Workshop on Patient Level
Simulation Modelling
Welcome and Introduction
Sheffield Experiences of
Patient Level Simulation
Alan Brennan and Jim Chilcott,
HEDS, ScHARR, CHEBS
Purpose of
Today / Focus Fortnight
1. When do we need a “patient level model”
rather than a “simpler cohort model”?
2. How many simulations?
• patient level (“1st order”) for convergence;
• To investigate parameter uncertainty in
probabilistic sensitivity analysis (“2nd order”)
3. When are ‘emulators’ helpful e.g. to replace the
computationally expensive patient level
simulation model with an analytic formula
Speakers
• 10.30
Alan Brennan and Jim Chilcott
• 11:00
Ruth Davies, Warwick
“5 minute” break
• 12:00
Steve Chick, INSEAD
1pm Lunch Break
• 2:00
Pelham Barton, Birmingham
• 3:00
Simon Eggington, ScHARR, Sheffield
• 3:30
Marc Kennedy, Sheffield
4pm Round Up Discussion
Questions throughout
Slides on www….
Health Economics Context
• Assess value of policies / health technologies
• Compare mean utility gain (QALYs) versus
current care for population
• Calculate incremental cost per QALY gained
• Choose option with max expected net benefit
(threshold * Q – C)
• Assess uncertainty by varying parameters
Influences on model
structure (‘in real’)
• Conceptual model of disease + patient pathways
• Published evidence on epidemiology,
effectiveness, utilities, costs
› Often defines health states
• Form of available data e.g.
› Individual level time in each health state
› Cross sectional ‘census’ of numbers
› Average ‘response’ or ‘relative risk’ plus confidence
intervals
• Tool-kit available to the analyst
Sheffield Experience of
Patient Level Simulation
• Service Planning Models e.g.
› East Anglia Ambulances
» Call arrival rates, Ambulances crew roster,
» Travel and service times
» Performance by ‘zone’ over a week (8 mins target)
› Theatre ~ Bed Simulation
» Weekly theatre schedule by case mix
» Minutes in theatre/recovery and days in hospital bed
» % theatre over-run and % over bed capacity
Health Economic Models (1)
Osteoporosis
• Complex pathway and time dependent prognosis
› Future risk of fracture dependent on …previous hip, wrist,
vertebral, other fractures, age, sex, duration on treatment, duration
since fracture
› ‘feedback’ i.e. risks increase given events
› Utility dependent also on nursing home admission
› Expected discounted Lifetime Cost and QALYs
• Annual time periods and probabilities of transtion to next
health states
•
Stevenson et al. HTA report(s) + Journal of OR Society
• Some Markov ‘competitor’ models
Health Economic Models (2)
Rheumatoid Arthritis
• Sequences of treatment, tracking of disability score
› Future disability dependent on …
»
»
»
»
extent of improvement given treatment,
duration of successful response,
response to next line therapy in a sequence etc …..
Mortality risk may depend on disability score
› Expected discounted Lifetime Cost and QALYs
• 6 monthly. Probabilities of response /withdrawal
•
Rheumatology 2003;42:1–13. Modelling the cost-effectiveness of etanercept in adults with
rheumatoid arthritis in the UK.
A. Brennan, N.
Bansback, A. Reynolds and P. Conway
• Some Markov (drug / disability band) , some patient level
‘competitor’ models
Health Economic Models (3)
Type II Diabetes
• Multiple disease states, sequences of treatment and time
dependent prognosis
› Future risk of heart disease, stroke, retinopathy, neuropathy and
renal disease dependent on …previous events, Hba1c over past
years, cholesterol, blood pressure, age, sex, improvement given
treatment, persistence or withdrawal, adherence …..
› Expected discounted Lifetime Cost and QALYs
• Annual time periods and probabilities of transition to next
health states in 5 parallel disease models
•
Chilcott JB, Whitby SM, Moore R. Clinical impact and health economic consequences of posttransplant type 2
diabetes mellitus. Transplantation Proceedings 2001 Aug;33(5A Suppl):32S-39S
• Mostly patient level ‘competitor’ models
Diabetes: Interaction between
metabolic variables + co-morbidities
Hypertension
Blood pressure
Nephropathy
Stroke
Total Cholesterol
Coronary Heart Disease
Neuropathy
Hyperglycaemia
(blood sugar) Hba1c
Retinopathy
Algorithm includes therapy targets
Simplified Algorithm
Rationale for Patient-Level
Diabetes Model (1)
• Type 2 diabetes affects a wide range of patients, i.e.
use policy model for subgroup analysis
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diagnosed at 40 or 60,
existing cardiovascular disease,
Smoker v non smoker,
some have large metabolic disorders,
others are newly diagnosed,
• Substantial evidence on risk of complications, e.g.
