Zongbo Li

All Publications

• Meta-Modeling as a Variance-Reduction Technique for Stochastic Model-Based Cost-Effectiveness Analyses MEDICAL DECISION MAKING Li, Z., Knowlton, G. S., Wheatley, M. M., Jenness, S. M., Enns, E. A. 2025; 45 (8): 976-986

  Abstract

  PurposeWhen using stochastic models for cost-effectiveness analysis (CEA), run-to-run outcome variability arising from model stochasticity can sometimes exceed the change in outcomes resulting from an intervention, especially when individual-level efficacy is small, leading to counterintuitive results. This issue is compounded for probabilistic sensitivity analyses (PSAs), in which stochastic noise can obscure the influence of parameter uncertainty. This study evaluates meta-modeling as a variance-reduction technique to mitigate stochastic noise while preserving parameter uncertainty in PSAs.MethodsWe applied meta-modeling to 2 simulation models: 1) a 4-state Sick-Sicker model and 2) an agent-based HIV transmission model among men who have sex with men (MSM). We conducted a PSA and applied 3 meta-modeling techniques-linear regression, generalized additive models, and artificial neural networks-to reduce stochastic noise. Model performance was assessed using R2 and root mean squared error (RMSE) values on a validation dataset. We compared PSA results by examining scatter plots of incremental costs and quality-adjusted life-years (QALYs), cost-effectiveness acceptability curves (CEACs), and the occurrence of unintuitive results, such as interventions appearing to reduce QALYs due to stochastic noise.ResultsIn the Sick-Sicker model, stochastic noise increased variance in incremental costs and QALYs. Applying meta-modeling techniques substantially reduced this variance and nearly eliminated unintuitive results, with R2 and RMSE values indicating good model fit. In the HIV agent-based model, all 3 meta-models effectively reduced outcome variability while retaining parameter uncertainty, yielding more informative CEACs with higher probabilities of being cost-effective for the optimal strategy.ConclusionsMeta-modeling effectively reduces stochastic noise in simulation models while maintaining parameter uncertainty in PSA, enhancing the reliability of CEA results without requiring an impractical number of simulations.HighlightsWhen using complex stochastic models for cost-effectiveness analysis (CEA), stochastic noise can overwhelm intervention effects and obscure the impact of parameter uncertainty on CEA outcomes in probabilistic sensitivity analysis (PSA).Meta-modeling offers a solution by effectively reducing stochastic noise in complex stochastic simulation models without increasing computational burden, thereby improving the interpretability of PSA results.

  View details for DOI 10.1177/0272989X251352210

  View details for Web of Science ID 001550247400001

  View details for PubMedID 40814193

• Improving racial/ethnic health equity and naloxone access among people at risk for opioid overdose: A simulation modeling analysis of community-based naloxone distribution strategies in Massachusetts, United States. Addiction (Abingdon, England) Zang, X., Skinner, A., Li, Z., Shaw, L. C., Behrends, C. N., Chatterjee, A., Jalali, A., Jordan, A. E., Morgan, J. R., Nolen, S., Schackman, B. R., Marshall, B. D., Walley, A. Y. 2025; 120 (2): 316-326

  Abstract

  During the COVID-19 pandemic, there was a surge in opioid overdose deaths (OODs) in Massachusetts, USA, particularly among Black and Hispanic/Latinx populations. Despite the increasing racial and ethnic disparities in OODs, there was no compensatory increase in naloxone distributed to these groups. We aimed to evaluate two community-based naloxone expansion strategies, with the objective of identifying approaches that could mitigate mortality and racial and ethnic disparities in OODs.Individual-based simulation model. We measured naloxone availability using naloxone kits per OOD and evaluated scenarios of achieving higher benchmarks for naloxone availability (i.e. 40, 60 and 80 kits per OOD) from 2022 levels (overall: 26.0, White: 28.8, Black: 17.3, Hispanic/Latinx: 18.9). We compared two naloxone distribution strategies: (1) proportional distribution: achieving the benchmark ratio at the overall population level while distributing additional kits proportional to the 2022 level for each racial/ethnic group (at 40 kits per OOD benchmark: overall: 40, White: 44.3, Black: 26.6, Hispanic/Latinx: 29.1), and (2) equity-focused distribution: achieving the benchmark ratio among each racial/ethnic group (at 40 kits per OOD benchmark: 40 for all groups).Massachusetts, United States.People at risk of OOD.Annual number and rate of OODs, total healthcare costs of increasing naloxone availability.Both naloxone distribution strategies yielded comparable predicted reductions in total OODs in 2025 and incurred similar incremental costs. However, the relative reduction in the rate of OODs differed across groups. For achieving an 80 kits per OOD benchmark, proportional distribution resulted in a projected 6.7%, 6.5% and 7.1% reduction in annual OODs in 2025 among White, Black and Hispanic/Latinx populations, respectively. In contrast, equity-focused distribution achieved a reduction of 5.7%, 11.3% and 10.2% in the respective groups. In all scenarios, the cost per OOD averted was lower than the generally accepted thresholds for cost per life saved.An equity-focused naloxone distribution strategy designed to reduce racial and ethnic disparities in naloxone availability could improve health equity among racial and ethnic groups while potentially improving overall population health at lower healthcare costs per opioid overdose death averted than a proportional distribution strategy.

