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Cost-effectiveness analysis using Markov modeling

Rahul Ganguly Ph.D.

November 25th, 2006

BITS, Pilani

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Learning objective

• What is Markov modeling and why do we need it?

• What are some of the important concepts around Markov modeling?

• How do we apply Markov modeling to answer research questions?

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Types of modeling techniques

• Simple decision tree– Deterministic

• Markov model– Timing of event and recursive

• Monte-carlo simulation– Stochastic

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Limitations of simple decision tree

ANTICOAGULANT

NO EVENT

EMBOLUS

BLEED

NON FATAL POST BLEED

FATAL DEAD

NON FATAL POST EMB

FATAL DEAD

WELL

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Limitations of simple decision tree

ANTICOAGULANT

NO EVENT

EMBOLUS

BLEED

NON FATAL

BLEED

FATAL DEAD

NON FATAL POST EMB

FATAL DEAD

WELL

EMBOLUS

NO EVENT

RECURRING EVENTSTIMING OF EVENTUTILITY

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Markov model

• Markov states– Well– Disabled (Non fatal Bleed, Embolus)– Death

• Markov cycle– During each cycle the patient may transition from one

state to another– Cycle length is a clinically meaningful time interval

• Time spent in each state– Cumulative cost / cumulative utility = CU ratio

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Example

WELL

DEAD

DISABLED Well Disabled Dead TOTALUtility 1 0.7 0Cycles 3 1

Quality adjusted life expectancy

3 0.7 0 3.7

Cost/cycle/state 50000 100000 0

Cost 150000 100000 0 250000

Expected utility = ts X us

S = 1 to n

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State transition probability

WELL

DEAD

DISABLED

P9

P5

P2

P6

P1

P7

P4

P3

P8Well Disabled Dead

Well 0.6 0.2 0.2Disabled 0 0.6 0.4

Dead 0 0 1

TO

FROM

MARKOV CHAIN (CONSTANT PROBABILITY)

P matrix

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Carrom example

• Each piece is a “markov state”

• Each strike is like a “markov cycle”

• Each piece has probability of moving to another place

• Consider the net as an “absorbing state”– Entire cohort is ultimately

absorbed into this state e.g. death

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Markov states

WELL

DEAD

DISABLED

STROKE

TEMPORARY STATE

POSTMI1

POST MI2

POSTMI3

POSTMI

TUNNEL STATES

DEAD

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Markov cohort simulation

WELL10 patients

DEATHDISABLED

WELL5 patients

DEATH2 patients

DISABLED3 patients

WELL0 patients

DEATH10 patients

DISABLED0 patients

N1 cycles

N2 cycles

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Markov cohort simulationUtility Utility Utility

1 0.7 0

Cycle Well Disabled DeadCycle sum

Cumulative utility

Start 10000.0 0.0 0.01 6000.0 2000.0 2000.0 7400. 7400.02 3600.0 2400.0 4000.0 5280. 12680.0

23 0.1 0.6 9999.3 0.5 23749.224 0.0 0.4 9999.6 0.3 23749

TOTAL 15000 12499

Well Disabled DeadWell 0.6 0.2 0.2

Disabled 0 0.6 0.4Dead 0 0 1

TO

FROM

What do the numbers mean?

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Markov cohort simulation

Utility Utility Utility1 0.7 0

Cycle Well Disabled DeadCycle sum

Cumulative utility

Start 10000.0 0.0 0.01 6000.0 2000.0 2000.0 7400.0 7400.02 3600.0 2400.0 4000.0 5280.0 12680.023 0.1 0.6 9999.3 0.5 23749.224 0.0 0.4 9999.6 0.3 23749

TOTAL 15000 12499

AVERAGE = TOTAL/10000

1.50 1.25 2.37

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Monte Carlo Simulation

WELLAJAYVIJAY

DEATHDISABLED

WELLVIJAY

DEATH2 patients

DISABLEDAJAY

WELL0 patients

DEATHAJAYVIJAY

DISABLED0 patients

N1 cycles

N2 cycles

Random number generationCan compute variance and Standard Deviation

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Using Markov modeling

• Freedberg KA et al “The cost-effectiveness of preventing AIDS-Related Opportunistic infections” JAMA January 14, 1998; 279: 130-136

• Background:– HIV results in various opportunistic infections

• Pneumonia (PCP)• Mycobacterium• Fungal infections

– Drug costs to treat vary ($60 to $15000)

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Step 1: Research question

• What is the clinical impact, cost, and cost-effectiveness of strategies for preventing opportunistic infections in patients with advanced HIV disease?

