Abstract
BackgroundParametric distributions based on individual patient data can be used to represent both stochastic and parameter uncertainty. Although general guidance is available on how parameter uncertainty should be accounted for in probabilistic sensitivity analysis, there is no comprehensive guidance on reflecting parameter uncertainty in the (correlated) parameters of distributions used to represent stochastic uncertainty in patient-level models. This study aims to provide this guidance by proposing appropriate methods and illustrating the impact of this uncertainty on modeling outcomes.MethodsTwo approaches, 1) using non-parametric bootstrapping and 2) using multivariate Normal distributions, were applied in a simulation and case study. The approaches were compared based on point-estimates and distributions of time-to-event and health economic outcomes. To assess sample size impact on the uncertainty in these outcomes, sample size was varied in the simulation study and subgroup analyses were performed for the case-study.ResultsAccounting for parameter uncertainty in distributions that reflect stochastic uncertainty substantially increased the uncertainty surrounding health economic outcomes, illustrated by larger confidence ellipses surrounding the cost-effectiveness point-estimates and different cost-effectiveness acceptability curves. Although both approaches performed similar for larger sample sizes (i.e. n = 500), the second approach was more sensitive to extreme values for small sample sizes (i.e. n = 25), yielding infeasible modeling outcomes.ConclusionsModelers should be aware that parameter uncertainty in distributions used to describe stochastic uncertainty needs to be reflected in probabilistic sensitivity analysis, as it could substantially impact the total amount of uncertainty surrounding health economic outcomes. If feasible, the bootstrap approach is recommended to account for this uncertainty.
Highlights
Parametric distributions based on individual patient data can be used to represent both stochastic and parameter uncertainty
The Bootstrap and The multivariate Normal distributions approach (MVNorm) approach yield incremental cost-effectiveness point-estimates similar to the “real” value, both approaches slightly overestimate the magnitude of the uncertainty for sample sizes of n = 100 and smaller, demonstrated by smaller confidence ellipses for the “real” uncertainty
For very small sample sizes (i.e. n = 25), the MVNorm approach generates unrealistic parameter values, e.g. indicating a mean survival far beyond life-expectancy, leading to extreme and unrealistic health economic outcomes, which results in an unrealistic large confidence ellipse
Summary
Parametric distributions based on individual patient data can be used to represent both stochastic and parameter uncertainty. To facilitate decision making, such models should adequately reflect all types of uncertainty in the synthesized evidence used for analysis [4]. This is relevant in patient-level modeling studies in which reflecting patient heterogeneity may effectively increase uncertainty, for example by relatively low sample sizes in defined subgroups or by an increasing number of parameters that need to be estimated to account for patient characteristics in individualized predictions. Uncertainty in evidence can be disaggregated into stochastic uncertainty (i.e. patient-level variation or first-order uncertainty) and parameter uncertainty (i.e. second-order uncertainty) [4] This can be illustrated using a time-toevent parameter, e.g. the time-to-progression after surgery
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