One-Way Sensitivity Analysis of Decision Inputs

Why Vary One Input at a Time?

A development decision may depend on uncertain inputs such as treatment effect, adverse-event risk, or treatment cost. A reference-case calculation gives a result for one chosen set of values, but it does not show how sensitive that result is to each input. One-way sensitivity analysis addresses this question by changing one input across selected values while keeping the other inputs fixed, then recalculating the decision output.

For example, a new treatment may have positive expected value under the reference assumptions. If a modestly smaller treatment effect would make its value negative, the decision depends strongly on that effect estimate. If the decision remains the same over a plausible range of effects, it is less sensitive to that input over that range. Neither finding establishes which input value is true; the analysis describes how the decision model responds to specified inputs.

Definition: One-way sensitivity analysis evaluates the effect of varying one decision input at a time over a specified range, while holding all other model inputs fixed. The model output is recalculated at each value. In a two-option decision, a decision output such as incremental net monetary benefit can show whether the preferred option changes.

A Decision Output for the Analysis

Consider a choice between a new treatment and standard care. Let $\Delta C$ be the new treatment's incremental cost, measured as new-treatment cost minus standard-care cost. Let $\Delta Q$ be its incremental health benefit, in quality-adjusted life-years (QALYs), and let $\lambda$ be the decision maker's value per QALY, in dollars per QALY. The incremental net monetary benefit (incremental NMB) is:

\Delta \mathrm{NMB} = \lambda \Delta Q - \Delta C

If $\Delta \mathrm{NMB} > 0$, the new treatment has greater net monetary benefit than standard care under the stated inputs and assumptions. If $\Delta \mathrm{NMB} < 0$, standard care has greater net monetary benefit. A value of zero indicates equal net monetary benefit in this comparison. This is a comparison of the options under the model, not a claim that either option is clinically best under every relevant criterion.

A safety input can also be included. Suppose $\Delta r$ is the excess probability of an adverse event with the new treatment, expressed as a proportion; $L$ is the QALY loss per event; and $C_{\mathrm{AE}}$ is the direct cost per event. Under the simplifying assumption that the expected safety burden is the excess event probability multiplied by the loss and cost per event, the decision output is:

\Delta \mathrm{NMB} = \lambda(\Delta Q_{\mathrm{benefit}} - \Delta r L) -\Delta C -\Delta r C_{\mathrm{AE}}

Here, $\Delta Q_{\mathrm{benefit}}$ is the incremental QALY benefit before this safety penalty. This expression treats the safety penalty as proportional to the excess event probability; a more detailed model may represent event severity, timing, duration, or multiple event types explicitly. The formula and its assumptions must be stated before interpreting the sensitivity results.

Set Up the One-Way Analysis

Begin with a reference case: specify the values used for all inputs and calculate the decision output. Then select one input, choose alternative values for it, and recalculate the output at each value. The remaining inputs do not change during that run. Plausible bounds should reflect the intended decision context and the evidence or assumptions supporting the model; selecting very wide bounds solely to produce a decision reversal can mislead.

State the decision and output.
Name the options being compared and the quantity used to rank them, such as incremental NMB.

Calculate the reference case.
Record the input values, units, and resulting output so the comparison has a clear anchor.

Choose one input and its values.
Vary that input over a justified range; keep the remaining model inputs at their reference-case values.

Recalculate and interpret.
For each selected value, report the output and whether the preferred option changes. State the range examined.

The method does not require the model to be linear. At each selected input value, use the model's actual equation or calculation procedure. A straight-line interpolation is justified only when the model supports it. The analysis is conditional: it asks what the model implies if the varied input takes a specified value and the other inputs remain as stated.

Worked Example: Varying Treatment Benefit

Hypothetical decision. A development team compares a new treatment with standard care at $\lambda = \$100{,}000$ per QALY. The incremental cost is $\Delta C = \$6{,}000$. For this example, the only input varied is the incremental QALY benefit, $\Delta Q$, and the model is $\Delta \mathrm{NMB} = \lambda\Delta Q - \Delta C$.

