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2. 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?. 3. Types of modeling techniques. Simple decision treeDeterministicMarkov modelTiming of event and
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1. 1 Cost-effectiveness analysis using Markov modeling Rahul Ganguly Ph.D.
November 25th, 2006
BITS, Pilani
2. 2 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?
3. 3 Types of modeling techniques Simple decision tree
Deterministic
Markov model
Timing of event and recursive
Monte-carlo simulation
Stochastic
4. 4 Limitations of simple decision tree
5. 5 Limitations of simple decision tree
6. 6 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 Cycle time depends on available probabilities, frequency of events (rare events have longer cycle times)Cycle time depends on available probabilities, frequency of events (rare events have longer cycle times)
7. 7 Example In this diagram Well, disabled and dead are the Markov states. The arrows indicate the various transitions that can happen in each cycle (explain). Dead is the absorbing state. In this diagram Well, disabled and dead are the Markov states. The arrows indicate the various transitions that can happen in each cycle (explain). Dead is the absorbing state.
8. 8 State transition probability Talk about non-constant probability
Talk about Memory markov states do not have a memory built in or the probability rate for well disabled is
Same for someone who spent n cycles in well vs. someone who spent 2n cycles in well. Talk about non-constant probability
Talk about Memory markov states do not have a memory built in or the probability rate for well disabled is
Same for someone who spent n cycles in well vs. someone who spent 2n cycles in well.
9. 9 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
10. 10 Markov states Not more than 1 cycle
Different transition probabilities
Cost and utility adjustment
Not more than 1 cycle
Different transition probabilities
Cost and utility adjustment
11. 11 Markov cohort simulation
12. 12 Markov cohort simulation
13. 13 Markov cohort simulation
14. 14 Monte Carlo Simulation
15. 15 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)
16. 16 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
17. 17 Step 2: Markov model
18. 18 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
19. 19 Rates to probabilities
20. 20 Step 4: Report base case
21. 21 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
22. 22 Are there any options you would never consider?
23. 23 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
24. 24 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