Framing an Indication Choice
When a development budget cannot support every attractive opportunity, the decision is not simply which indication has the largest potential benefit or the highest chance of success. A useful comparison accounts for the clinical value created if development succeeds, the probability of reaching that outcome, and the costs incurred along the way. It also asks whether the ranking is stable when model predictions are uncertain.
The calculations below use a common present-value date and a single decision metric, expressed in millions of dollars of value-equivalent units. The clinical value is an explicitly monetized representation of the value assigned to an approved treatment in the target indication; it is not necessarily sales revenue. A decision team would need to justify this valuation and its perspective. The examples assume no value is realized if regulatory success is not achieved.
The product \(p_Tp_R\) follows the probability chain rule: \(P(T\text{ and }R)=P(T)P(R\mid T)\). It does not require technical and regulatory outcomes to be independent. The conditional probability \(p_R\) must, however, refer to regulatory success among programs that have achieved technical success.
The formula assumes the program stops and incurs no \(C_1\) if it fails technically; the additional cost \(C_1\) is incurred whenever technical success occurs, including when the program later fails at the regulatory stage. It also assumes the value and costs are measured on the same basis and date, and that there are no salvage values, shared costs, or other benefits. If costs or benefits occur at different times, they must first be put on a consistent discounted-value basis.
Worked Portfolio Comparison
Consider two hypothetical indication programs competing for a maximum authorized development budget of $340 million. The budget is a cap on the maximum planned spend for a selected program, not a requirement to spend the full amount. Both programs are individually feasible, but their maximum planned costs together exceed the cap.
| Quantity ($ millions unless noted) | Indication A | Indication B |
|---|---|---|
| Technical success probability, \(p_T\) | 0.75 | 0.85 |
| Regulatory success probability given technical success, \(p_R\) | 0.70 | 0.55 |
| Value if successful, \(V\) | 900 | 1,100 |
| Initial cost, \(C_0\) | 120 | 100 |
| Additional cost after technical success, \(C_1\) | 180 | 230 |
Worked Example: Ranking Two Feasible Indications
Calculate the overall success probability, expected costs, and expected net value for each program. Then choose the higher expected-net-value program, subject to the stated budget.
For Indication A, the probability of technical and regulatory success is $$ P(T\text{ and }R)=0.75(0.70)=0.525. $$ Thus, the value contribution in expectation is \(0.525(\$900\text{ million})=\$472.5\text{ million}\). Expected development cost is the certain initial cost plus the probability-weighted additional cost: $$ E(C_A)=\$120\text{ million}+0.75(\$180\text{ million})=\$255\text{ million}. $$ Therefore, $$ \operatorname{ENV}_A=\$472.5\text{ million}-\$255\text{ million}=\$217.5\text{ million}. $$
For Indication B, the overall success probability is \(0.85(0.55)=0.4675\), and its expected value contribution is \(0.4675(\$1{,}100\text{ million})=\$514.25\text{ million}\). Its expected cost is $$ E(C_B)=\$100\text{ million}+0.85(\$230\text{ million})=\$295.5\text{ million}. $$ So, $$ \operatorname{ENV}_B=\$514.25\text{ million}-\$295.5\text{ million}=\$218.75\text{ million}. $$
The maximum planned cost is \(\$120+\$180=\$300\) million for A and \(\$100+\$230=\$330\) million for B. Each fits within the \(\$340\) million cap, but funding both would require up to \(\$630\) million. Under this model and a choice of one program, B has the higher expected net value by \(\$218.75-\$217.5=\$1.25\) million. This is a narrow ranking, not evidence that B is clearly superior.
Why Expected Net Value Has This Form
The value term is received only if both development stages succeed. Its expected contribution is therefore the successful-outcome value multiplied by the probability of that outcome. Costs follow a different event structure: \(C_0\) is always incurred, while \(C_1\) is incurred only if technical success occurs. The expectation of the total cost is consequently \(C_0+P(T)C_1\).
This derivation uses linearity of expectation: the expected net value equals expected value minus expected cost. It does not require the cost and success outcome to be statistically independent, provided the costs have the stated event structure and the value \(V\) is received only on joint success. If a cost is also incurred only after regulatory success, or if a partial benefit occurs after technical success alone, its probability-weighted term must reflect that different structure.
Uncertainty in Model Predictions
The inputs \(p_T\), \(p_R\), and \(V\) are predictions, not known constants. A single set of point estimates can conceal uncertainty in the model, its parameters, or the evidence used to calibrate it. One practical check is to calculate expected net value under a small set of coherent predictive scenarios and assign explicit scenario weights. These weights represent the decision team's stated uncertainty about which predictive scenario is relevant; they should not be presented as objective frequencies unless that interpretation is justified.
Worked Example: Propagating Two Model Scenarios
Suppose a model review assigns equal weight to a lower and a higher predictive scenario for each program. The scenario inputs are as follows: for A, \((p_T,p_R)=(0.65,0.60)\) in the lower scenario and \((0.85,0.80)\) in the higher scenario; for B, they are \((0.75,0.45)\) and \((0.95,0.65)\). Values and costs remain as in the table.
For A in the lower scenario, expected net value is $$ 0.65(0.60)(\$900)-\$120-0.65(\$180)=\$114\text{ million}. $$ In the higher scenario it is $$ 0.85(0.80)(\$900)-\$120-0.85(\$180)=\$339\text{ million}. $$ With equal scenario weights, A's scenario-averaged expected net value is $$ 0.5(\$114)+0.5(\$339)=\$226.5\text{ million}. $$
For B, the lower-scenario calculation is $$ 0.75(0.45)(\$1{,}100)-\$100-0.75(\$230)=\$98.75\text{ million}, $$ and the higher-scenario calculation is $$ 0.95(0.65)(\$1{,}100)-\$100-0.95(\$230)=\$360.75\text{ million}. $$ Its scenario-averaged expected net value is \(0.5(\$98.75)+0.5(\$360.75)=\$229.75\) million. The scenario average still ranks B slightly higher, by \(\$3.25\) million, but A is higher in the lower scenario and B is higher in the higher scenario. The ranking is therefore sensitive to the predictive scenario.
