Question

Problem 5a. 0.0/1.0 point (graded)

While Sunesis had sufficient capital to fund the original Phase-III design of the trial, the company was seeking an additional $25 million to fund a potential expansion of the study based on the results of an interim analysis. At that time, an independent data safety monitoring board (DSMB) would decide whether to stop the study early for efficacy or futility, continue the study as planned, or implement a one-time increase in sample size with an additional 225 patients. By designing the study this way, Sunesis could avoid conducting an unnecessarily large trial in certain cases, potentially reducing the overall cost and risk of their study.
After conducting its due diligence, Royalty Pharma conditionally agreed to pay Sunesis the $25 million to acquire a royalty interest on the future net sales of Vosaroxin. However, under the terms of the agreement, Royalty Pharma would only invest the $25 million if, following the interim analysis, the study was stopped early for efficacy or if the sample-size increase was implemented. In return, assume Royalty Pharma would get a 3.6% royalty interest on future net sales of the drug if the study was stopped early for efficacy, or a 6.75% royalty on future net sales if the sample size was increased. Assume these scenarios were estimated to occur with probability 10% and 40%, respectively. Furthermore, the probability that the study would be terminated early for futility and abandoned was estimated to be 5%. If the sample size was increased, Royalty Pharma estimated there was a 10% chance the therapy would show a strong effect, a 65% chance that it would show a weak effect, and a 25% chance that it would show no effect and be abandoned.
Finally, if the DSMB decided that the trial should continue as planned, Royalty Pharma would have the option of making the $25 million investment upon the un-blinding of the study (i.e., the results were made known) in exchange for a 3.6% royalty interest on future net sales. Given this scenario, Royalty Pharma estimated there was a 15% chance the therapy would show a strong effect, a 60% chance that it would show a weak effect, and a 25% chance that it would show no effect and be abandoned. As such, Royalty Pharma would be able to significantly limit its exposure to the risk of an undesirable outcome of the clinical trial and, at the same time, position itself to receive a sizable royalty in the event that Vosaroxin was approved.
Vosaroxin was projected to be highly profitable, especially if it the trial was stopped early for efficacy. Under this scenario, future net sales were projected to have a present value of $4 billion. If, however, the trial required a sample-size increase, then future net sales were projected to have a present value of only $2.5 billion under the strong effect scenario, and 0.5 billion under the weak effect scenario. Finally, if the DSMB decided that the trial should continue as planned, the future net sales would have a present value of $3 billion under the strong effect scenario, and $0.5 billion under the weak effect scenario.
Build a decision tree for Royalty Pharma that shows the cash flows and probabilities of each possible scenario. Your tree should have 8 outcomes with 3 failures and 5 successes.
What is the probability that the clinical trial fails and the project is abandoned? (Note: Your answer should be a number in percentage form. Do not enter '%'.)

Answer 1

To determine the probability that the clinical trial fails and the project is abandoned, we need to analyze the given information and construct a decision tree to visualize the different scenarios and their probabilities.

The decision tree should have 8 outcomes, consisting of 3 failures and 5 successes. Let's break down the tree and calculate the probability of the desired outcome:

• Decision Node: Interim Analysis

• Stop Early for Efficacy (10% probability)

Implement Sample-Size Increase (40% probability)

Continue as Planned (50% probability)

• Stop Early for Efficacy (10% probability):

Royalty Interest: 3.6%

Future Net Sales Present Value: $4 billion

• Implement Sample-Size Increase (40% probability):

Royalty Interest: 6.75%

Strong Effect (10% probability):

Future Net Sales Present Value: $2.5 billion

Weak Effect (65% probability):

Future Net Sales Present Value: $0.5 billion

No Effect and Abandoned (25% probability)

• Continue as Planned (50% probability):

Royalty Interest: 3.6%

Strong Effect (15% probability):

Future Net Sales Present Value: $3 billion

Weak Effect (60% probability):

Future Net Sales Present Value: $0.5 billion

No Effect and Abandoned (25% probability)

Now let's calculate the probability of the clinical trial failing and the project being abandoned:

Probability = Probability of Implementing Sample-Size Increase × Probability of No Effect and Abandoned

= (40% × 25%) = 10%

Therefore, the probability that the clinical trial fails and the project is abandoned is 10%.