Stochastic One-Way Sensitivity Analysis Christopher McCabe1, Mike Paulden2, Isaac Awotwe3, Andrew Sutton1, Peter Hall4

1Institute of Health Economics, Alberta Canada 2Department of Emergency Medicine, University of Alberta, Canada 3School of Public Health, University of Alberta 4Department of Oncology, University of Edinburgh, United Kingdom Introduction •Using decision analytic modelling as part of cost effectiveness analysis allows us to: •Facilitate use of multiple sources of data •Go beyond scope of single-clinical trial in terms of: •Patient group •Interventions •Time horizon Introduction •Need to consider uncertainty in parameter values, how these impact on conclusions drawn from a modelling analysis

•Sensitivity analysis: •is the process of varying model input values and recording the impact of those changes on the model outputs

•A deterministic one-way sensitivity analysis - varies the value of the parameter of interest whilst holding all other parameters constant at their expected value. 1-Way Sensitivity Analysis Tornado Diagram

-60000 -40000 -20000 0 20000 40000 60000 80000 100000 120000

Loco-regional recurrence Distant recurrence Mortality after distant recurrence Cost of Treatment Adverse Event on Chemotherapy Utility in Remission Utility in distant recurrent Cost in remission Cost of surgery Peri-surgical utility Issues with this approach: •Probability that parameter takes extreme values not considered •Correlation between parameters also not considered Stochastic One-Way Sensitivity Analysis • The analysis of the impact of varying the value of one parameter on the expected cost effectiveness that: – incorporates the probability that the parameter will take that value; – and – respects the correlation between that parameter and other parameters in the model Stochastic one-way sensitivity analysis Calculating SOWSA

1. Take 1st centile of distribution describing parameter of interest (Outer-loop Value) 2. Hold the parameter constant at that value 3. Run stochastic model analysis multiple times 4. Record model outputs 5. Repeat 1-4 for remaining centiles (2-99) Stochastic One-Way Sensitivity Analysis Stochastic One-Way Sensitivity Analysis Stochastic One-Way Sensitivity Analysis • The focus is on expected values of the model outputs. – ICER conditional upon the selected value of the SOWSA parameter Repeat Until… Stochastic one-way sensitivity analysis - Results

• SOWSA produces the Expected Incremental Cost Effectiveness Ratio conditional upon the parameter of interest taking a specific value; (Conditional ICER) • Comparing this to Lambda allows the calculation of the Net Monetary Benefit (Conditional NMB)

• The probability distribution for the parameter provides information on probability that any specific value will be observed.

• Combining these two pieces of information provides a credible range for the Conditional NMB that can be plotted as a Tornado Diagram. SOWSA Tornado Diagram: 99% credible range for ICERs by parameter Stochastic one-way sensitivity analysis - Results

• For each centile of the input parameter distribution the SWOSA analysis provides the conditional ICER or conditional Net Monetary Benefit. • We can plot a line graph of the centiles of the input distribution against the Conditional Net Monetary Benefit

• From the SOWSA Line Graph a decision maker can: • Identify whether there are any values for a specific parameter that will change the Expected Net Monetary Benefit from positive to negative, or vice versa; and • The probability that any of those values will be observed. SOWSA Line Graph Conclusion • Traditional one-way deterministic sensitivity analysis: • Does not consider the likelihood that a parameter will take a specific value within a range – Conclusions may be drawn based on very unlikely parameter values • Does not allow for possibility that parameters may be correlated • Stochastic one-way sensitivity analysis • Incorporates probability that parameter will take specific value • Allows for correlation between parameters