![[ Visit Client Website ]](images/banner.gif)
Methods: We propose that the maximization step in the EVPPI calculation can be transformed into a root-finding problem. The domain of the parameter of interest (θi) is divided into discrete intervals defined by the roots of the incremental net benefit (INB) functions on θi. Since the strategy with the highest expected Net Benefit (NB) remains the same within each interval there is no need to perform the maximization step at each value of θi. Root finding is performed by maximizing a ‘score’ function for a solution for the number and location of roots and using model comparison techniques to find the optimal solution. The algorithm requires N random draws and corresponding NB estimates from the whole set of parameters (including θi) from a one-level MCS.
Results: We compared the performance of our algorithm in terms of the bias and standard deviation (SD) of the estimates with that of the conventional two-level algorithm on both a simple model (with 3 parameters) for which EVPPIs can be derived analytically, and on 2 selected parameters of a more complex Markov model (Table).
Method# | Sample size | Model1.P1 EVPPI=3120.6 | Model1.P2 | Model3.P3 EVPPI=0 | Model2.P1 | Model2.P2 |
Bias (SD) | Mean (SD)* | |||||
Conventional: Two-level MCS | 1000X100 | 23.8 (299.7) | 25.9 (112.1) | 20.5 (225.4) | 62.7 (254.4) | 978.4 (426.5) |
1000X1000 | 23.7 (307.7) | 2.6 (108.0) | 28.5 (244.0) | 77.3 (257.4) | 925.8 (397.3) | |
10000X1000 | 3.2 (82.8) | 1.2 (32.9) | 1.4 (74.5) | 57.0 (84.3) | 937.7 (133.0) | |
New: One-level MCS | 1000 | 49.5 (215.2) | 73.1 (251.1) | 5.6 (24.3) | 72.4 (59.9) | 950.0 (82.3) |
10000 | 14.8 (71.9) | 17.7 (124.9) | 0.7 (3.3) | 66.7 (28.5) | 943.1 (27.5) | |
100000 | 3.2 (22.5) | 5.8 (23.0) | 0.1 (0.3) | 65.8 (1.5) | 944.4 (8.5) | |
*Bias could not be reported for the complex model as the true EVPPIs are not precisely known # Based on 1000 repetitions | ||||||
Conclusion: The high processing power required to determine EVPPI has been a major drawback to its uptake. Our approach uses a fraction of the computational resources and appears to generate accurate results. Careful examination of this approach using more complex models, more enhanced methods for the root finding step, and extensions to multivariate EVPPI calculations are the focus of further research.