Integrated Go Or No-Go and VOI Case Study

From a Probability Estimate to a Development Decision

A probability of success (PoS) is useful for a development decision only when it is tied to a clearly defined success event and a set of available actions. A program may have an estimated chance of meeting a clinical milestone, but that estimate alone does not say whether to invest: the value of success, the cost of continuing, and the option to stop also matter. A study can add value when its results are expected to change which action is best.

This case uses hypothetical values for a single development milestone. The objective is to compare an immediate go/no-go decision with a decision to collect one more signal before committing. All monetary amounts are in millions of dollars. The calculation assumes a risk-neutral decision maker who selects the action with the greatest expected monetary value. The probabilities and financial values are decision inputs for this example, not empirical claims about any real program.

Definition: Let $p$ be the probability that the defined milestone succeeds, conditional on the evidence currently available. If continuing costs $C$, yields net value $V$ upon success, and yields no value upon failure, the expected value of continuing is $pV-C$. If stopping has value zero, the immediate go/no-go rule is to continue when $pV-C>0$, stop when $pV-C<0$, and regard the actions as equal when $pV-C=0$.

Estimating the Milestone Probability of Success

The success event must be stated before probabilities are combined. Here, success means that the program meets the specified efficacy criterion, meets the safety criterion, and completes the required operational milestone. Suppose the current evidence supports these hypothetical sequential probabilities:

The probability of meeting the efficacy criterion is $0.50$.
Given that efficacy criterion is met, the probability of meeting the safety criterion is $0.60$.
Given that both clinical criteria are met, the probability of completing the operational milestone is $0.60$.

Because these are conditional probabilities along a defined sequence, their product is the probability of the joint success event. No assumption that the components are independent is needed when the probabilities are correctly specified as successive conditional probabilities. If instead they were marginal probabilities, multiplying them would require an appropriate independence assumption.

Worked Example: Combining Conditional Milestone Probabilities

Calculate the probability that all three criteria are met.

Formula. By the multiplication rule for conditional probabilities,

p=P(E)\,P(S\mid E)\,P(O\mid E,S)

Here, $E$ denotes meeting the efficacy criterion, $S$ meeting the safety criterion, and $O$ completing the operational milestone. Substituting the case inputs gives

$$ p=0.50(0.60)(0.60)=0.180 $$

Thus the estimated probability of the defined joint milestone success is $0.180$, or $18.0\%$. This is not the probability of efficacy alone: the success event includes safety and operational completion as well. The estimate is meaningful only if the inputs refer to the stated conditional events and the same development decision.

Immediate Go/No-Go Values

Suppose continuing now costs $C=\$40$ million. If the milestone succeeds, the program has a net value of $V=\$300$ million after the milestone, and if it fails the program has no further value. Stopping has value zero. The stipulated $\$300$ million is the success payoff used in this decision calculation; the $\$40$ million continuation cost is paid whether the milestone ultimately succeeds or fails.

The expected value of continuation is the probability-weighted success value less the cost paid to continue. Its break-even probability follows by setting that value equal to the stopping value. This gives the precise threshold rather than a rounded approximation used as if it were exact.

Derivation: Continue and stop have equal value when $pV-C=0$. Solving for $p$ gives $p=C/V$. In this case the exact break-even probability is $40/300=2/15\approx0.1333$. Continuing has greater expected value for $p>2/15$; stopping has greater expected value for $p<2/15$; and the two actions are equal at $p=2/15$.

Worked Example: Comparing Continuation With Stopping

Use the estimated $p=0.180$ to choose between immediate continuation and stopping.

Continuation value. The formula is $pV-C$. Substituting the values gives

(0.180)(\$300\text{ million})-\$40\text{ million} =\$54\text{ million}-\$40\text{ million} =\$14\text{ million}

Stopping value. By assumption, stopping has value $\$0$ million. Since $\$14$ million is greater than $\$0$ million, the immediate risk-neutral decision is to continue. This is consistent with the threshold check: $0.180>2/15$.

The threshold is a decision boundary under these particular payoff and cost assumptions, not a universal PoS target. For example, increasing the cost while holding the success value fixed would raise the break-even probability.

Valuing a Study Before Committing

Now suppose a study can produce a positive or negative signal about the defined milestone success. For this hypothetical study, assume $P(+\mid\text{success})=0.75$ and $P(-\mid\text{failure})=0.80$. Thus $P(-\mid\text{success})=0.25$, and $P(+\mid\text{failure})=0.20$. The study costs $\$6$ million. Assume it reports before the continuation decision, does not change the success payoff or continuation cost, and creates no other delay, operational failure, or value. These simplifying assumptions let the calculation isolate the information value and the stated study cost.

The study's signal probabilities are calculated using the current $p=0.180$. The posterior probability after each result is obtained by Bayes' rule. The action after each signal must then be chosen by comparing its conditional continuation value with stopping at zero. EVSI, the expected value of sample information, is the expected value after observing the study result and choosing the best action for that result, minus the best value available before the study. This gross EVSI does not include the study's cost.

Worked Example: Posterior Probabilities and the Action After Each Signal

Positive signal probability. A positive signal can occur after success or failure, so

P(+)=P(+\mid\text{success})P(\text{success})+ P(+\mid\text{failure})P(\text{failure})

Substitution gives $P(+)=0.75(0.180)+0.20(0.820)=0.135+0.164=0.299$. Therefore $P(-)=1-0.299=0.701$.

Posterior after a positive signal. Bayes' rule gives

P(\text{success}\mid+)=\frac{0.75(0.180)}{0.299} =\frac{0.135}{0.299} \approx0.4515

The conditional continuation value is

\left(\frac{0.135}{0.299}\right)(\$300\text{ million})-\$40\text{ million} \approx \$95.45\text{ million}

This is positive, so the action after a positive signal is to continue.