› UKPDS CHD risk engine (logistic regression model)
› Eastman risk equations for retinopathy
Rationale for Patient-Level
Diabetes Model (2)
• Risk is not linear with risk factors – most relationships
are exponential (some strongly)
• Covariance between some of the characteristics,
› older patients more likely to have diabetes for longer
duration
› metabolic abnormalities tend to cluster
› blood pressure varies according to gender
• Interaction between metabolic variables and size of
response to therapy
• RESULT : the average of risks is not same as the risk
for the patient with ‘average’ characteristics
Health Economic Models (4)
Others
• Patient Level
› Venous Leg Ulcers
› Breast Cancer
› Deep Vein Thrombosis
• Cohort
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Multiple Sclerosis
Bowel Cancer Screening
Carotid Stenosis Assessment
Anti-platelet therapy
1. When do we need a
“patient level model” issues
•
We are refining the question this fortnight e.g.
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Discrete time individual patient simulation versus
discrete event (continuous time) individual but
interacting patient simulation
More than one way to represent Markovian behaviour
in a “simpler cohort model”
Other model frameworks e.g. systems dynamics flows
Some criteria are easy
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Interacting time dependent patient prognosis
Competing for resources and undergoing waiting time
Explosion of hundreds of thousands of states
1. When do we need a
“patient level model” issues
•
Markov criteria mean must have
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Probability of transition depends only on current state
Constant rate of transition per period, implying
exponential survival time in state
Note, there are rules for appropriate cycle length
But there is some Markov flexibility
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Merged states or phasing can help generalise beyond
exponential survival time in state
Many models have time dependent transition
probabilities i.e. different in period 1 to period 2
1. When do we need a
“patient level model” issues
•
The hardest question (for me anyway)
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OK, there is the concept that complex event histories
with prognosis depending on the accumulated history
means that a patient level model is necessary.
But …… What if you simplify
e.g. use Markov assumptions knowing they may be
wrong but thinking it ‘will all come out in the wash’
Can you know a priori when such simplification will
work i.e. give the correct (same) decision as the full
individual level model
1. When do we need a
“patient level model” issues
•
And what about hybrids?
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In fact all 3 models above have some level of
individual variability built in
But … some parameters attached to the simulated
individual are estimates of population means e.g
» utility of diabetic health states
» Annual cost associated with Rheumatoid disability score
» .
2. How many simulations?
issues
•
In practice, we use 10,000 patients (1st order)
because it seems enough to reduce variability in
mean QALY
•
However, when treatments are close (i.e. QALY
difference is small) we have used more
2. How many simulations?
issues
•
In health economic modelling Probabilistic sensitivity
Analysis (PSA) is usually done using 1,000 or 10,000
simulations allowing the uncertain parameters to vary
across their plausible ranges by Monte Carlo sampling
from their defined prior distributions
•
So do we need 1,000 (2nd order) x 10,000 (1st order) = 10
million model runs to get a CEAC ?
•
The mathematics of the optimum balance between 1st
order and 2nd order is under investigation by Tony
O’Hagan (does not like the terminology 1st and 2nd order)
3. Emulators
•
The challenge of undertaking PSA for the Osteoporosis
model that led us to Emulators and Gaussian Processes
•
The process involved ….
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Producing 100 or 200 runs of the model with 10,000 simulated
patients in each (i.e. 100 hours).
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Allowing Jeremy Oakley to fit a Gaussian Process emulator to
approximate the results of the individual patient level model for
any set of input parameters
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Programming the function into EXCEL, then doing 10,000 runs
over uncertain parameters to undertake PSA and draw the CEAC
Stevenson et al. Medical Decision Making 2003
Software we have used
• Visual Basic (VBA) with EXCEL front end
• Simul8
• R
Aside: Bayesian Clinical
Trial Programme Simulation
• Given current therapy uncertainty you can model
› patients in a clinical trial of sample size n
› simulated trial outputs and the decision algorithm for
moving to next stage e.g. phase II
› Phase II probability of success conditional on previous
stage success etc.
› Similarly Phase III and hence regulatory approval
Recommendations
• Attend this workshop……..
• Join the OR Society !
• Read Pidd, Law and Kelton
• Go to the conferences