Uncertainty and Sensitivity Analyses of a Decision
Analytic Model for PostEradication 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):855876
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 posteradication 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 middleincome countries).
 Among the uncertain model inputs related to outbreaks, the impact of a
reduction in SIAs on the frequency of circulating vaccinederived 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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What are the study’s main recommendations?
 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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How does the model characterize uncertainty?
 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, lowermiddle,
uppermiddle, 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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How does the analysis determine importance ranking of uncertain model inputs?
 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 oneway sensitivity analyses and a small designofexperiments analysis.
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