1. 1 Cost-effectiveness analysis using Markov modeling Rahul Ganguly Ph.D. November 25 th, 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 ANTICOAGULANT NO EVENT EMBOLUS BLEED NON FATALPOST BLEED FATALDEAD NON FATALPOST EMB FATALDEAD WELL

5. 5 Limitations of simple decision tree ANTICOAGULANT NO EVENT EMBOLUS BLEED NON FATAL BLEED FATALDEAD NON FATALPOST EMB FATAL DEAD WELL EMBOLUS NO EVENT  RECURRING EVENTS  TIMING OF EVENT  UTILITY

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

7. 7 Example WELL DEAD DISABLED Expected utility =  t s X u s S = 1 to n

8. 8 State transition probability WELL DEAD DISABLED P9P9 P5P5 P2P2 P6P6 P1P1 P7P7 P4P4 P3P3 P8P8 MARKOV CHAIN (CONSTANT PROBABILITY) P matrix

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 WELL DEAD DISABLED STROKE TEMPORARY STATE POST MI1 POST MI2 POST MI3 POST MI TUNNEL STATES DEAD

11. 11 Markov cohort simulation WELL 10 patients DEATHDISABLED WELL 5 patients DEATH 2 patients DISABLED 3 patients WELL 0 patients DEATH 10 patients DISABLED 0 patients N1 cycles N2 cycles

12. 12 Markov cohort simulation What do the numbers mean?

13. 13 Markov cohort simulation

14. 14 Monte Carlo Simulation WELL AJAY VIJAY DEATHDISABLED WELL VIJAY DEATH 2 patients DISABLED AJAY WELL 0 patients DEATH AJAY VIJAY DISABLED 0 patients N1 cycles N2 cycles Random number generation Can compute variance and Standard Deviation

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 Chronic CD4 count OI history Death Acute CD4 count OI history 0.051 x 10 9 /l 0.201 x 10 9 /l 0.300 x 10 9 /l 0.101 x 10 9 /l 0.00 x 10 9 /l  Used C/C++ programming  Model can be built on Microsoft excel  Other software - Treeage CD4 COUNTOpportunistic Infections (OI)  PCP (Pneumonia)  Toxoplasmosis  MAC (Bacterial)  Fungal  CMV (VIRAL) Cycle length = 1 month Cohort simulation = 1 million patients

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

20. 20 Step 4: Report base case Research question What is an acceptable incremental quality adjusted life year value For India? (describe how will you estimate it)

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 “…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?

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 Research question Strategies to decrease Tuberculosis in Rural India? ?