Cost-effectiveness analysis using Markov modeling

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