Sensitivity Analysis

KISS Principle: Change one parameter in the model, keep everything else constant, and observe how the model outputs change.
Parameter on x-axis, output of interest on y-axis.
Change parameter, run model, record result, repeat.
Parameter change on the horizontal (x-axis).
Model output on the vertical (y-axis).
Consistent with statistical models where X is the independent variable and Y is the dependent variable.
Example: Markov Model
- Change relative risk of moving between states.
- Observe changes in average costs.
- Recalculate ICER (Incremental Cost-Effectiveness Ratio) based on those changes.
Excel can be used; a macro can be used; but Monte Carlo simulations are preferred.
- Macros: Recorded set of keystrokes in Excel (less preferred method).
- Monte Carlo Simulation: Change one variable, observe what happens; repeat multiple times. Change input, note changes, and plot them.

Graphical representation of one-way sensitivity analysis results.
Helps identify parameters that most influence the outcome.
- Wider parts of the diagram indicate parameters with a significant impact.
- Narrow parts suggest parameters with less influence.
Not as important to include the narrow parts but needs to be included to not bias the output.
Elements of Tornado Diagram
- Drug price for combined therapy.
- Relative risk of progressing through different stages.
- Drug price for monotherapy.
Combined therapy price has a more significant impact if its distribution is wider.
Creating a Tornado Diagram
- Start with data, including the base case (most likely estimate).
- Determine the lowest and highest expected outcomes.
- Repeat for all parameters.
- Base case is the best estimate (baseline value).
- Determine the range for each parameter, possibly using pharmaceutical distributors, hospitals, clinics, meta-analysis, literary values, and confidence intervals.
- Calculate ICER for the lower and upper bounds of each parameter.
- The difference between the ICERs gives the range.
- Plot lower and upper bounds to form the diagram; the range is represented by a bar.

Centered on the base-case ICER (e.g., $11,500$ ).
A vertical line is drawn at the base-case outcome.
The drug price for the combination therapy is the most influential variable if it has the widest range.
The tornado diagram is essentially a bar char.

Changing two variables at the same time.
Communication of results becomes challenging due to multiple variations.
- E.g., Changing relative risk and cost of monotherapy, cost of monotherapy and combined therapy.

Changing several parameters simultaneously.
Creating different combinations of parameters in the model.
- Example: Reduce the cost of the combo medication by 25% and change the relative risk.
Record results and reset parameters for new scenarios.

Changing multiple variables simultaneously (or even all variables).
Can be performed using a second-order Markov simulation.
Probability Distributions
- Instead of a range, assign a probability distribution to each value.
- E.g., normal or binomial distribution to a parameter.
Normal distribution parameters: mean and variance.
Rare Approach: Assigning probability distributions that can take many different possible values to infinity.
Generating Random Values
- Use statistical software or Excel to generate random values based on the assigned probability distribution.
- Determine the distribution for each variable. Let Excel generate a sample of possible values randomly, subject to the specified probability distribution, mean, and variance/standard deviation.
- $(\text{Mean})$ and $(\text{Variance})$ are parameters to control the probability distribution.