So far in this series you've learned why to do CEAs and key elements of how the incremental
cost-effectiveness ratio, DALYs and QALYs, sensitivity analyses, and other issues. In
the last segment you learned how to present CEA in a research proposal.
In this segment, we will look at decision trees for CEA. We have a few introductory
comments and then a short animation on the use of decision trees to structure your analysis.
The decision tree is a great tool for cost-effectiveness analysis because it's designed to show potential
options for action and the consequences of those options. Trees structure the analysis
and guide calculations.
I love decision trees as a way to structure analyses. Some of my colleagues say I'm a
tree hugger. I am they are so helpful. You can do CEAs without trees, but in this series
we highlight the tree approach.
There are 3 major components of a decision tree:
action options, which show the decision being considered;
consequences, which describe the mix of outcomes and their probabilities;
and the value of health and cost outcomes for each set of consequences.
Once you have these in a tree you can calculate the expected value of each action option for
health and cost outcomes and then you can determine your cost effectiveness ratio to
make better decisions about health spending.
Let's look at an example.
Here's a basic decision tree to assess the cost-effectiveness of a mobile camp for adult
male circumcision in rural Zambia, to prevent HIV infection. This is a simplified version
of the research question in segment #7.
You start with a description of the population, in this case young men at risk of acquiring
HIV infection. Let's say we have a hundred such men. You can portray any number of individuals,
but it's easier to show and understand the calculations if you use a large round number
like 100 or 1000.
This square represents a decision node: the choice of no camp versus a circumcision camp.
As we've said, CEA always examines a comparison. Here, the comparison option is doing no camp.
So in this tree all 100 men go to either no camp or circumcision camp. The subsequent
branches show what happens as a result.
Next comes this circle, which is a chance node. Chance nodes show the mix of possible
consequences for each option. In this simple tree, there is only one chance node per option.
In most trees there are many branching chance nodes. For learning, we'll keep it simple.
The upper chance node shows that with no circumcision camp, the likelihood of getting HIV infection
is 0.4, or 40%. So, the chance of not getting HIV infection is 60%. These probabilities
always add up to one.
It's best for chance nodes to be dichotomous, like this one, to facilitate sensitivity analyses.
But it's also ok to show three or more mutually exclusive outcomes in one chance node.
With the circumcision camp, the chance of HIV infection is specified as 20%. This is
based on three excellent clinical trials, which show that circumcision lowers the risk
of HIV infection by 50%. Half of 0.4 is 0.2. Thus the likelihood of no HIV infection is
80%.
This is the core structure of the decision tree: action options followed by chance nodes
which represent consequences.
Next we want to calculate how many individuals end up following each path in the tree. Remember
that we started with 100 individuals. So, if with no camp the chance of HIV infection
is 0.4, the number in that path is 40, which equals 100 times 0.4. Similarly, the number
not getting HIV infection is 60. Thus, all 100 men who started that option follow one
of these two tree paths.
Below, with circumcision camp, the 100 men are divided into 20 who get HIV infection,
that's 100 times 0.2, and 80 who do not.
The difference between action options in these outcomes -- HIV infection vs. not drives both
health and cost outcomes for the analysis. This could be said more generally, the differences
in the distribution of clinical outcomes influences CEA results.
Next we need to attach DALYs to each path. The added DALY burden due to each new HIV
infection is estimated at 7, based on studies that portray health status over time with
and without HIV infection, allowing for the use of anti-retroviral therapy. Thus we put
7 next to paths with HIV infection, and zero next to paths without HIV infection because
no DALYs are incurred with no HIV infection. We calculate the expected DALYs due to HIV
in each path as the product of the number of individuals in the path times the DALYs.
For the no camp option with HIV infection, that is, the first path in the tree, we calculate
280 DALYs, as the product of 40 and 7. The next path, no camp and no HIV infection, has
no DALYs, in the absence of HIV infection. Thus the total of DALYs for no camp equals
280.
For the circumcision camp paths, we similarly calculate 140 and zero DALYs, respectively,
for a total of 140 DALYs with the camp. Thus, the circumcision camp averts an estimated
140 DALYs per 100 individuals. That's the health benefit.
Adding costs to each path is a very similar process. There are two types of costs. First
is the cost to implement the circumcision camp, usually referred to as program or intervention
cost. This is $100 per person with the camp, and $0 with no camp.
The second type of cost is for HIV medical care, required for individuals who become
HIV-infected. Based on empirical and modeling studies in Africa, we estimate this at $6,000.
The total cost for each path is the sum of circumcision camp and HIV medical care costs,
multiplied by the number of individuals in that path. In the first path, which is no
camp followed by HIV infection, the estimated total cost is $240,000, which is the product
of 40 and $6,000. The next path has zero costs, since there is no camp and no HIV infection.
Thus total costs for no camp equal $240,000. For the circumcision camp part of the tree,
the cost with HIV infection is $122,000, representing mainly the HIV care costs but also camp costs.
The cost with no HIV infection is $8,000, representing 80 individuals and $100 per person
for the camp. The total for the circumcision camp part of the tree is $130,000. Thus the
camp saves $110,000 per 100 participants.
Since the camp reduces DALYs and also saves money, we say it is dominant both better and
cheaper. By the way, the best evidence for male circumcision definitely supports the
idea that you save more than you spend. Therefore, as we can see in this table, male circumcision
is an efficient strategy. If the camp didn't save money but did improve
health (that is, decrease DALYs), we'd calculate the ICER as the difference in total cost divided
by the difference in DALYs. But when an intervention is dominant, we don't calculate the ICER.
See in this modified tree a hypothetical example[1] if the camps were much more expensive ($250
per client) and lifetime HIV medical care costs were only $1000, With those assumptions,
the ICER would be $36.
Now you know how decision trees work. Adding more action options or a more complex set of outcomes
is conceptually the same, just with added detail. Any CEA can be structured this way.
I hope you too become a tree hugger.