DECISIONS, DECISIONS: CAN DIRECT-SEARCH OPTIMIZATION OF CONTINUOUS DECISION VARIABLES RESULT IN SUBSTANTIAL WELFARE GAINS COMPARED TO USUAL METHODS?

Purpose: In cost-effectiveness analyses (CEAs) involving continuous decision variables (such as screening rates or treatment thresholds), the strategies being evaluated are generally pre-specified using arbitrary thresholds or round numbers.  The objective of this study was to evaluate the potential gains in welfare, defined by average net monetary benefit (NMB), from direct-search optimization of continuous decision variables (cardiovascular disease [CVD] screening/treatment thresholds) compared to solely focusing on pre-specified strategies.

Method: We used a CVD micro-simulation model to estimate the lifetime health benefits (quality-adjusted life years [QALYs]) and screening, treatment, and event costs under various multi-staged screening/treatment strategies for a representative cohort of 10,000 adults (aged 25-74 years) in the U.S. without history of CVD.  Screening/treatment strategies were defined by the numbers of individuals receiving non-laboratory-based or cholesterol-based risk assessment, and by the proportions of individuals ultimately receiving lipid-lowering and/or blood pressure treatment.  In total, 36 age- and sex-specific continuous decision variables collectively defined any screening/treatment strategy.  Fifty pre-specified strategies were determined based on commonly-used treatment thresholds and/or plausible screening/treatment cutoffs that spanned a considerable range of the decision variable space.   These strategies were compared to an optimized set of decision variables that was determined using the Nelder-Mead algorithm, a direct-search method that aimed to maximize average NMB (discounted at 3%, using a willingness-to-pay [WTP] value of $100,000/QALY).   Common random numbers were employed to produce stable results across model runs.

Result: Among the pre-specified strategies, the optimal option under conventional incremental CEA rules yielded discounted per-person averages of 20.422 QALYs, costs of $12,734, and average NMB of $2.0295 million.  The corresponding results from the direct-search optimization were 20.419 QALYs, costs of $11,456, and average NMB of $2.0305 million.  Extrapolated to the relevant U.S. population eligible for primary CVD prevention (~136 million adults), the total difference in average NMB between these approaches would be >$130 billion.

Conclusion: We found that direct-search optimization of multistage CVD screening/treatment thresholds resulted in meaningful gains in welfare (average NMB) compared to a traditional CEA of pre-specified strategies.  Future CEA studies involving many (>10) continuous decision variables might also benefit from employing direct-search or other optimization algorithms, although the gains in NMB should be weighed against potential losses from increased complexity of model results and subsequent clinical guidance (i.e., nuanced screening/treatment guidelines).