Sensitivity Analysis on a Probability

Assessing probabilities is often the most time consuming part of building a decision model. It's natural to want to know how much impact the choice of numbers has on the recommended policy.

Consider the model below. A research lab has developed a new drug that looks promising in preliminary tests. If it decides to market this drug it will have to pay for some field tests and will only be able to sell the drug if it gets regulatory approval.

The team consensus is that the probability of getting the drug approved is 70%. However, one dissenter believes that the probability of approval is really closer to 50%, and asserts that if aspirin were invented today it would have only a 75% chance of being approved.

With approval at 70% the model gives a strong go signal, with an expected profit of $29.25 million. What happens at a lower approval probability?

If you choose Analysis | Rainbow Diagram with the model as it stands now, only Testing_Cost and Sales will be available, there are no probabilities. To perform a sensitivity analysis on a probability, you have to create a value node for it. In this case, call it Approval_Prob.

The data for Approval prob is 0.7. Change the probability of Regulatory_Approval being Yes from 0.7 to Approval_Prob, and Regulatory_Approval No from 0.3 to blank. It's important to remember to leave the last probability blank - DPL requires this with non-constant probability expressions.

Now you're ready to run a sensitivity analysis. Choose a range of 0.4 to 0.7 (40% to 70%), and an interval of 0.05. The graph indicates that even with approval probability at 40%, the lab should still go ahead with their plans.

Performing a sensitivity analysis on a probability for a chance node with more than two states is slightly more complex.

Sales is also an important uncertainty in the model. The initial estimate is that Sales will take the values 60, 90 and 120 (millions of dollars) with probabilities 25%, 50%, 25%. The Low Sales number is based on the case where a competitor introduces a similar drug at about the same time. This is difficult to asses the likelihood of and the team would like to perform a sensitivity analysis on the probability of Low Sales.

In the previous example, Regulatory Approval only had two states, so decreasing the probability of approval meant increasing the probability of disapproval. In this case, we have to decide how a change in the probability of Low Sales should be reflected in the Nominal and High probabilities. After some discussion, the team decides that the probability of Nominal Sales should always be twice as high as the probability of High Sales.

Next create a new value node called Low_ Sales_Prob and give it 0.25 for data. Then create a black arrow from Low_Sales_Prob to Sales, and enter the following for Sales node data:

Since the probability for High is blank, DPL will give it probability (1.0 - Low_Sales_Prob) * 1/3 at runtime. This means that as the probability of Low Sales increases, the probabilities of Nominal and High Sales decrease, but keep the same proportion. Performing a sensitivity analysis on Low_Sales_Prob with a range of 0.25 to 0.5 and an interval of 0.025, generates the following result:

Click here to download the DPL file we used in this article.