BC Screening Research Article Appendix

Appendix for Ensuring Epidemiological Consistency in Risk-Stratified Health Economic Models: A Case Study in Breast Cancer Screening Supplement 1: Scoping Review Materials The scoping review discussed in the manuscript was performed to underline the gap of our novel approach and to assess whether our approach is, in fact, novel. We employed a broad search string (( cancer AND screening) AND (” Markov model” OR” Markov models” OR” Markov chain”) ) AND (” Risk Stratification” OR” risk stratified” OR” Risk-based”) aimed to mimic the search strategy a health economic researcher might employ to start a risk-stratified cancer screening evaluation. We included Markov models aimed at risk-stratified cancer screening, excluding those that worked on pre-stratified populations (meaning that the model made no stratification itself but only modelled a single high-risk population). The besides ascertaining the relevant gap for our proposed method, we looked at three specific characteristics in the articles. Namely the source of the (1) initial transition probabilities (TP) (before any risk-adjustments), (2) the method of applying risk-stratification (RS) in the model, and (3) whether the epidemiological predictions where explicitly verified in the paper. For the first question, we have three general categories for the TP sources: internal literature (dedicated observational studies, pilot studies, or epidemiological studies directly focused on the same population as the model), public registry data (raw prevalence and/or incidence data from which transition probabilities are extracted) and external literature (studies that published a model about a different target population). In some cases the article discusses taking the model from an external source without explicitly mentioning the TP one way or the other, in which case we assume that the external model is also the TP source. We assumed that generally, internal literature is a better source than national registry data, which itself is better than using an external source. For the second question, we found that all models (100%) directly embedded the risk-adjustment directly intro the TP, validating our assessment that our approach was a novel approach. We further looked at the most used methods of applying the risk-adjustments (using a multiplier method such as a risk-ratio, using pre-adjusted probabilities from the external source, or making an internal estimation of the adjusted TP). Lastly, we checked if the article explicitly validates the epidemiological results, differentiating between studies that mentioned doing this and studies that explicitly showed the results. While showing these results is important for a number of reasons (it increases transparency, trust, and helps other researchers select the best performing models) we also point out that not showing these results is not always the choice of the researcher. Flow diagram of review with summary results of included articles. Result tables of included articles. Ref DOI Country Cancer Model Type Primary TP Source Epidemiological Validation 1A 10.1371/journal.pone.0202796 UK Bladder Decision Tree & Markov External Literature Yes, Discussed 2A 10.1093/jnci/djae019 USA Breast Markov Cohort Model External Literature No 3A 10.1186/s12913-021-06396-2 Singapore Breast Markov Cohort Model Internal Literature / Pilot study No 4A 10.1038/s41598-023-29985-z China Breast Markov Cohort Model External Literature Yes, Shown 5A 10.1371/journal.pone.0217213 Germany Breast Markov MicroSim Model National Registry Data No 6A 10.1016/j.jval.2017.12.022 Germany Breast Markov MicroSim Model Internal Literature / Pilot study Yes, Shown 7A 10.1186/s12913-024-11226-2 Malawi Cervical Markov Cohort Model External Literature No 8A 10.1111/jgh.15033 Japan Colorectal Markov Cohort Model Internal Literature / Pilot study Yes, Discussed 9A 10.1186/1471-2407-14-261 Australia Colorectal Markov MicroSim Model Internal Literature / Pilot study Yes, Discussed 10A 10.1007/s10198-017-0901-y Japan Gastric