Posterior after a negative signal. The joint probability of success and a negative signal is $0.25(0.180)=0.045$. Hence

P(\text{success}\mid-)=\frac{0.25(0.180)}{0.701} =\frac{0.045}{0.701} \approx0.06419

The conditional continuation value is

\left(\frac{0.045}{0.701}\right)(\$300\text{ million})-\$40\text{ million} \approx -\$20.74\text{ million}

This is less than the stopping value of zero, so the action after a negative signal is to stop. The signal is decision-relevant in this case because the optimal action differs across its two possible results.

Calculating EVSI and Selecting the Action

The expected value after the study is calculated by weighting each result-specific best action value by the probability of that result. For a positive signal, continue; for a negative signal, stop. The expected value of the positive branch can be computed either from the posterior continuation value or directly from its joint probability. The latter makes the arithmetic easy to audit.

Worked Example: Gross EVSI and Net Study Value

Expected value after observing the signal and choosing optimally. The positive branch contributes its probability times its conditional continuation value. Equivalently, its value is the expected success payoff on that branch minus the continuation cost weighted by the probability of that branch:

P(+)\left[P(\text{success}\mid+)V-C\right] =0.75(0.180)(\$300\text{ million})-0.299(\$40\text{ million})

The arithmetic is $\$40.50$ million minus $\$11.96$ million, or $\$28.54$ million. The negative branch contributes zero because stopping is optimal there. Therefore the expected value with study information, before the study cost, is $\$28.54$ million.

Gross EVSI. The best value without the study is the immediate continuation value of $\$14$ million. Thus

\text{EVSI}=\$28.54\text{ million}-\$14\text{ million} =\$14.54\text{ million}

Net value after study cost. Subtract the $\$6$ million study cost from the value after information: $\$28.54-\$6=\$22.54$ million. Relative to continuing immediately, the study's net incremental value is $\$22.54-\$14=\$8.54$ million, which also equals gross EVSI minus study cost. Under the case assumptions, choose the study, continue after a positive result, and stop after a negative result.

Theorem: With the same available actions and payoffs before and after a study, perfect implementation of the decision rule, and no study cost included in the gross calculation, expected value after observing the result cannot be lower than the best expected value before observing it. The decision maker can always ignore the result and take the original best action. A negative gross EVSI in a calculation with these conditions indicates an arithmetic or decision-rule error; net value can be negative after study cost.

Checks, Alternatives, and Common Pitfalls

Several checks help detect an incoherent analysis. First, confirm that the probability refers to the exact success event linked to the stated payoff. Second, check that probabilities for the study's possible results sum to one and that each posterior follows from the corresponding joint probability. Third, verify that each result-specific action is optimal: compare its conditional continuation value with zero rather than automatically continuing after every signal. Finally, calculate gross EVSI against the best current action, not against an arbitrary alternative.

The principal alternative to immediate investment is to stop now; in this example, a study is a third choice that may improve the decision by changing what happens next. A study with excellent predictive performance can still have little or no EVSI if every possible result leads to the same action. Conversely, a result that changes the decision does not guarantee positive net value: the gross value of the improved choices must exceed the study cost and any other properly specified costs.

Pitfall: treating a rounded threshold as exact. The threshold is $2/15$, not exactly $0.1333$. For instance, $p=0.1333$ gives $300(0.1333)-40=-\$0.01$ million, so stopping is slightly better at that value. State the exact threshold first and use the rounded value only as an approximation.
Pitfall: mixing rounded posteriors with unrounded arithmetic. Use the unrounded ratio in the calculation, or report a value consistent with the displayed rounded probability. Here the positive branch is calculated using $0.135/0.299$, not an intermediate rounded posterior.
Pitfall: calling the value after a study its EVSI. The value after information is $\$28.54$ million; gross EVSI is the increment over the best current value, $\$14.54$ million. Net value additionally accounts for the study cost.
Pitfall: multiplying marginal probabilities without justification. The PoS product here uses sequential conditional probabilities. Multiplying unrelated marginal probabilities would require a defensible dependence assumption.

These conclusions are limited to the specified event, values, study signal, and assumptions. A decision maker using a different utility scale, different costs, constraints, or a study that changes timing or the available actions would need to represent those features in the decision calculation. The introductory material on value of information establishes the general comparison; this case shows how the probability estimate, branch-specific choices, and cost accounting fit together numerically.

Check Your Understanding

Use the case assumptions above unless a question changes them. Solutions are given after the questions.

If the success payoff remains $\$300$ million and the continuation cost rises to $\$60$ million, what is the exact break-even probability?
With prior $p=0.180$, what is the probability of a negative study signal?
At what posterior probability does continuation break even in this case, and should the program continue after a negative signal?
What is the gross EVSI, and what is the net incremental value of the study relative to immediate continuation?
Suppose every possible study result led to the same action as the current best action. What would the gross EVSI be under the same-action, same-payoff assumptions?

Solutions. (1) The threshold is $C/V=60/300=0.20$, or $20.0\%$. (2) The negative signal probability is $P(-)=0.25(0.180)+0.80(0.820)=0.045+0.656=0.701$. (3) Break-even is $40/300=2/15\approx0.1333$. The negative-signal posterior is $0.045/0.701\approx0.06419$, which is below the threshold, so stop. (4) Gross EVSI is $\$28.54-\$14=\$14.54$ million; net incremental value is $\$14.54-\$6=\$8.54$ million. (5) Gross EVSI is zero if the result cannot change the action and all payoffs and costs are otherwise unchanged: observing the signal then leaves the expected value of the chosen action the same as without the signal.