When averaging across uncertain predictions, calculate the expected net value within each coherent scenario first, then average those values using the stated scenario weights. In general, multiplying separately averaged probabilities can give a different result from averaging their products. In this example, technical and regulatory predictions move together across scenarios, so their joint success probabilities cannot be recovered by multiplying the separate average probabilities.
Decision Thresholds and Budget Use
A threshold calculation identifies how much an uncertain input must change before the preferred program changes. It is especially informative when the expected-value difference is small. Holding A's inputs and B's other inputs fixed, B exceeds A when
Worked Example: Finding the Regulatory-Success Threshold
Using the point estimates from the portfolio comparison, B's conditional regulatory success probability must exceed $$ \frac{\$217.5+\$100+0.85(\$230)} {0.85(\$1{,}100)} = \frac{\$513}{\$935} =0.5487 $$ to have greater expected net value than A. The point estimate for B is 0.55, only 0.0013 above this threshold. If a defensible estimate were 0.54 instead, B's expected value would be \(0.85(0.54)(\$1{,}100)=\$504.9\) million, and its expected net value would be \(\$504.9-\$295.5=\$209.4\) million. A would then lead by \(\$8.1\) million. The threshold makes clear which assumption is decision-sensitive; it does not establish that either probability estimate is correct.
Budget feasibility and program ranking are separate questions. First exclude choices that violate the budget or other operational constraints. Then compare feasible choices using the decision criterion that has been agreed in advance. With a maximum-spend cap, check the maximum required authorization as well as expected spending. If the budget instead limits expected expenditure, or if cash must be available at each stage, the feasibility calculation changes. If funding some of each program is possible, the choice becomes a portfolio-allocation problem: diversification may matter because outcomes can be uncertain and correlated, and simply selecting the two highest standalone expected values may not be feasible or optimal.
Diagnostics, Alternatives, and Limitations
Before relying on the ranking, check that the inputs and event tree match the actual development plan. In particular, confirm that regulatory success is conditional on technical success; that every cost is assigned to the stage when it is incurred; that value is counted only for outcomes that actually deliver it; and that costs and value use consistent timing, currency, and perspective. Recalculate the result under plausible changes to the key probabilities, cost estimates, and value assumptions. A ranking that changes under small, credible changes should be reported as fragile rather than as a decisive preference.
Expected net value is appropriate when the decision maker is willing to use a probability-weighted average value as the principal criterion and the inputs are sufficiently credible for that purpose. It is not the only reasonable decision rule. A team may also examine probability of success, a conservative scenario, or a risk-adjusted objective when losses are difficult to absorb. These alternatives answer different questions: the program with the greatest success probability need not have the greatest expected net value, and choosing the best result under a worst-case scenario may be deliberately more conservative than maximizing an average.
A major limitation is that monetizing clinical value can conceal important distributional or clinical priorities. If the value metric does not represent the decision maker's perspective or the health consequences that matter, precise arithmetic does not fix the mismatch. Expected values also compress a range of possible outcomes into one number. Scenario analysis reveals some sensitivity but does not eliminate model misspecification, dependence between programs, or uncertainty about scenario weights. A decision should therefore report the assumptions and the size of the margin, not only the winning indication.
- Wrong reasoning: “B has the higher chance of technical success, so it is the better indication.”
- Correction: Technical success is only one stage. Compare the probability of the full successful pathway, the value conditional on that outcome, and the costs incurred at each stage.
- Wrong reasoning: “The expected net values are nearly equal, so either choice is equally well supported.”
- Correction: A narrow difference signals that assumptions may determine the ranking. Show thresholds and uncertainty, then decide whether the evidence is adequate for a choice or whether a different decision criterion is needed.
Check Your Understanding
Use the stated stage structure in each question. Solutions are included below the questions so the calculations can be checked.
- A hypothetical program has \(p_T=0.80\), \(p_R=0.60\), \(V=\$500\) million, \(C_0=\$50\) million, and \(C_1=\$100\) million. What is its overall success probability and expected net value?
- For the program in Question 1, what is the maximum planned spend? Would it satisfy a maximum authorization cap of \(\$125\) million?
- Why is it generally incorrect to calculate expected development cost as \(C_0+C_1\) when \(C_1\) is incurred only after technical success?
- If two prediction scenarios have different technical and conditional regulatory success probabilities, should the scenario-average joint success probability generally be calculated by multiplying the separately averaged probabilities? Explain.
Solutions. (1) Overall success probability is \(0.80(0.60)=0.48\). Expected value contribution is \(0.48(\$500)=\$240\) million; expected cost is \(\$50+0.80(\$100)=\$130\) million; expected net value is \(\$240-\$130=\$110\) million. (2) Maximum planned spend is \(\$50+\$100=\$150\) million, so it exceeds the \(\$125\) million cap, even though expected spending is \(\$130\) million. (3) Adding both costs without weighting assumes \(C_1\) is certain to be incurred. Since it occurs only after technical success, its expected contribution is \(p_TC_1\). (4) No, not in general. The scenario-average joint probability is the weighted average of \(p_Tp_R\) within each scenario; it need not equal the product of the separately weighted average probabilities, especially when the predictions co-vary across scenarios.