Cost-effectiveness analysis using Markov modeling

1. Cost-effectiveness analysis using Markov modeling Rahul Ganguly Ph.D. November 25th, 2006 BITS, Pilani

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 tree • Deterministic • Markov model • Timing of event and recursive • Monte-carlo simulation • Stochastic

4. Limitations of simple decision tree FATAL DEAD BLEED NON FATAL POST BLEED ANTICOAGULANT FATAL DEAD EMBOLUS NON FATAL POST EMB NO EVENT WELL

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

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. Example WELL DISABLED DEAD Expected utility = ts X us S = 1 to n

8. State transition probability P1 P4 MARKOV CHAIN (CONSTANT PROBABILITY) P matrix WELL DISABLED P2 P3 P8 P5 P9 P6 DEAD P7

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

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

12. Markov cohort simulation What do the numbers mean?

13. Markov cohort simulation

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

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. 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. Step 2: Markov model CD4 COUNT Opportunistic Infections (OI) Chronic CD4 count OI history Acute CD4 count OI history 0.300 x 109/l • PCP (Pneumonia) • Toxoplasmosis • MAC (Bacterial) • Fungal • CMV (VIRAL) 0.201 x 109/l Death 0.101 x 109/l 0.051 x 109/l Cycle length = 1 month Cohort simulation = 1 million patients 0.00 x 109/l • Used C/C++ programming • Model can be built on Microsoft excel • Other software - Treeage

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

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. 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. Are there any options you would never consider?

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. 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? ?