Probabilistic Sensitivity Analysis (PSA)

Probabilistic sensitivity analysis is a method used in health economic evaluations that assigns probability distributions to uncertain model input parameters and runs the model many times (typically thousands of iterations via Monte Carlo simulation) to characterize the parameter uncertainty surrounding the cost effectiveness estimate. Rather than testing one parameter at a time, PSA simultaneously varies all uncertain inputs, producing a distribution of possible outcomes.

Health economic models rely on numerous input parameters, including treatment efficacy, costs, transition probabilities, and utility values, each of which carries uncertainty. Decision makers need to understand not just the point estimate of cost effectiveness but also the probability that the intervention is cost effective at different willingness to pay thresholds. PSA provides this information, enabling more informed resource allocation decisions under uncertainty. Health technology assessment agencies, including NICE in England and Canada's Drug Agency (formerly CADTH), expect PSA as part of economic evaluation submissions.

The PSA process begins by specifying a probability distribution for each uncertain input parameter. Common choices include beta distributions for probabilities and for utilities that stay between zero and one, gamma or log normal distributions for costs and relative risks (bounded at zero), and normal distributions for parameters with symmetric uncertainty. The choice of distribution should reflect the nature of the parameter and the available evidence.

Once distributions are specified, Monte Carlo simulation draws a random value from each parameter's distribution simultaneously, producing one complete set of inputs. The economic model is then run with these inputs to generate a single pair of incremental cost and incremental effectiveness values. This process is repeated thousands of times (typically 1,000 to 10,000 iterations) to build up a joint distribution of cost effectiveness results.

The results of PSA are typically presented in three ways. The cost effectiveness plane is a scatter plot of the incremental cost and incremental effectiveness pairs from each simulation run, showing the spread of uncertainty. The cost effectiveness acceptability curve (CEAC) plots the probability that the intervention is cost effective as a function of the willingness to pay threshold, providing a decision relevant summary. The expected value of perfect information (EVPI), derived from the PSA results, quantifies the expected benefit of eliminating all parameter uncertainty, informing decisions about whether further research is worthwhile.

PSA requires careful parameterization, and the quality of the analysis depends on the appropriateness of the chosen distributions and the completeness of the uncertainty characterization. Parameters that are assumed to be known with certainty (fixed parameters) are not varied in the PSA and should be justified.

Conduct PSA in any decision analytic economic evaluation where input parameters carry uncertainty, which is virtually all economic models. Many health technology assessment agencies, including NICE and Canada's Drug Agency, expect it in submissions supporting reimbursement or coverage decisions. PSA is particularly informative when the base case result is close to the willingness to pay threshold, as it quantifies the probability that the decision would change under different parameter values. Deterministic sensitivity analysis (varying one parameter at a time) can complement PSA but does not replace it, as it fails to capture the combined effect of simultaneous parameter uncertainty.

A common error is specifying parameter distributions without adequate justification, choosing distributions arbitrarily rather than based on the parameter's characteristics and available data. Another mistake is using too few Monte Carlo iterations, producing a PSA that has not converged and yields unstable results. Researchers sometimes treat the PSA as if it captured all uncertainty, when a standard PSA covers parameter uncertainty only; structural uncertainty (such as model structure choices) needs separate scenario analyses, and ignoring it underestimates total decision uncertainty. Finally, presenting PSA results without a cost effectiveness acceptability curve makes it difficult for decision makers to interpret the findings at their relevant willingness to pay threshold.

In a hypothetical example, a health economic model compares a new oral anticoagulant against warfarin for stroke prevention in atrial fibrillation. The model includes 32 uncertain parameters with specified distributions. A PSA with 5,000 Monte Carlo iterations produces a scatter plot showing 62% of iterations in the southeast quadrant (lower cost, greater effectiveness) and 28% in the northeast quadrant (higher cost, greater effectiveness). The cost effectiveness acceptability curve shows a 73% probability that the new anticoagulant is cost effective at a willingness to pay threshold of $50,000 per QALY and 81% at $100,000 per QALY.