Economic Evaluation in Health · Faculty workshop · Session 7
Modelling in half an hour
Why a model exists, what a decision tree and a Markov model do, what a cycle is,
and what to distrust. For reading models, not building them.
Drummond et al., 4th ed., Chapter 9
By the end of this session
Say why most economic evaluations are models, not trials
Read a decision tree and roll it back
Say what a Markov model and a cycle are
Name what the Markov assumption forgets
Ask seven questions of any published model
Why a model at all?
A trial gives you
A decision needs
two or three arms
every relevant option, including current practice
one to three years of follow-up
a lifetime, if survival differs
clinical outcomes
QALYs, costs, Indian prices
a selected population, often abroad
Indian patients in Indian facilities
A model is a framework for combining evidence from many sources
to answer a question no single study answered.
Two shapes you will meet
Decision tree
Branches for choices and chance events, ending in outcomes. Events happen
once, over a short period.
A test, a course of treatment, an acute episode.
Markov model
A few health states; people move between them in repeated cycles.
Events recur over a long period.
Chronic disease, cancer recurrence, a lifetime horizon.
Many papers use both: a tree for the first event, a Markov
model for what follows.
A decision tree
Constructed example. Square: a choice. Circle: chance. Triangle: where a path ends.
Rolling it back
Multiply along each path, then add the paths.
Expected cost
First-line cures
Drug A
10,000 + 0.2 × 20,000 = ₹14,000
0.8
Drug B
4,000 + 0.4 × 20,000 = ₹12,000
0.6
A versus B
+₹2,000
+0.2
ICER = 2,000 ÷ 0.2 = ₹10,000 per additional cure
Drug A costs six thousand rupees more at the counter but only two thousand more
overall, because it avoids second-line treatment.
Constructed example.
When a tree breaks
Events recur: relapse, re-admission, a second stroke
Risk changes with time: age, years since surgery
The horizon is long, so the tree would need thousands of branches
Then you stop drawing every path and instead track how many
people are in each state, year by year.
A Markov model
States are exhaustive and exclusive: everyone is in exactly one.
Arrows carry the probability of moving in one cycle. Each state's
arrows add to 1.
Dead is absorbing: nobody leaves.
Each state carries a cost and a utility per cycle.
Constructed example.
What a cycle is
Start 1,000 people in Well. Apply the arrows once per cycle, here one year.
Cycle
Well
Sick
Dead
QALYs this cycle
0
1,000
0
0
n/a
1
880
100
20
852
2
774
168
58
798
QALYs = people × utility (Well 0.9, Sick 0.6). Do the same with
costs. Run until nearly everyone is dead, discount, add up. Then do it again for the other option.
Constructed example. Cycle 2: Well 880 × 0.88; Sick 100 × 0.80 + 880 × 0.10; Dead the rest.
What the model forgets
The Markov assumption: where you go next depends only on the state you
are in now, not on how you got there or how long you have been there.
The problem
Recurrence after cancer surgery is highest in
the first two years. A single "disease-free" state gives everyone the same risk in year 1 and year 10.
The usual fixes
Split the state by time since event
("tunnel" states), let probabilities change with age, or simulate individuals instead of a cohort.
If history matters clinically, check that the model
remembers it.
How long is a cycle?
Short enough that two events rarely happen in one cycle
Matched to the disease: months for cancer on treatment, a year for slow chronic disease
People move at the end of a cycle but really move halfway through on average, so
careful models apply a half-cycle correction
You need not compute any of this. You need to find the cycle length
in the paper, and notice if it is missing.
Where the numbers come from
Input
Usual source
What to ask
Transition probabilities
trials, cohorts, registries
From India? Over what follow-up?
Beyond follow-up
extrapolation
How was it extended, and was it tested?
Utilities
EQ-5D surveys
Indian value set?
Costs per state
costing studies, package rates
The five costing errors
A model built entirely on borrowed numbers can be internally
perfect and still answer someone else's question.
Seven questions for any published model
Is there a diagram of the structure? Could you redraw it?
Do the states include every event that differs between the options?
Is the cycle length stated and sensible?
Where do the probabilities come from, and from which country?
How far does it extrapolate beyond the evidence?
Was it validated: does it reproduce known survival or incidence?
Were structural alternatives tested, or only parameters?
And your paper
Is it a model? A tree, a Markov model, both, or neither?
Name the health states and the cycle length
Which of the seven questions can the paper not answer?
Two sentences on its structure, ready for the report-back.
Sources
Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015. Chapter 9, Economic evaluation using decision analytic modelling.
Briggs A, Sculpher M. An introduction to Markov modelling for economic evaluation. PharmacoEconomics 1998;13(4):397–409. PMID 10178664
Caro JJ, Briggs AH, Siebert U, Kuntz KM. Modeling good research practices: overview. A report of the ISPOR-SMDM Modeling Good Research Practices Task Force-1. Value Health 2012;15(6):796–803. PMID 22990082