Probabilistic Sensitivity Analysis

Steps for Probabilistic Sensitivity Analysis:

  • Step 1: Assign Probability Distributions:

    • Assign a probability distribution to each parameter in your model.

    • Spreadsheets will be provided to assist in this task.

  • Step 2: Draw Random Numbers:

    • Use a computer to draw a random number from each assigned distribution.

  • Step 3: Model Rerunning:

    • Input the random numbers into your model.

    • Rerun the model to obtain the output.

  • Step 4: ICER Calculation:

    • Calculate the Incremental Cost-Effectiveness Ratio (ICER) for the event before the intervention.

    • The ICER can be calculated for any outcome, but the primary focus is on the ICER.

  • Step 5: Plotting:

    • Save the calculated ICER.

    • Plot the ICER values on a graph.

    • Dependent variable (e.g., cost) on the Y-axis, independent variable (e.g., effect) on the X-axis.

    • Repeat the procedure multiple times.

  • Step 6: Cost-Effectiveness Plane:

    • Plot all ICERs on the cost-effectiveness plane (as discussed previously).

  • Step 7: Statistical Analysis:

    • Calculate statistics such as probabilities or frequency distributions.

    • Determine the percentage of times the ICER falls below or above an acceptance threshold.

    • Assess the frequency of occurrences where the ICER plots in an undesirable quadrant.

Cloud Diagram Interpretation:

  • The result is a cloud diagram, which visually represents the uncertainty in the model.

  • A larger cloud indicates greater uncertainty.

  • A smaller, denser cloud indicates greater reliability or certainty in the outputs.

Probability Distributions:

  • Normal Distribution:

    • While commonly used in statistics, it is often unsuitable for cost-effectiveness analysis.

    • Costs cannot be normally distributed because they must be greater than zero and tend to be right-skewed.

    • Prices for inputs may sometimes be normally distributed, but negative prices are unlikely.

    • Utilities and probabilities (ranging from 0% to 100%) cannot be normally distributed either.

  • Common Distributions:

    • Gamma distribution

    • Beta distribution

    • Log-normal distribution

    • Poisson distributions

  • Matching Distribution to Parameter:

    • Crucially, the selected distribution must align with the characteristics of the parameter being modeled.

    • The use of inappropriate distributions will be challenged (e.g., in a thesis).

    • Normal distributions may not be suitable for integers like the number of tests or doses.

Graphical Examples of Distributions:

  • Normal Distribution:

    • Bell-shaped curve with clear peak and tails.

  • Gamma Distribution:

    • Defined by shape and scale parameters.

    • Tends to lean to the left, with higher frequency outcomes toward the left.

  • Beta Distribution:

    • Resembles a normal distribution but leans more toward the left.

  • Log-Normal Distribution:

    • Defined by mean and standard deviation.

Applying Distributions:

  • Gamma Distribution:

    • Parameters: shape and scale.

    • Scale: ranges from greater than zero to infinity.

    • Use case: simulating costs because costs are positive and tend to skew.

  • Beta Distribution:

    • Parameters: aimed at shape.

    • Support values: 0 to 1.

    • Use case: simulating measures of utility and probabilities.

    • Bounded between zero and one.

  • Log-Normal Distribution:

    • Exponent of a normal distribution used for very large numbers.

    • Log transformation reduces the scale of numbers and brings widely distributed values closer together.

  • Domain (or Support):

    • The range of values for which the distribution is defined.

    • Support = domain = range of values.

Simulation Implementation:

  • Software:

    • Statistical packages like SAS or Stata.

    • Excel (with additional steps).

  • Excel:

    • Requires calculating a random value from each distribution in multiple steps.

    • For gamma and beta distributions, using a statistical package is recommended or seeking assistance with the two-step process in Excel.

  • Random Number Generators:

    • Most software includes a random number generator.

  • Inverse Transform Method:

    • Used to simulate values from continuous distributions.