• Perspective: Societal

• How will we use the results?– Decide which strategy is most beneficial

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Step 2: Markov model

ChronicCD4 countOI history

Death

AcuteCD4 countOI history

0.051 x 109/l

0.201 x 109/l

0.300 x 109/l

0.101 x 109/l

0.00 x 109/l

Used C/C++ programmingModel can be built on Microsoft excelOther software - Treeage

CD4 COUNT OpportunisticInfections (OI)

PCP (Pneumonia)ToxoplasmosisMAC (Bacterial)FungalCMV (VIRAL)

Cycle length = 1 monthCohort simulation = 1 million patients

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Step 3: Model parameters

• Drug efficacy– % reduction in the incidence of opportunistic infection

• Transition probabilities– From published literature and websites– Remember to convert “rates” to “probabilities”

• Cost – Existing data from surveys and clinical trials– Cost to charge ratio– Conversion to most recent rupees (accounting for inflation)

• Utilities– From rating scales – have to convert to utilities

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Rates to probabilities

r r/100 p = 1- exp(-rt) p = 1 - exp(-r/12)Yearly

incidence rateYearly incidence

rate/100Yearly

ProbabilityMonthly probability

2 0.02 0.019799294 0.0016651065 0.05 0.048765644 0.004157568

20 0.2 0.181252269 0.01652684740 0.4 0.329652153 0.03278055760 0.6 0.451154221 0.04876564480 0.8 0.550633764 0.06448654890 0.9 0.593392399 0.072249299100 1 0.632082414 0.079947636

Beck JR, Paucker SG “The markov process in medical prognosis” Medical Decision Making, 1983; 3: 419-458

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Step 4: Report base case

Infection Drug CostQuality adjusted life expectancy

Incremental CE ratio

No prophylaxis None $40,228 39.08 -

PneumoniaTrimethoprim-sulfamethoxazole

$44,786 42.56 $15,717

Bacterial Azithromycin $40,749 39.24 $39,075Clarithromycin $41,164 39.26 $62,400Rifabutin $41,068 39.21 $77,538

Fungal Fluconazole $41,426 39.22 $102,686Viral Ganciclovir $46,009 39.3 $315,327

Research questionWhat is an acceptable incremental quality adjusted life year valueFor India? (describe how will you estimate it)

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Step 5: Sensitivity analysis

• “…when we doubled the incidence of each opportunistic infection, prophylaxis became more cost-effective”

Policy implication

May be treatment should be targeted at more vulnerable patients only

• “…to achieve a cost-effectiveness threshold of $50,000 per QALY saved, however, the cost of fluconazole would have to be reduced to approx $100 per month”

Policy implication

Can the government negotiate a better price for the drug?

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Are there any options you would never consider?

Infection CostQuality

adjusted life expectancy

No prophylaxis $40,228 39.08TMP-SMX $44,786 42.56TMP-SMX, Azithro $45,944 43.04TMP-SMX, Fluconazole $47,046 43.01TMP-SMX,Azithro, Fluconazole $48,596 43.60TMP-SMX, Ganciclovir $54,628 43.20TMP-SMX,Azithro, Ganciclovir $56,812 43.83TMP-SMX,Fluconazole Ganciclovir $58,082 43.80TMP-SMX, Azithro, Fluconazole, Ganciclovir

$61,119 44.62

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Step 6: Conclusion

• “Pneumonia prophylaxis should be made available to all patients”

• “Next priority should be MAC (Bacterial infection) prophylaxis, where azithromycin is most cost-effective”

• “Only when patients have access to those medications is it reasonable, from CE perspective, to consider fluconazole and perhaps oral ganciclovir”

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Markov modeling in India

• Agarwal R, Ghoshal UC, Naik SR “Assessment of cost-effectiveness of universal hepatitis B immunization in low-income country with intermediary endemicity using markov model” Journal of hepatology 38 (2003) 215-222

Research questionStrategies to decrease Tuberculosis in Rural India??