Markov Cohort Model External Literature No 11A 10.1136/gutjnl-2021-325948 China Gastric Markov Cohort Model National Registry Data Yes, Shown 12A 10.1016/j.jval.2021.04.1286 Australia Liver Markov Cohort Model External Literature No 13A 10.1038/ctg.2017.26 USA Liver Markov Cohort Model External Literature Yes, Shown 14A 10.1186/s12916-024-03292-4 China Lung Markov Cohort Model National Registry Data Yes, Shown 15A 10.3389/fpubh.2024.1375533 China Nasal Markov Cohort Model Internal Literature / Pilot study Yes, Discussed 16A 10.1016/j.ctarc.2024.100791 Iran Prostate Markov Cohort Model External Literature No 17A 10.3390/genes10090641 Taiwan Prostate Markov Cohort Model External Literature No 18A 10.1371/journal.pmed.1002998 USA Prostate Markov Cohort Model Internal Literature / Pilot study No 19A 10.1002/pros.22964 Finland Prostate Markov Cohort Model Internal Literature / Pilot study Yes, Discussed 20A 10.1001/jamanetworkopen.2020.37657 UK Prostate Markov MicroSim Model External Literature No 21A 10.1016/j.gie.2021.08.008 China Stomach Markov Cohort Model External Literature Yes, Discussed 22A 10.1007/s40273-022-01160-8 China Stomach Markov MicroSim Model External Literature Yes, Discussed 23A 10.1001/jamanetworkopen.2020.37657 USA Prostate Markov Cohort Model National Registry Data Yes, Shown Table 1: General characteristics of Included articles, source of the primary Transition Probabilities (TP) and if the article discussed the epidemiological validation. Ref DOI Risk Stratification in Model Risk Stratification Method Embedding Method 1A 10.1371/journal.pone.0202796 Yes, Risk factors Embedded into TP Risk Ratios 2A 10.1093/jnci/djae019 Yes, Risk factors Embedded into TP Embedded in External Sources 3A 10.1186/s12913-021-06396-2 Yes, PRS stratified Embedded into TP Risk Ratios 4A 10.1038/s41598-023-29985-z Yes, Risk factors (history, breast tissue) Embedded into TP Embedded in External Sources 5A 10.1371/journal.pone.0217213 Yes, Lifetime Risk Embedded into TP Risk Ratios 6A 10.1016/j.jval.2017.12.022 Yes, Risk factors (history, breast tissue) Embedded into TP Risk Ratios 7A 10.1186/s12913-024-11226-2 Yes, Risk factors (history, HIV) Embedded into TP Embedded in External Sources 8A 10.1111/jgh.15033 Yes, PRS stratified Embedded into TP Risk Ratios 9A 10.1186/1471-2407-14-261 Yes, History Embedded into TP Risk Ratios 10A 10.1007/s10198-017-0901-y Yes, Risk factors Embedded into TP Risk Ratios 11A 10.1136/gutjnl-2021-325948 Yes, Risk factors (history, Smoking) Embedded into TP Risk Ratios 12A 10.1016/j.jval.2021.04.1286 Yes, History Embedded into TP Embedded in External Sources 13A 10.1038/ctg.2017.26 Yes, Risk factors Embedded into TP Risk Ratios 14A 10.1186/s12916-024-03292-4 Yes, Risk factors (history, smoking tissue) Embedded into TP Risk Ratios 15A 10.3389/fpubh.2024.1375533 Yes, PRS stratified Embedded into TP Risk Ratios 16A 10.1016/j.ctarc.2024.100791 Yes, PSA Embedded into TP Embedded in External Sources 17A 10.3390/genes10090641 Yes, PRS stratified Embedded into TP Risk Ratios 18A 10.1371/journal.pmed.1002998 Yes, PRS stratified Embedded into TP Risk Ratios 19A 10.1002/pros.22964 Yes, PRS stratified Embedded into TP Direct Estimation of TP 20A 10.1001/jamanetworkopen.2020.37657 Yes, History Embedded into TP Risk Ratios 21A 10.1016/j.gie.2021.08.008 Yes, Lifetime Risk Embedded into TP Embedded in External Sources 22A 10.1007/s40273-022-01160-8 Yes, History Embedded into TP Risk Ratios 23A 10.1001/jamanetworkopen.2020.37657 Yes, PRS stratified Embedded into TP Risk Ratios Table 2: Risk-stratification in included articles, including the basis for the risk-stratification (general risk factors, Polygenic Risk Scores, family history, medical or social factors), the overall method of including a risk-adjustment to the model (in all cases it was directly embedded into the transition probabilities) and if embedded, in what way. References of Included articles 1A. Sutton, A. J., Lamont, J. V., Evans, R. M., Williamson, K., O’Rourke, D., Duggan, B., … Ruddock, M. W. (2018). An early analysis of the cost-effectiveness of a diagnostic classifier for risk stratification of haematuria patients (DCRSHP) compared to flexible cystoscopy in the diagnosis of bladder cancer (K. Thavorn, Ed.). Public Library of Science (PLoS). https://doi.org/10.1371/journal.pone.0202796 2A. Yanguela, J., Jackson, B. E., Reeder-Hayes, K. E., Roberson, M. L., Rocque, G. B., Kuo, T.