Allocating Resources Across Indications

Why Allocate Resources Across Indications?

A development asset may have opportunities in several indications, each with a different probability of success, potential value, cost, and timing. The allocation question is not simply which indication has the largest market or the highest probability of success. It is which feasible set of investments produces the greatest incremental value for the development program, given the resources available and the decision-maker’s objectives.

The relevant comparison is made from the current decision point. Costs already incurred are sunk and do not change when choosing among future investments. Forecast future costs and benefits should be expressed on a consistent basis, such as present value in millions of dollars at the decision date. The basic calculations below assume a risk-neutral decision-maker who evaluates expected monetary value, that the stated probabilities and payoffs apply to the actions under consideration, and that there are no unmodelled interactions among indications. Later sections explain why those assumptions matter.

Definition: The incremental expected value of an indication is the expected value of the portfolio after investing in that indication minus the expected value of the portfolio without that investment. In the simple case where success produces an incremental payoff $V_s$, failure produces $V_f$, and the investment costs $C$, the indication’s incremental expected value is $pV_s+(1-p)V_f-C$, where $p$ is the probability of success. All values must use the same currency, valuation date, and scope.

“Success” must be defined for the decision being evaluated: for example, achieving a specified development milestone or reaching a defined commercial outcome. The probability must correspond to that definition and to the proposed investment. If the payoff already incorporates a sequence of clinical, regulatory, and commercial outcomes, do not multiply by those probabilities a second time. Likewise, use an incremental payoff: value attributable to the indication relative to the no-investment alternative, not the total value of an asset that the program already owns.

From an Indication Estimate to an Allocation Decision

For a set of indications with binary invest-or-do-not-invest choices, let $x_i=1$ mean indication $i$ is funded and $x_i=0$ mean it is not. If each investment has cost $C_i$ and incremental expected value $\Delta EV_i$, a basic allocation rule is to choose the feasible combination with the highest total incremental expected value:

\max_{x_1,\ldots,x_k}\ \sum_{i=1}^{k}x_i\Delta EV_i \qquad\text{subject to}\qquad \sum_{i=1}^{k}x_iC_i\leq B,\quad x_i\in\{0,1\}.

Here $B$ is the available budget. This formulation assumes that indication values add: investing in one does not change the payoffs, costs, or success probabilities of another. When this assumption holds, the expected value of the portfolio is the sum of its expected incremental values. The allocation remains a discrete optimization problem: the best set need not be the indication with the highest expected value per dollar.

Expected value per dollar, $\Delta EV_i/C_i$, can be a useful screening measure when investment amounts are comparable or divisible. It is not generally a valid substitute for comparing feasible combinations of indivisible projects. A high ratio can describe a small opportunity that leaves much of the budget unused, while a lower-ratio project may combine with another to create greater total value. The decision-maker should also compare each option with the no-investment baseline: a positive expected value is not enough if it cannot fit within the available resources or if a different feasible portfolio is better.

Worked Example: Comparing Two Indications

Suppose a hypothetical sponsor is considering one investment in either indication A or indication B. All values are present values in millions of dollars at the current decision date. If an indication fails, its incremental payoff is zero. For A, the probability of success is 0.35, success payoff is $180 million, and investment is $40 million. For B, the corresponding values are 0.55, $110 million, and $35 million.

For A, expected value before subtracting investment is $0.35(180)+0.65(0)=63$ million dollars. Therefore:

\Delta EV_A=0.35(180)+0.65(0)-40=23.0\text{ million dollars}.

For B, expected value before subtracting investment is $0.55(110)+0.45(0)=60.5$ million dollars. Thus:

\Delta EV_B=0.55(110)+0.45(0)-35=25.5\text{ million dollars}.

If only one can be funded, B has the greater incremental expected value, by $25.5-23.0=2.5$ million dollars. Its expected value per investment dollar is $25.5/35=0.729$, compared with $23.0/40=0.575$ for A. Both measures favor B in this example, but the feasible portfolio comparison—not the ratio alone—is the allocation criterion when several investments can be combined.

Choosing a Feasible Combination

The following example uses the same kind of present-value calculations for three hypothetical indications. A budget constraint can make the best allocation different from a simple ranking of stand-alone expected values. The calculation requires checking which combinations are feasible, not merely sorting the indications.

Worked Example: Selecting Indications Under a Budget

A sponsor has a budget of $70 million. Three mutually compatible hypothetical projects have these estimates, in millions of dollars: A has cost $40 million and incremental expected value $23 million; B has cost $35 million and incremental expected value $25.5 million; C has cost $30 million and incremental expected value $18 million. Each expected value is already net of the project’s investment cost.

The feasible pairs are A+C, costing $40+30=70$ million dollars, and B+C, costing $35+30=65$ million dollars. Their total incremental expected values are:

\Delta EV_{A+C}=23+18=41\text{ million dollars}, \qquad \Delta EV_{B+C}=25.5+18=43.5\text{ million dollars}.

A+B would cost $40+35=75$ million dollars and is infeasible. The individual projects are feasible, with values of $23 million, $25.5 million, and $18 million; funding none gives zero incremental value. Among the feasible choices, B+C has the highest total expected value, $43.5 million, and leaves $5 million unspent. Spending the entire budget is not required when the remaining amount cannot be used for a feasible investment with greater value.

The result depends on the stated compatibility and additivity assumptions. If B and C compete for the same clinical sites, share a fixed cost, or change each other’s expected payoffs, their joint value cannot be calculated by simply adding the stand-alone values. Such effects must be included in the portfolio calculation.

How the Allocation Changes the Portfolio

For additive monetary payoffs, the expected value of a selected portfolio is the sum of its expected values. This follows from linearity of expectation and does not require independent outcomes. If $Y_i$ is the net incremental monetary value from indication $i$, then:

E\!\left[\sum_{i=1}^{k}x_iY_i\right] =\sum_{i=1}^{k}x_iE[Y_i].