At the reference value $\Delta Q = 0.08$ QALY, the calculation is:

\Delta \mathrm{NMB} = (\$100{,}000/\mathrm{QALY})(0.08\ \mathrm{QALY}) -\$6{,}000 = \$8{,}000-\$6{,}000 = \$2{,}000

The new treatment has greater net monetary benefit by \$2,000 under the reference inputs. Now vary only $\Delta Q$; keep $\lambda$ and $\Delta C$ fixed.

Incremental benefit $\Delta Q$ (QALY)	Calculation	Incremental NMB	Preferred option by NMB
0.04	\$100,000 × 0.04 − \$6,000	−\$2,000	Standard care
0.08	\$100,000 × 0.08 − \$6,000	\$2,000	New treatment
0.10	\$100,000 × 0.10 − \$6,000	\$4,000	New treatment

Within the displayed values, the preferred option changes between 0.04 and 0.08 QALY. The result depends on the benefit input over this range. This calculation does not estimate the probability that the true benefit lies at any row in the table.

Worked Example: Varying Excess Adverse-Event Risk

Hypothetical decision. A new treatment has a benefit before safety penalties of $\Delta Q_{\mathrm{benefit}}=0.08$ QALY and an incremental cost of $\Delta C=\$6{,}500$. Set $\lambda=\$100{,}000$ per QALY, an event-related QALY loss of $L=0.15$ QALY per event, and a direct event cost of $C_{\mathrm{AE}}=\$2{,}000$ per event. Vary only the excess event probability $\Delta r$. For this calculation, assume the expected burden is proportional to $\Delta r$, as in the stated incremental NMB formula.

At the reference excess risk $\Delta r=0.03$, the expected safety penalty is $\$17{,}000$ per unit probability multiplied by 0.03. The coefficient combines the monetary value of event-related health loss and direct cost:

\lambda L + C_{\mathrm{AE}} = (\$100{,}000/\mathrm{QALY})(0.15\ \mathrm{QALY}) +\$2{,}000 = \$15{,}000+\$2{,}000 = \$17{,}000

Thus, at $\Delta r=0.03$:

\Delta \mathrm{NMB} = (\$100{,}000/\mathrm{QALY})(0.08\ \mathrm{QALY}) -\$6{,}500 -(0.03)(\$17{,}000) = \$8{,}000-\$6{,}500-\$510 = \$990

Now vary only $\Delta r$, keeping the benefit, cost, and event consequences fixed.

Excess event probability $\Delta r$	Expected safety penalty	Incremental NMB	Preferred option by NMB
0.02	0.02 × \$17,000 = \$340	\$8,000 − \$6,500 − \$340 = \$1,160	New treatment
0.03	0.03 × \$17,000 = \$510	\$8,000 − \$6,500 − \$510 = \$990	New treatment
0.10	0.10 × \$17,000 = \$1,700	\$8,000 − \$6,500 − \$1,700 = −\$200	Standard care

Under this model, the preferred option changes across the examined range: the new treatment has higher NMB at risks of 0.02 and 0.03, whereas standard care has higher NMB at 0.10. The table is conditional on the assumed event burden and does not account for uncertainty in the other inputs.

Worked Example: Varying Incremental Cost

Hypothetical decision. Let the treatment benefit be $\Delta Q_{\mathrm{benefit}}=0.07$ QALY, the excess adverse-event probability be $\Delta r=0.03$, the event-related QALY loss be $L=0.15$ QALY, and the direct event cost be $C_{\mathrm{AE}}=\$2{,}000$. Set $\lambda=\$100{,}000$ per QALY. This time vary only the incremental treatment cost, $\Delta C$.

The value of the treatment benefit before incremental treatment cost is:

\lambda(\Delta Q_{\mathrm{benefit}}-\Delta rL)-\Delta rC_{\mathrm{AE}} = \$100{,}000(0.07-0.03\times0.15) -0.03\times\$2{,}000 = \$100{,}000(0.0655)-\$60 = \$6{,}490

At the reference incremental cost of $\$6{,}000$, the incremental NMB is $\$6{,}490-\$6{,}000=\$490$, favoring the new treatment by NMB. Keeping all other inputs fixed gives:

Incremental cost $\Delta C$	Calculation	Incremental NMB	Preferred option by NMB
\$5,000	\$6,490 − \$5,000	\$1,490	New treatment
\$6,000	\$6,490 − \$6,000	\$490	New treatment
\$7,000	\$6,490 − \$7,000	−\$510	Standard care

The preferred option changes across the selected cost values. This is not a cost-effectiveness conclusion independent of the chosen QALY value, safety assumptions, and decision context; those inputs were held fixed for this one-way calculation.

