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Purpose: Remaining life expectancy (RLE) and quality-adjusted life expectancy (QALE) are standard outcomes of decision-analytic Markov models, but their evaluation in decision trees is less straightforward. We sought to compare the performance of Gompertz approximation (GPA) and Declining Exponential Approximation of Life Expectancy (DEALE), using life table method as gold standard for calculating RLE and QALE.
Methods: All analyses were performed for two different underlying models for disease-specific mortality rates (DSM). For the multiplicative model, DSM was modeled as age-independent mortality rate ratio, multiplied by the age-specific background mortality. For the additive model, DSM was modeled as age-independent mortality rate difference, added to the background mortality. Background mortality was estimated from statistical life table data. In our basecase analysis, we set DSM being 2 x background mortality at age 45. This represents the mortality rate difference in the additive model and translates to a relative mortality rate ratio of 3 in the multiplicative model. We used (1) the closed formulas by Pollard based on the Gompertz function and (2) the closed DEALE formulas to calculate undiscounted and discounted RLE and QALE. Results were compared to actuarial life table analysis representing the gold standard for age-dependent RLE and QALE. For the discounted basecase, we used a 3% annual discount rate. Bias was defined as percent deviation from the sum of RLE for ages 30-89. All analyses were performed separately for men and women. DSM and discount rates were varied in one-way sensitivity analysis.
Results: Both approximation methods underestimated the actual undiscounted RLE for both the additive and multiplicative model. Basecase results for men: for the multiplicative model, GPA (bias -4%) performed better than DEALE (-49%), whereas for the additive model, DEALE (-6%) was superior to GPA (-25%). Results for women showed similar patterns regarding magnitude and direction of bias. The use of time-independent disease-specific utility decrements yielded similar patterns for QALE. When varying DSM in sensitivity analysis, bias was positively correlated with DSM, but bias direction (sign) and ranking of both methods did not change. Similarly, changing discount rates did not alter the bias pattern.
Conclusions: Based on our simple model, the Gompertz function should be preferred for multiplicative and the DEALE approach for additive models. The magnitude of the bias depends strongly on model parameters.
See more of Poster Session - Utility Theory; Health Economics; Patient & Physician Preferences; Simulation; Technology Assessment
See more of The 26th Annual Meeting of the Society for Medical Decision Making (October 17-20, 2004)