  View details for DOI 10.1111/add.16691

  View details for PubMedID 39450522

  View details for PubMedCentralID PMC11707306

• A Sequential Calibration Approach to Address Challenges of Repeated Calibration of a COVID-19 Model. Medical decision making : an international journal of the Society for Medical Decision Making Enns, E. A., Li, Z., McKearnan, S. B., Kao, S. Z., Sanstead, E. C., Simon, A. B., Mink, P. J., Gildemeister, S., Kuntz, K. M. 2025; 45 (1): 3-16

  Abstract

  Mathematical models served a critical role in COVID-19 decision making throughout the pandemic. Model calibration is an essential, but often computationally burdensome, step in model development that provides estimates for difficult-to-measure parameters and establishes an up-to-date modeling platform for scenario analysis. In the evolving COVID-19 pandemic, frequent recalibration was necessary to provide ongoing support to decision makers. In this study, we address the computational challenges of frequent recalibration with a new calibration approach.We calibrated and recalibrated an age-stratified dynamic compartmental model of COVID-19 in Minnesota to statewide COVID-19 cumulative mortality and prevalent age-specific hospitalizations from March 22, 2020 through August 20, 2021. This period was divided into 10 calibration periods, reflecting significant changes in policies, messaging, and/or epidemiological conditions in Minnesota. When recalibrating the model from one period to the next, we employed a sequential calibration approach that leveraged calibration results from previous periods and adjusted only parameters most relevant to the calibration target data of the new calibration period to improve computational efficiency. We compared computational burden and performance of the sequential calibration approach to a more traditional calibration method, in which all parameters were readjusted with each recalibration.Both calibration methods identified parameter sets closely reproducing prevalent hospitalizations and cumulative deaths over time. By the last calibration period, both approaches converged to similar parameter values. However, the sequential calibration approach identified parameter sets that more tightly fit calibration targets and required substantially less computation time than traditional calibration.Sequential calibration is an efficient approach to maintaining up-to-date models with evolving, time-varying parameters and potentially identifies better-fitting parameter sets than traditional calibration.This study used a sequential calibration approach, which takes advantage of previous calibration results to reduce the number of parameters to be estimated in each round of calibration, improving computational efficiency and algorithm convergence to best-fitting parameter values.Both sequential and traditional calibration approaches were able to identify parameter sets that closely reproduced calibration targets. However, the sequential calibration approach generated parameter sets that yielded tighter fits and was less computationally burdensome.Sequential calibration is an efficient approach to maintaining up-to-date models with evolving, time-varying parameters.

  View details for DOI 10.1177/0272989X241292012

  View details for PubMedID 39545378

• Adaptive COVID-19 Mitigation Strategies: Tradeoffs between Trigger Thresholds, Response Timing, and Effectiveness. MDM policy & practice Sanstead, E. C., Li, Z., McKearnan, S. B., Kao, S. Z., Mink, P. J., Simon, A. B., Kuntz, K. M., Gildemeister, S., Enns, E. A. 2023; 8 (2): 23814683231202716