What the Results Do and Do Not Show

A one-way analysis is useful for identifying which individual inputs can alter a decision across their specified ranges. It can also make the implications of an assumption transparent: a reader can see the input value, the fixed assumptions, and the recalculated decision output. Report the reference case, the varied input and units, the values examined, and the output at each value. A statement such as “the decision is robust” needs qualification: it can mean only that the preferred option did not change over the particular range examined, under the assumptions held fixed.

The analysis does not assign probabilities to the selected values, quantify the chance of each decision, or show the effect of changing several uncertain inputs together. Those questions require other analyses. It also does not automatically reflect dependence among inputs. For instance, if a change in treatment effect would normally coincide with a change in dose or safety risk, varying the effect alone while leaving those linked inputs unchanged may describe an implausible combination. State this limitation rather than interpreting the result as a complete uncertainty assessment.

One-way sensitivity analysis is distinct from a multi-assumption scenario comparison: a scenario can change several assumptions together, whereas a one-way analysis deliberately changes just one. It is also distinct from evaluating a distribution of possible input values. The latter would incorporate uncertainty across inputs rather than only showing conditional results at selected values.

Diagnostics and Common Pitfalls

Check the reference calculation. Recalculate the reference output directly from the stated formula and units. A sign error in incremental cost or treatment effect can reverse the preferred option.
Verify that only one input changes. If several inputs differ between rows, the output difference cannot be attributed to the named input alone.
Check units and scales. A probability of 0.03 is 3%, not 0.03%; a cost must be in the same currency and time basis as the other monetary quantities.
Inspect the selected range. Values outside a clinically or operationally plausible range can create dramatic but irrelevant changes. Values too narrowly chosen may conceal meaningful sensitivity.
Do not mistake a decision change for evidence about the input. A reversal shows what the model implies at the specified values, not that the input is likely to cross that range.

Common mistake: “The new treatment is preferred at the reference value, so the decision is robust.” This does not follow from a single calculation. Robustness over an input range requires recalculating the decision across that range and confirming that the preferred option remains unchanged. Conversely, a reversal over an extreme or implausible range does not by itself undermine the decision in the relevant context.

Check Your Understanding

Answer each question using the stated decision model and assumptions.

A new treatment has $\Delta Q=0.06$ QALY, $\Delta C=\$5{,}000$, and $\lambda=\$100{,}000$ per QALY. Calculate incremental NMB and state the preferred option by NMB.
In a one-way analysis, treatment benefit is varied while cost is fixed. What can be concluded if incremental NMB is positive at every selected benefit value?
For $\Delta Q_{\mathrm{benefit}}=0.08$ QALY, $\Delta C=\$6{,}500$, $\lambda=\$100{,}000$ per QALY, and an event penalty coefficient of $\$17{,}000$, calculate incremental NMB at $\Delta r=0.05$.
A table compares a low-cost, low-benefit assumption with a high-cost, high-benefit assumption. Is it a one-way sensitivity analysis? Explain.

Solutions. (1) $\Delta\mathrm{NMB}=(\$100{,}000/\mathrm{QALY})(0.06\ \mathrm{QALY})-\$5{,}000=\$6{,}000-\$5{,}000=\$1{,}000$. The new treatment is preferred by NMB under these inputs. (2) The new treatment has higher NMB at all selected benefit values, conditional on the fixed inputs and the examined range. This does not establish that the benefit values are likely or that the decision is robust to other inputs. (3) $\Delta\mathrm{NMB}=\$8{,}000-\$6{,}500-(0.05)(\$17{,}000)=\$8{,}000-\$6{,}500-\$850=\$650$. The new treatment is preferred by NMB. (4) No. Both benefit and cost change, so the output difference cannot be attributed to one input alone; this is a comparison of combined assumptions.