**Uncertainty and Sensitivity Analyses of a Decision
Analytic Model for Post-Eradication Polio Risk Management**

by Radboud J. Duintjer Tebbens, Mark A. Pallansch, Olen M.Kew, Roland W. Sutter,
R. Bruce Aylward, Margaret Watkins, Howard E. Gary, James P. Alexander, Hamid
Jafari, Stephen L. Cochi, and Kimberly M. Thompson, *Risk Analysis* 2008;28(4):855-876. PDF

Technical appendix

**Answers to frequently asked questions**

What are the study’s main findings?

What are the study’s main recommendations?

How does the model characterize uncertainty?

How does the analysis determine importance ranking of uncertain model inputs?

Background on polio

**What are the study’s main findings?**

- Policy implications from a dynamic probabilistic model for post-eradication polio risk management policies are relatively robust to stochastic variations, model input uncertainty, and modification of key assumptions.
- Model inputs related to vaccine prices and administration costs represent the main drivers of the uncertainty in incremental net benefit estimates for the main policy comparisons at the global level (i.e., of “no routine” vs. continued OPV with supplemental immunization activities (SIAs) and of IPV vs. continued OPV with SIAs in low- and middle-income countries).
- Among the uncertain model inputs related to outbreaks, the impact of a reduction in SIAs on the frequency of circulating vaccine-derived polioviruses emerges as the most important driver of incremental net benefit comparisons. The transmissibility of polioviruses (R0) and delays in outbreak detection and response represent inputs wtih a potentially major impact on the expected number of cases for individual policy options.
- While the probability of outbreaks rapidly decreases
after OPV cessation, the expected number of cases per year may increase
long after cessation due to substantial reductions in population immunity.

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- Technological advances to reduce the cost of the IPV antigen and/or its delivery could greatly improve the expected net benefits of IPV vs. OPV.
- Future stochastic models of poliovirus transmission may help reduce the uncertainty about continued undetected wild poliovirus circulation after apparent eradication, and may also prove helpful in studying specific outbreak response strategies and the behavior of OPV viruses used for outbreak response after cessation of routine IPV use.
- Further empirical studies on the ability of IPV to stop poliovirus transmission in developing countries may narrow the uncertainty regarding the benefits of IPV and support better decisions related to future use of IPV. Similarly, expert elicitation on modes and intensity of transmission might yield better characterizations of the uncertainty and variability in R0.
- Further research is needed to refine the economic estimates, optimize policy
decisions at a more detailed level, and address remaining open questions.

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- The following influence diagram provides an overview of the model components.
- The model characterizes the uncertainty in most model inputs as triangular or lognormal distributions over uncertainty ranges for cost and risk inputs. For lognormal distributions, we assume maximums of the ranges corresponded to the 99th percentiles.
- We assumed discrete distribution for some inputs (i.e., R0, coverage prior to an outbreak, cVDPV risk case, and heterogeneity in SIA frequency and quality for policies involving continued SIAs) whose values we resampled for every outbreak. To analyze sensitivity to those inputs, we varied the parameters of those distributions.
- The model accounts for some of the global variability that exists in costs and poliovirus transmission by using four World Bank income levels (low, lower-middle, upper-middle, and high), but it does not address variability at a national level. We also assumed independence among uncertain inputs, except for the dependencies implied by stratification by income level.
- Details of the model appear in the technical appendix.

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- We ranked the continuously distributed inputs according to the absolute values of rank correlations between model inputs and outputs, and we also reported product moment correlations and correlation ratios.
- For all other inputs and assumptions, we determined their importance based
on one-way sensitivity analyses and a small design-of-experiments analysis.

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