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Decision Trees: Sensitivity Analysis, Deterministic
All decision analyses have to deal with various forms of uncertainty in a manner that informs the decisions being made. In particular, it is essential to establish the degree to which the results of an analysis are sensitive to a change in a parameter or an assumption and the extent to which the conclusions of the analysis are robust to such changes. The assessment of sensitivity or robustness is known as sensitivity analysis. Such an analysis would consider, for example, the fact that the mean length of inpatient hospital stay associated with a particular clinical event is estimated with uncertainty (reflected in its standard error) and would consider how the results of the study would change if a higher or lower value were used for this parameter. Two different forms of sensitivity analysis are used in this situation: (1) deterministic analysis, which varies the parameter (or assumption) in one or a small number of stages and assesses the implications for results, and (2) probabilistic analysis, which uses simulation methods to simultaneously vary a number of parameters in terms of a large number of possible alternative values they could take. This entry considers deterministic sensitivity analysis.
Different Types of Uncertainty in Decision Analysis
The uncertainties relevant to a decision model have been categorized in various ways in the literature. The main distinction is between parameter and model (or structural) uncertainty. The former refers to the uncertainty that exists in the parameter inputs that are incorporated into models—for example, the baseline risk of a clinical event in a particular patient group under current treatment, the risk reduction in the event associated with a new intervention relative to current practice, the mean cost of the event, or the mean decrement in health-related quality of life associated with the event. Model uncertainty relates to a range of possible assumptions that are made in developing a model. These could include the extent to which the baseline risk of an event changes over time, the duration of the risk reduction associated with a new intervention, or whether or not to include a particular study in a meta-analysis to estimate the relative treatment effect. The distinction between parameter and model uncertainty is blurred in that many forms of model uncertainty could be expressed in terms of an uncertain parameter.
Deterministic sensitivity analysis can also be used to address heterogeneity rather than uncertainty—that is, to assess the extent to which the results of an analysis change for different types of patients. For example, a treatment may be more effective in females than in males, so the results of the analysis could be separately reported for the two genders. This is probably more correctly labeled as a subgroup, rather than a sensitivity, analysis and is not further discussed here.
Different Forms of Deterministic Sensitivity Analysis
Deterministic sensitivity analysis can be characterized in a number of ways. One is whether a parameter is varied across a range or simply takes on discrete values. In the case of model assumptions that have not been formerly parameterized, the use of discrete values is usually required. Table 1 shows an example of this form of sensitivity analysis (which can also be described as a scenario analysis) in the context of a cost-effectiveness model of endovascular abdominal aortic aneurysm repair (EVAR) compared with open surgery for abdominal aortic aneurysm. It shows the impact of variation on the difference in costs, quality-adjusted life years (QALYs), and the incremental cost-effectiveness ratio relative to the “base-case” or primary analysis. It also shows the results of a probabilistic sensitivity analysis in terms of the probability that EVAR is more cost-effective conditional on a threshold cost-effectiveness ratio. The table mostly includes assessment of uncertainty in the parameter estimates used in the model. However, there are also examples of modeling assumptions that have been varied, for example, Scenario 6 (source of a parameter); and some subgroup analyses are reported (e.g., Scenarios 10 and 11).
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