Understanding bias in probabilistic analysis in model-based health economic evaluation

Guidelines of economic evaluations suggest that probabilistic analysis (using probability distributions as inputs) provides less biased estimates than deterministic analysis (using point estimates) owing to the non-linear relationship of model inputs and model outputs. However, other factors can also impact the magnitude of bias for model results. We evaluate bias in probabilistic analysis and deterministic analysis through three simulation studies. The simulation studies illustrate that in some cases, compared with deterministic analyses, probabilistic analyses may be associated with greater biases in model inputs (risk ratios and mean cost estimates using the smearing estimator), as well as model outputs (life-years in a Markov model). Point estimates often represent the most likely value of the parameter in the population, given the observed data. When model parameters have wide, asymmetric confidence intervals, model inputs with larger likelihoods (e.g., point estimates) may result in less bias in model outputs (e.g., costs and life-years) than inputs with lower likelihoods (e.g., probability distributions). Further, when the variance of a parameter is large, simulations from probabilistic analyses may yield extreme values that tend to bias the results of some non-linear models. Deterministic analysis can avoid extreme values that probabilistic analysis may encounter. We conclude that there is no definitive answer on which analytical approach (probabilistic or deterministic) is associated with a less-biased estimate in non-linear models. Health economists should consider the bias of probabilistic analysis and select the most suitable approach for their analyses.