of Breast Cancer

• Many are treatments available.

• Treatment depends on the severity of cancer.

Stage I: Small moveable tumour in breast only.

Stage II:Tumour not advanced but spread to lymph nodes.

Stage III:Locally advanced tumour. May be attached to chest muscles.

Stage IV:Distant metastases.

• Mortality rate is a measures of the goodness of treatment.

• Mortality rates vary between hospitals and between countries.

Treatment Model

Stage 1

Stage 2

Stage 3

Stage 4

Treatment

Treatment

Diseasefree

Noresponse

Response

Treatment

Death from Other causes

Progressive disease

Local

Distant

Local and distant

Death from Breast cancer

Illustrative Results From Treatment Model

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Survival Time (Years)

Pro

babi

lity

Stage 1 Stage 2 Stage 3 Stage 4

Survival by cancer stage at diagnosis.

Illustrative Results From Treatment Model

Survival by age at diagnosis.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Survival Time (Years)

Pro

babi

lity

30-39 40-49 50-59 60-69


Particular Diseases

Asthma, Breast Cancer, Cataracts,

Cervical Cancer, Chlamydial Infection,

Colorectal Cancer, Depressive Illness,

Diabetes, HIV/AIDS, Trachoma

Some Southampton Health Care Models

Use of Good Databases in Health Services

Practical dataCollection Options• Bar coding• Keyboard entry• Scanning forms• Hand held devices• Voice input

Practical data Collection Options• Bar coding• Keyboard entry• Scanning forms• Hand held devices• Voice input

Purpose built databases • Economical• Secure• Easy to use and modify

Mathematical and statisticaltools for exploring databases

and obtaining inputs for models

Models

Automatic generation of• Graphs and Tables• Summary reports• Patient level reports • Warning signals•Links with other databases•Links with spread sheetsSpread sheets


Contact Details

Dr Arjan Shahani,

Director,

Health Data Analysis and Modelling Group,

GeoData Institute,

University of Southampton,

Southampton SO15 7PJ

UK

[email protected]

[email protected]

Documents

Geo Data Institute, University of Southampton