Choosing Plausible Scenario Bounds

Why Scenario Bounds Need a Defensible Basis

Scenario analysis asks how a decision-relevant result changes under alternative assumptions. The usefulness of that analysis depends on the alternatives chosen. Bounds that are too narrow can conceal a plausible change in the decision; bounds that are too broad can make a decision appear fragile because of cases that are not credible for the program. A range is not defensible simply because it is wide, symmetrical around a base case, or easy to explain.

The earlier material on scenario analysis for alternative development assumptions establishes the use of coherent alternative assumptions to explore decision consequences. Here the focus is how to select the lower and upper values of an uncertain input, explain why they are plausible, and check what conclusions those bounds support. A scenario bound describes an assumption to examine; it does not, by itself, say how likely that assumption is.

Build Bounds From Evidence and Context

A defensible range starts with a precisely defined input. State what is being varied, its units, the population and setting to which it applies, and the decision timeframe. For example, “monthly enrollment rate” is incomplete if it does not specify the type of sites, eligible population, and whether the rate means screened, randomized, or treated participants. Bounds selected for one quantity may not transfer to another merely because their labels sound similar.

Use evidence that is relevant to the planned use. Sources may include program data, comparable trials, published studies, model validation results, and expert judgment. Relevance depends on more than numerical similarity: population, treatment, endpoint, study design, calendar period, and operational setting can all affect whether an observed value supports a bound. Record those similarities and differences rather than treating all available values as interchangeable.

When data are available, inspect their range and distribution, but do not mechanically set the bounds to the smallest and largest observed values. A single unusual observation may not represent a plausible future scenario; conversely, a small data set may not contain a value that is quite plausible in the target setting. Quantiles can help summarize data, but a selected percentile range is not a guarantee that future values lie within it. It also does not become a confidence interval just because it has two endpoints.

Literature can provide a useful external reference, especially where program data are sparse. Check whether the reported estimate measures the same quantity and whether the study population and methods are sufficiently comparable. If differences require adjustment, state the adjustment and its rationale. Expert judgment can fill gaps, but it should be elicited transparently: identify the experts’ relevant experience, the question asked, the evidence they considered, and whether their judgments represent a central estimate, a plausible lower case, or an upper case.

Bounds should also describe coherent scenarios. If several inputs change together, do not pair individually extreme values automatically when that combination contradicts clinical or operational knowledge. For example, a low screening rate combined with unusually rapid enrollment after screening may require a specific explanation. Documented scenarios make such assumptions visible; unexplained combinations can produce consequences that are mathematically possible but not credible.

Check What the Bounds Do to a Decision

Bounds matter because the decision rule may change across the selected range. A useful check is to calculate the consequence at both endpoints and ask whether those outcomes lead to different actions, different levels of concern, or the same conclusion. If an endpoint changes the action, investigate whether it is supported by evidence and whether it represents a coherent scenario. Do not move a bound merely to obtain a preferred decision.

The following simple calculation illustrates why a decision threshold is useful when assessing bounds. Suppose a hypothetical program has a benefit of \(B\) million dollars if successful, an estimated probability of success \(p\), and a development cost \(C\) million dollars regardless of success. Under this simplified expected-net-value rule, the program proceeds when \(V(p)=pB-C>0\). Setting the value to zero gives the break-even probability:

This result follows because \(pB-C>0\) if and only if \(p>C/B\), given \(B>0\). It is a decision threshold within the simplified model, not a universal development rule. The calculation assumes that the stated benefit and cost are appropriate, that the probability estimate is the relevant success probability, and that no other decision consequences need to be included.

Diagnose Bounds That Are Too Narrow or Too Broad

A range can be too narrow when it reflects only measurement precision, a convenient central estimate, or a limited set of observations that omit plausible differences in setting. Warning signs include a decision-changing assumption lying just outside a bound, substantial variation among relevant studies that the bounds ignore, or experts describing credible cases beyond the stated range. Narrow bounds can create apparent decision stability by excluding the very uncertainty that could alter the conclusion.

A range can be too broad when it combines values from dissimilar populations, treats remote possibilities as routine scenarios, or uses extremes without evidence that they are relevant. Such bounds may make the decision look unstable even when the credible cases support the same action. Very broad bounds also reduce interpretability: stakeholders may be unable to tell which evidence or assumptions produced the endpoint.

A practical diagnostic is to trace each endpoint back to its source and then forward to its consequence. Ask: What observation, publication, or expert judgment supports this value? What differences from the target setting matter? Is the scenario internally coherent? What decision result follows at the endpoint? If an endpoint has no traceable rationale, or the rationale does not fit the target context, revise it or label it explicitly as a stress test rather than a plausible bound.

Choose the Right Kind of Range

Scenario bounds, statistical intervals, and probability distributions answer different questions. A confidence interval quantifies uncertainty about a parameter under a specified statistical procedure and its assumptions. A scenario range identifies selected alternative input values for decision exploration. A probability distribution assigns probabilities across possible values and can support probabilistic calculations, if that distribution is justified. One should not be substituted for another without explanation.

A single base case is easier to communicate, but it hides how results might change under alternatives. A broad stress test can reveal consequences under severe conditions, but it may include cases judged implausible. Expert judgment is often necessary when evidence is limited, but unsupported judgment should not be disguised as data. These approaches can complement one another when each is labeled clearly: identify the base case, the evidence-supported scenario bounds, and any separate stress-test values.

Bound selection does not remove uncertainty. It makes a chosen set of alternatives explicit. The range remains limited by the evidence available, the quality of comparisons, and the assumptions used to translate those sources into the target decision context. If the evidence cannot support precise endpoints, say so; precision in the written values does not create precision in the underlying knowledge.

Common Mistake and Practical Record

Wrong reasoning: “The most extreme values found in the literature are the correct lower and upper bounds, so any result inside them is plausible.” This confuses observed extremes with context-specific plausible alternatives. Literature studies may differ in population, design, measurement, and relevance; an extreme may be an outlier or may describe a setting unlike the program.

Correction: Evaluate each candidate value for relevance, not just extremity. State why it represents a plausible lower or upper scenario for the target setting, what evidence supports it, and what limitations remain. If an extreme is retained only to test a severe case, label it a stress test rather than an ordinary plausible bound.

For each bounded input, a concise record should name the input and units; give the base case and lower and upper values; identify data, literature, or expert sources; explain adjustments and applicability; describe assumptions needed for a coherent scenario; and state whether the bounds cross a decision-relevant threshold. This record allows reviewers to challenge the evidence and the scope of the range without confusing scenario choice with probability.