Two Way Sensitivity Analysis

Two-way sensitivity analysis is a technique used in economic evaluation to assess the robustness of the overall result (typically from a model-based analysis) when varying the values of two key input variables (parameters) simultaneously. This method is particularly useful for understanding the combined impact of correlated parameters on the model’s outcome.

Key aspects of two-way sensitivity analysis include:

– Simultaneous Variation: Unlike univariate sensitivity analysis, which varies one parameter at a time, two-way sensitivity analysis simultaneously varies two parameters across their plausible ranges. This helps to explore the interaction between the two variables and their combined effect on the model outcome.

– Correlation of Parameters: This method is especially valuable when the two parameters being tested are correlated. For example, in cancer therapy, the hazard ratios for progression-free survival and overall survival are often related. Varying these parameters independently might provide a misleading view, whereas two-way sensitivity analysis can capture their interdependence.

– Grid or Matrix Representation: The results are typically displayed in a grid or matrix format, where each cell represents the outcome of the model (e.g., incremental cost-effectiveness ratio, ICER) for a specific combination of values for the two parameters. This visual representation helps in identifying regions of the parameter space where the model outcome changes significantly.

– Decision-Making Insights: By revealing how the model’s results are affected by simultaneous changes in two parameters, this analysis provides deeper insights into the robustness and reliability of the economic evaluation. It helps decision-makers understand the potential variability in outcomes and prioritize areas for further data collection or research.


Consider an economic model evaluating the cost-effectiveness of a new cancer treatment. Two key parameters might be the hazard ratio for progression-free survival and the hazard ratio for overall survival. In a two-way sensitivity analysis, both parameters are varied simultaneously across their plausible ranges (e.g., 0.5 to 1.5 for hazard ratios). The resulting ICERs are plotted in a matrix, showing how different combinations of these hazard ratios impact the cost-effectiveness of the treatment.

Steps to Conduct Two-Way Sensitivity Analysis:

  1. Identify Key Parameters: Select two parameters that are likely to have a significant impact on the model outcome and may be correlated.
  2. Define Ranges: Determine the plausible range for each parameter based on available data or expert opinion.
  3. Simulate Outcomes: Run the model for each combination of parameter values within the defined ranges.
  4. Visualize Results: Plot the outcomes in a grid or matrix format to visualize the impact of varying the two parameters simultaneously.
  5. Interpret Findings: Analyze the results to identify areas of high sensitivity and assess the robustness of the model’s conclusions.

Two-way sensitivity analysis enhances the understanding of the interactions between key parameters in economic evaluations, providing a more comprehensive view of uncertainty and aiding in more informed decision-making.