This identity justifies adding indication-level expected values when the outcomes and costs are defined consistently and one indication does not alter another’s value. Dependence between outcomes still matters for the distribution of portfolio results, such as the probability of at least one success or the chance of a large loss. It does not, by itself, change the expected sum when each marginal expected value and the additive-payoff assumption remain unchanged.

Worked Example: Expected Value and Chance of Portfolio Success

Consider funding B and C from the previous example. Assume their success outcomes are independent, with probabilities 0.55 and 0.40, respectively. Success produces incremental payoffs of $110 million for B and $120 million for C; failure produces zero payoff. Their combined investment is $65 million.

The probability of at least one success is one minus the probability that both fail:

P(\text{at least one success}) =1-(1-0.55)(1-0.40) =1-(0.45)(0.60) =0.73.

To check the portfolio’s expected net value directly, enumerate the outcomes. If both succeed, the probability is $0.55(0.40)=0.22$, and the net value is $110+120-65=165$ million dollars. If only B succeeds, the probability is $0.55(0.60)=0.33$, and the net value is $110-65=45$ million dollars. If only C succeeds, the probability is $0.45(0.40)=0.18$, and the net value is $120-65=55$ million dollars. If neither succeeds, the probability is $0.45(0.60)=0.27$, and the net value is $-65$ million dollars.

Weighting these outcomes by their probabilities gives:

E[\text{net portfolio value}] =0.22(165)+0.33(45)+0.18(55)+0.27(-65) =36.3+14.85+9.90-17.55 =43.5\text{ million dollars}.

This agrees with the sum of the indication-level expected values, $25.5+18=43.5$ million dollars. The $43.5 million is the expected net monetary value under the stated assumptions; it is not a promise that the realized portfolio will return that amount. The 0.73 is the probability of at least one success under the independence assumption, not the probability that the portfolio will have positive net value. In this example, a single success still leaves the portfolio with positive net value, but that need not hold for other costs and payoffs.

Assumptions, Diagnostics, and Alternatives

Before ranking indications, check that the calculations answer the same decision question. The probability of success, payoffs, and costs should refer to the proposed actions and the same decision date. Costs should include the relevant future investment needed to realize the modeled payoff, and should exclude sunk costs that cannot be changed by the current choice. When costs or payoffs occur at different times, convert them to a consistent valuation date. Verify that a payoff is not counted both as a commercial value and again as a separately added benefit.

A useful diagnostic in the simple case with zero payoff on failure is the break-even success probability. The investment has positive expected value when $pV_s-C>0$, or equivalently $p>C/V_s$, provided $V_s>0$. For indication A above, the break-even probability is $40/180=0.222$. The assumed probability of 0.35 exceeds that threshold, consistent with its positive expected value. This check can expose a calculation or input that is inconsistent with the stated costs and payoffs; it does not establish that the probability estimate is accurate.

The additive allocation model is not appropriate without modification when indications share infrastructure, compete for patients, alter one another’s development strategy, or have a common fixed cost. In those cases, calculate the incremental value of each candidate portfolio relative to the same baseline, including interaction effects only once. A practical general definition is:

\Delta EV_i(P)=E[U(P\cup\{i\})]-E[U(P)],

where $P$ is the current portfolio and $U$ is the value assigned to its outcomes and costs. If the value of adding an indication depends on which indications are already funded, the marginal value $\Delta EV_i(P)$ can differ across portfolios. The simple sum-of-values rule then requires those interactions to be represented explicitly rather than assumed away.

The main alternative to maximizing expected monetary value is to use a different objective, such as a portfolio criterion that places explicit weight on downside exposure, strategic fit, or a required probability of meeting a program target. Such a criterion may be appropriate, but it is not the same as maximizing expected value and should be stated as part of the decision. Similarly, expected value per dollar is a screening comparison, not a complete allocation method when projects are indivisible, costs are shared, or resources other than money are limiting.

Common pitfall: “Indication A has the highest probability of success, so it should receive the funding.” A high probability alone does not determine expected value: payoff, investment, and feasible alternatives also matter. Compare incremental values on a common basis, then select the best feasible portfolio under the stated objective. Do not add stand-alone values if costs or outcomes overlap.

A final review should ask whether the funding mix is feasible in practice, not just within the monetary budget. Clinical capacity, manufacturing slots, personnel, and timing may impose additional constraints. The expected-value result is only as useful as its inputs and the decision structure: it describes what follows from the stated assumptions, not a guarantee of realized performance.

Check Your Understanding

Answer each question, then compare your work with the solutions.

An indication has a 0.30 probability of success, a $150 million payoff on success, zero payoff on failure, and a $35 million investment. What is its incremental expected value?
Two projects have positive expected values, but their combined investment exceeds the budget. Why is adding their values not a valid recommendation to fund both?
For a project with zero failure payoff, a $48 million investment, and a $160 million success payoff, calculate the break-even success probability.
If indication outcomes are dependent but monetary portfolio payoffs are additive, does dependence alone change the expected total value? Does it change the probability of at least one success?

Solutions. (1) $0.30(150)+0.70(0)-35=10$ million dollars. The project has a positive incremental expected value of $10 million under the stated assumptions. (2) The combination is infeasible under the budget constraint, so it is not an available allocation. Compare feasible sets, including funding only one project or neither, rather than recommending an unaffordable pair. (3) The break-even probability is $48/160=0.300$, or 30.0%; the expected value is positive when the probability is greater than 30.0%. (4) With additive payoffs and unchanged marginal expected values, dependence alone does not change the expected sum. It can change the probability of at least one success because that probability depends on the joint distribution of outcomes.