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
Geo Data Institute, University of Southampton
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
Geo Data Institute, University of Southampton
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.
Geo Data Institute, University of Southampton
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 + ……..
Geo Data Institute, University of Southampton
• 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.
Geo Data Institute, University of Southampton
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
Geo Data Institute, University of Southampton
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
Geo Data Institute, University of Southampton
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%
Geo Data Institute, University of Southampton
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
Geo Data Institute, University of Southampton
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
Geo Data Institute, University of Southampton
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%
Geo Data Institute, University of Southampton
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
Geo Data Institute, University of Southampton
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
Geo Data Institute, University of Southampton
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
Geo Data Institute, University of Southampton
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
Geo Data Institute, University of Southampton
Contact Details
Dr Arjan Shahani,
Director,
Health Data Analysis and Modelling Group,
GeoData Institute,
University of Southampton,
Southampton SO15 7PJ
UK