  Abstract

  Background. To support proactive decision making during the COVID-19 pandemic, mathematical models have been leveraged to identify surveillance indicator thresholds at which strengthening nonpharmaceutical interventions (NPIs) is necessary to protect health care capacity. Understanding tradeoffs between different adaptive COVID-19 response components is important when designing strategies that balance public preference and public health goals. Methods. We considered 3 components of an adaptive COVID-19 response: 1) the threshold at which to implement the NPI, 2) the time needed to implement the NPI, and 3) the effectiveness of the NPI. Using a compartmental model of SARS-CoV-2 transmission calibrated to Minnesota state data, we evaluated different adaptive policies in terms of the peak number of hospitalizations and the time spent with the NPI in force. Scenarios were compared with a reference strategy, in which an NPI with an 80% contact reduction was triggered when new weekly hospitalizations surpassed 8 per 100,000 population, with a 7-day implementation period. Assumptions were varied in sensitivity analysis. Results. All adaptive response scenarios substantially reduced peak hospitalizations relative to no response. Among adaptive response scenarios, slower NPI implementation resulted in somewhat higher peak hospitalization and a longer time spent under the NPIs than the reference scenario. A stronger NPI response resulted in slightly less time with the NPIs in place and smaller hospitalization peak. A higher trigger threshold resulted in greater peak hospitalizations with little reduction in the length of time under the NPIs. Conclusions. An adaptive NPI response can substantially reduce infection circulation and prevent health care capacity from being exceeded. However, population preferences as well as the feasibility and timeliness of compliance with reenacting NPIs should inform response design.This study uses a mathematical model to compare different adaptive nonpharmaceutical intervention (NPI) strategies for COVID-19 management across 3 dimensions: threshold when the NPI should be implemented, time it takes to implement the NPI, and the effectiveness of the NPI.All adaptive NPI response scenarios considered substantially reduced peak hospitalizations compared with no response.Slower NPI implementation results in a somewhat higher peak hospitalization and longer time spent with the NPI in place but may make an adaptive strategy more feasible by allowing the population sufficient time to prepare for changing restrictions.A stronger, more effective NPI response results in a modest reduction in the time spent under the NPIs and slightly lower peak hospitalizations.A higher threshold for triggering the NPI delays the time at which the NPI starts but results in a higher peak hospitalization and does not substantially reduce the time the NPI remains in force.

  View details for DOI 10.1177/23814683231202716

  View details for PubMedID 37841496

  View details for PubMedCentralID PMC10568986

• Serotype distribution and antibiotic resistance of Streptococcus pneumoniae isolates from 17 Chinese cities from 2011 to 2016. BMC infectious diseases Zhao, C., Li, Z., Zhang, F., Zhang, X., Ji, P., Zeng, J., Hu, B., Hu, Z., Liao, K., Sun, H., Zhang, R., Cao, B., Zhuo, C., Jia, W., Mei, Y., Chu, Y., Xu, X., Yang, Q., Jin, Y., Fu, Q., Xu, X., Li, H., Wang, L., Ni, Y., Liang, H., Wang, H. 2017; 17 (1): 804

  Abstract

  Streptococcus pneumoniae, the leading pathogen of bacterial infections in infants and the elderly, is responsible for pneumococcal diseases with severe morbidity and mortality. Emergence of drug-resistant strains presented new challenges for treatment and prevention. Vaccination has proven to be an effective means of preventing pneumococcal infection worldwide. Detailed epidemiological information of antibiotic susceptibilities and serotype distribution will be of great help to the management of pneumococcal infections.A total of 881 S. pneumoniae isolates were collected from patients at 23 teaching hospitals in 17 different cities from 2011 to 2016. The main specimen types included sputum, blood, broncho-alveolar lavage fluid, pharyngeal swabs, and cerebrospinal fluid. Minimum inhibitory concentrations (MICs) were determined using the agar dilution method. Capsular serotypes were identified using latex agglutination and quellung reaction test. Molecular epidemiology was investigated using multilocus sequence typing.S. pneumoniae isolates were highly resistant to macrolides, tetracycline, and trimethoprim/sulfamethoxazole. The rate of resistance to penicillin was 51.6% (oral breakpoint). However, levofloxacin and moxifloxacin maintained excellent antimicrobial activity and all of the isolated strains were susceptible to vancomycin. Twenty-two serotypes were identified among the 881 isolates. Prevalent serotypes were 19F (25.7%), 19A (14.0%), 15 (6.8%), 6B (3.6%), 6A (3.0%), and 17 (2.8%). The overall vaccine coverage rates for 7- and 13-valent pneumococcal conjugate vaccines were 37.5% and 58.3%, respectively. Vaccine coverage rates in young children and economically underdeveloped regions were higher than those in older adults and developed regions. Vaccine-covered serotypes demonstrated higher resistance compared with uncovered serotypes. Molecular epidemiological typing demonstrated that S. pneumoniae showed significant clonal dissemination and that ST271 (120, 28.3%), ST320 (73, 17.2%) and ST81 (27, 6.6%) were the major STs.High resistance to clinical routine antibiotics was observed for all 881 S. pneumoniae strains. Drug resistance varied among different serotypes and age groups. Prevalent serotypes among the isolates were 19F, 19A, 15, 6B, 6A, and 17. Community-acquired strains should also be included in future studies to gain a better understanding of the prevalence and resistance of S. pneumoniae in China.

  View details for DOI 10.1186/s12879-017-2880-0

  View details for PubMedID 29284419

  View details for PubMedCentralID PMC5747162