As described in our evidence synthesis paper, we populated model parameters for each city by synthesizing evidence from 59 peer-reviewed publications and 24 public health and surveillance reports and executed primary analyses using 11 data sets (Krebs et al. 2019). Where data were not available, we conducted extensive model validation and calibration to ensure that uncertain model parameters produced results that matched real-world outcomes. We identified parameters that required city-specific data and stratification by gender, risk group and race/ethnicity a priori and sought out databases for primary analysis to augment our evidence synthesis. We also derived information and values for the free parameters; “free parameters” are key uncertain parameters which are not predefined by the model and lead to the most significant uncertainty in target outcomes. The Morris method (Morris 1991; Tian et al. 2016; Wu et al. 2013) was used to select the most influential parameters for calibration, and the Nelder-Mead algorithm (Helton and Davis 2003; Taylor et al. 2010) was used to iteratively calibrate the model to generate 2,000 best-fitting parameter sets.
Through this iterative calibration to specific targets/endpoints in each city - the number of diagnosed PLHIV at each year end (stratified by sex, race/ethnicity and risk group), the annual number of new HIV diagnoses (separately for the overall estimate, African/American (Black) population, and MSM), and the annual number of all-cause mortality deaths among PLHIV (separately for the overall estimate, African/American (Black) population, and MSM), free parameters and their weights were determined. Further details are provided in our calibration manuscript (Zang et al. 2020). All of this information is stored in Evidence-Inputs-Master.xlsx, Evidence-Inputs-Master-Ideal.xlsx and cali_par_all.xlsx found in the Data Files directory, and read-in using the CascadeCEA-Model-1-Module-Data.input.R script.
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In this component we generate grouping indicators for the 42 population groups; descriptions and R name for each are presented below in Table 1.This function is in the CascadeCEA-Model-0-Group.number.R script in the R directory.
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Table 1: Description of intial model parameters with their R name and values
| Group Indicator Name | Description | R name | # of groups |
|---|---|---|---|
| Male | Gender - male | m |
30 |
| Female | Gender - female | f |
12 |
| White | Race/ethnicity - White | white |
14 |
| Black | Race/ethnicity - Blacks/African Americans | black |
14 |
| Hispanic | Race/ethnicity - Hispanics/Latinos | hisp |
14 |
| All MSM | All MSM groups including MWID | all.msm |
18 |
| All PWID | All PWID groups including MWID | all.idu |
24 |
| All MSM and PWID | Intersection of all.msm and all.idu | midu |
12 |
| Opioid Agonist Therapy (OAT) | oat |
12 | |
| Heterosexual | het |
12 | |
| Low risk | All low-risk groups, excludes PWID | low |
15 |
| High risk | All high-risk groups, excludes PWID | high |
15 |
| Low-risk MSM | Intersection of all.msm and low | msm.l |
9 |
| High-risk MSM | Difference between all.msm and low | msm.h |
9 |
| Low-risk heterosexuals | Intersection of het and low | het.l |
6 |
| Low-risk male heterosexuals | Intersection of het.l and m | het.m.l |
6 |
| Low-risk female heterosexuals | Intersection of het.l and f | het.f.l |
6 |
| MSM only | Difference between all.msm and all.idu | msm |
6 |
| PWID only | Difference between all.idu and all.msm | idu |
12 |
| Heterosexual males | Intersection of het and m | het.m |
6 |
| Heterosexual females | Intersection of het and f | het.f |
6 |
| Off Opioid Agonist Therapy (OAT) | Difference between all.idu and oat | off.oat |
12 |
| Male PWID | Intersection of idu and m. Excludes MSM | idu.m |
6 |
| Female PWID | Intersection of idu and f | idu.f |
6 |
| Low-risk MSM | Intersection of msm and low | msmL |
3 |
| High-risk MSM | Intersection of msm and high | msmH |
3 |
| Low-risk MSM-IDU | Intersection of midu and low | miduL |
6 |
| HIgh-risk MSM-IDU | Intersection of midu and high | miduH |
6 |
| Low-risk hetersoexual males | Intersection of het.m and low | het.mL |
3 |
| High-risk hetersoexual males | Intersection of het.m and high | het.mH |
3 |
| Low-risk hetersoexual females | Intersection of het.f and low | het.fL |
3 |
| High-risk hetersoexual females | Intersection of het.f and high | het.fH |
3 |
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In this component, we calculate initial cell sizes for all 42 population strata and 19 model states/compartments using the model_initial function.
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In this component, we set values for model paramaters with multiple dimensions using CascadeCEA-Model-0-Parameterization.R in the R directory. This includes loading population demographic parameters and parameters that require manipulation (either through calibration, or modification as a result of interventions). Cost-effectiveness analyses (CEA) parameters including QALY parameters, state-level costs, and intervention costs are also initialized in this step.
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In this component, values for the free parameters are derived, calibrated and updated using CascadeCEA-Model-0-Parameter.update.R in the R directory. Note that this component (1.4 Assign free parameter values) only needs to be done once - when running the model for the first time.
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Helton, J. C., and F. J. Davis. 2003. “Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems.” Journal Article. Reliability Engineering & System Safety 81 (1): 23–69. https://doi.org/https://doi.org/10.1016/S0951-8320(03)00058-9.
Krebs, E., B. Enns, L. Wang, X. Zang, D. Panagiotoglou, C. Del Rio, J. Dombrowski, et al. 2019. “Developing a Dynamic Hiv Transmission Model for 6 U.s. Cities: An Evidence Synthesis.” Journal Article. PLoS One 14 (5): e0217559. https://doi.org/10.1371/journal.pone.0217559.
Morris, Max D. 1991. “Factorial Sampling Plans for Preliminary Computational Experiments.” Journal Article. Technometrics 33 (2): 161–74. https://doi.org/10.2307/1269043.
Taylor, D. C., V. Pawar, D. Kruzikas, K. E. Gilmore, A. Pandya, R. Iskandar, and M. C. Weinstein. 2010. “Methods of Model Calibration: Observations from a Mathematical Model of Cervical Cancer.” Journal Article. Pharmacoeconomics 28 (11): 995–1000. https://doi.org/10.2165/11538660-000000000-00000.
Tian, Y., K. Hassmiller Lich, N. D. Osgood, K. Eom, and D. B. Matchar. 2016. “Linked Sensitivity Analysis, Calibration, and Uncertainty Analysis Using a System Dynamics Model for Stroke Comparative Effectiveness Research.” Journal Article. Med Decis Making 36 (8): 1043–57. https://doi.org/10.1177/0272989X16643940.
Wu, J., R. Dhingra, M. Gambhir, and J. V. Remais. 2013. “Sensitivity Analysis of Infectious Disease Models: Methods, Advances and Their Application.” Journal Article. J R Soc Interface 10 (86): 20121018. https://doi.org/10.1098/rsif.2012.1018.
Zang, X., E. Krebs, J. E. Min, A. Pandya, B. D. L. Marshall, B. R. Schackman, C. N. Behrends, D. J. Feaster, B. Nosyk, and Localized HIV Modeling Study Group. 2020. “Development and Calibration of a Dynamic Hiv Transmission Model for 6 Us Cities.” Journal Article. Med Decis Making 40 (1): 3–16. https://doi.org/10.1177/0272989X19889356.