Introduction of the computation in expected value of perfect information (EVPI)
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Eckermann and Willan published an article introducing the theory of expected value of information. Since the EVPI is a very promising approach in health economic analysis and its calculation process is relatively complex, I would like to illustrate it in the MAZE example.

Author: Xuanqian Xie

Eckermann and Willan published an article introducing the theory of expected value of information (Eckermann & Willan, 2007). The well recognized HTA report by NICE also applies EVPI in their economic analysis (Collins et al, 2007). And some researchers in McMaster University in Canada applied it in more complex conditions, such as expected value of partial perfect information (EVPPI) (Xie F. et al. 2009). But, as far as I know, the expected value of perfect information (EVPI) has not been used very frequently in medical publications. I once used EVPI in the MAZE project, but this section was trimmed in the final publication (Quenneville SP. et al. 2009). Since the EVPI is a very promising approach in health economic analysis and its calculation process is relatively complex, I would like to illustrate it in the MAZE example.

I used nonparametric approach for EVPI by no assumption of distribution of net monetary benefit. EVPI can be calculated using in parametric method but this approach is not widely accepted, due to without good reason to define the net benefit following certain distributions. The calculation of EVPI for net health benefit is also based on similar concepts. Detailed theory and calculation can be found in Briggs et al. book, Decision modeling for health economic evaluation, 2006, Oxford university press.

Briefly, EVPI is equal to expected outcomes with perfect information minus expected outcomes without perfect information. We define input variables with distributions, rather than a single value to model the uncertainties of variables. The perfect information removes uncertainties by selecting the best alternative. Small EVPI means that we can gain very little extra values even obtaining best information, indicating not worth for further research. Theoretically, EVPI can be both cost and effectiveness, but usually researchers use net monetary benefit of EVPI in health economic studies.

 

 

One payoff

 

Let us assume the simplest condition: treatment A and B, and only 1 payoff, life-years. Mean of life-years in 1000 iterations of A and B are 6 and 7, respectively. Here, we do not consider costs, so treatment B should be chosen for higher average life-years. The first 10 iterations of A and B are listed in table 1, respectively.

 

As a whole, treatment B is better than A. But, Treatment A can be better than B in some iterations by chances, like the 4th, 6th and 10th iterations. Therefore, choosing B means “wrong decision” in some iterations. Assuming we know the perfect information, we would choose A in 4th, 6th and 10th iterations, and choose B in other iterations. The average of expect maximum benefit is 7.9 (Optimal choice) and currently value is 7 (B treatment), so theoretically we lose up to 0.9 life years in average, which is the fundamental concept of EVPI. If 1000 patients are relevant in this condition, the estimated maximum opportunity loss (population based EVPI) is 900 life-years.

 

 

 

The example from MAZE project

When we can have 3 or more treatments and consider both cost and effectiveness, and the maximum willingness to pay (WTP), it becomes more complicated. But, the concept is same as the one payoff example above. Next, I use part of our data to describe the process of calculating EVPI (I choose some typical data to illustrate EVPI). Ten samples are show in table 2.

 

 

Next, we can calculate net benefit.

Net monetary benefit= QALY*WTP-Cost,

For sample 1 of MAZE strategy, if WTP= 50,000, then the

Net benefit= 6.77*50,000-184787=153591

 

When WTP=50, 000, results are in table 3.

 

When WTP=20, 000, results are in table 4.

 

Please note when WTP are different, the different samples could meet the opportunity loss. As a result, the shape of EVPI graph with increased WTP is very flexible (sometimes, no clear tendency), and nearly any shape is possible.

 

 


Other issues:

 

Population EVPI: Population EVPI equals individual EVPI multiplied by number of relevant population. It is context based, because we can define relevant population in different level, like province level, national level, or even global level by WHO, which may lead quiet different results.

 

 


Small Population EVPI: Assuming the clinical trials provided the accurate unbiased results, and the population EVPI is very small, according to the principles of health economics, we believe that it is not necessary to conduct further investigations on this issue. But actually, we deleted the sentence like “We therefore do not think it is worthwhile from an economic point of view to carry out additional investigations” in one article because from clinical perspective, further research is still important on this area.

 

 

 


Reference:

 

Briggs A, Sculpher M and Claxton K, Decision modeling for health economic evaluation, 2006, Oxford university press.

Collins R, Fenwick E, Trowman R et al. A systematic review and economic model of the clinical effectiveness and cost-effectiveness of docetaxel in combination with prednisone or prednisolone for the treatment of hormone-refractory metastatic prostate cancer. Health Technology Assessment 2007; 11(2).

Eckermann S, Willan AR. Expected value of information and decision making in HTA. Health Economics 2007; 16(2):195-209.

Quenneville SP, Xie X, Brophy JM. The cost-effectiveness of Maze procedures using ablation techniques at the time of mitral valve surgery. Int J Technol Assess Health Care 2009; 25(4):485-96

Xie F, Blackhouse G, Assasi N, Campbell K, Levin M, Bowen J, Tarride JE, Pi D, Goeree R. Results of a model analysis to estimate cost utility and value of information for intravenous immunoglobulin in canadian adults with chronic immune thrombocytopenic purpura. Clinical Therapeutics 2009; 31(5): 1082-1091

 

 

 

 

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