Benefit packages design based on the optimization of depression burden

Under universal health coverage, allocating antidepressant benefits requires balancing health costs, clinical efficacy, and patient financial protection. Health insurers must decide on antidepressant inclusion in benefit packages and reimbursement levels, and benefit-package decisions involve both clinical effectiveness and patient out-of-pocket spending. To that end, a new study develops a model for comparing benefit-package options under a constrained healthcare insurance budget.

The study proposes a dual-objective model for the burden of depressive disorder. The model jointly considers clinical efficacy and household out-of-pocket expenditure when designing benefit packages.

“Given the model's high-dimensional non-convex characteristics, we developed the triple-population cooperative particle swarm optimization for the burden of depressive disorder (TPCPSO_BD),” shares corresponding author Jue Liu.

Validated using real-world data from City S, China, TPCPSO_BD was found to perform better than comparison algorithms in small, medium and large test cases. “In the large test case, an optimized benefit package reduced direct household expenditure per unit of societal disease burden by 48.97% compared with the benchmark algorithms,” says Liu.

Notably, the average cost-effectiveness ratio fell from 13.30 under the current value-based procurement formulary to 5.49 under the optimized formulary, representing a 58.72% decrease. A lower ratio indicates lower cost relative to the clinical benefit achieved.

Meanwhile, drug-selection results showed joint effects from drug price, out-of-pocket rate and clinical efficacy. “Sertraline and duloxetine appeared frequently among the nondominated solutions, reflecting favourable combinations of clinical efficacy and cost,” says Liu. “Agomelatine, however, appeared less frequently despite its clinical efficacy, consistent with the higher cost associated with the drug.

“Drug efficacy and household costs should be considered together when benefit packages are designed,” first-author Ben Niu adds. “The model provides several feasible options, so policymakers can choose a package that matches local budgets and reimbursement needs.” 

Contact the author:

Prof. Jue Liu, School of Public Health, Institute for Global Health and Development, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, China. Email: jueliu@bjmu.edu.cn

Funder:

Ben Niu was supported by Key Program of National Natural Science Foundation of China (No. 72334004) and Natural Science Foundation of Guangdong Province (No. 2024A1515011712). Jue Liu was supported by National Natural Science Foundation of China (No. 72474005). The funders had no role in study design, data collection, data analysis, data interpretation, or writing of the report.

Conflict of interest:

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 

See the article:

Ben Niu, Yaqi Zhang, Ying Chen, Tingting Liu and Jue Liu, “Benefit packages design based on the optimization of depression burden: Evidence from urban China,” Journal of Management Science and Engineering, Volume 11, Issue 3, 2026, Pages 653–668, ISSN 2096-2320, https://doi.org/10.1016/j.jmse.2026.06.003.