-M., … Wheeler, S. B. (2024). Simulating the population impact of interventions to reduce racial gaps in breast cancer treatment. Oxford University Press (OUP). https://doi.org/10.1093/jnci/djae019 3A. Wong, J. Z. Y., Chai, J. H., Yeoh, Y. S., Mohamed Riza, N. K., Liu, J., Teo, Y.-Y., … Hartman, M. (2021). Cost effectiveness analysis of a polygenic risk tailored breast cancer screening programme in Singapore. Springer Science and Business Media LLC. https://doi.org/10.1186/s12913-021-06396-2 4A. Shi, J., Guan, Y., Liang, D., Li, D., He, Y., & Liu, Y. (2023). Cost-effectiveness evaluation of riskbased breast cancer screening in Urban Hebei Province. Springer Science and Business Media LLC. https://doi.org/10.1038/s41598-023-29985-z 5A. Arnold, M., Pfeifer, K., & Quante, A. S. (2019). Is risk-stratified breast cancer screening economically efficient in Germany? (J. Bohlius, Ed.). Public Library of Science (PLoS). https://doi.org/10.1371/journal.pone.0217213 6A. Arnold, M., & Quante, A. S. (2018). Personalized Mammography Screening and Screening Adherence—A Simulation and Economic Evaluation. Elsevier BV. https://doi.org/10.1016/j.jval.2017.12.022 7A. Rasmussen, P. W., Hoffman, R. M., Phiri, S., Makwaya, A., Kominski, G. F., Bastani, R., … Moucheraud, C. (2024). Cost-effectiveness of approaches to cervical cancer screening in Malawi: comparison of frequencies, lesion treatment techniques, and risk-stratified approaches. Springer Science and Business Media LLC. https://doi.org/10.1186/s12913-024-11226-2 8A. Sekiguchi, M., Igarashi, A., Sakamoto, T., Saito, Y., Esaki, M., & Matsuda, T. (2020). Cost‐ effectiveness analysis of colorectal cancer screening using colonoscopy, fecal immunochemical test, and risk score. Wiley. https://doi.org/10.1111/jgh.15033 9A. Ouakrim, D. A., Boussioutas, A., Lockett, T., Hopper, J. L., & Jenkins, M. A. (2014). Costeffectiveness of family history-based colorectal cancer screening in Australia. Springer Science and Business Media LLC. https://doi.org/10.1186/1471-2407-14-261 10A. Saito, S., Azumi, M., Muneoka, Y., Nishino, K., Ishikawa, T., Sato, Y., … Akazawa, K. (2017). Costeffectiveness of combined serum anti-Helicobacter pylori IgG antibody and serum pepsinogen concentrations for screening for gastric cancer risk in Japan. Springer Science and Business Media LLC. https://doi.org/10.1007/s10198-017-0901-y 11A. Wang, Z., Han, W., Xue, F., Zhao, Y., Wu, P., Chen, Y., … Jiang, J. (2022). Nationwide gastric cancer prevention in China, 2021–2035: a decision analysis on effect, affordability and cost-effectiveness optimisation. BMJ. https://doi.org/10.1136/gutjnl-2021-325948 12A. Carter, H. E., Jeffrey, G. P., Ramm, G. A., & Gordon, L. G. (2021). Cost-Effectiveness of a Serum Biomarker Test for Risk-Stratified Liver Ultrasound Screening for Hepatocellular Carcinoma. Elsevier BV. https://doi.org/10.1016/j.jval.2021.04.1286 13A. Goossens, N., Singal, A. G., King, L. Y., Andersson, K. L., Fuchs, B. C., Besa, C., … Hoshida, Y. (2017). Cost-Effectiveness of Risk Score–Stratified Hepatocellular Carcinoma Screening in Patients with Cirrhosis. Ovid Technologies (Wolters Kluwer Health). https://doi.org/10.1038/ctg.2017.26 14A. Liu, Y., Xu, H., Lv, L., Wang, X., Kang, R., Guo, X., … Zhang, S. (2024). Risk-based lung cancer screening in heavy smokers: a benefit–harm and cost-effectiveness modeling study. Springer Science and Business Media LLC. https://doi.org/10.1186/s12916-024-03292-4 15A. Yang, D.-W., Miller, J. A., Xue, W.-Q., Tang, M., Lei, L., Zheng, Y., … Jia, W.-H. (2024). Polygenic risk-stratified screening for nasopharyngeal carcinoma in high-risk endemic areas of China: a costeffectiveness study. Frontiers Media SA. https://doi.org/10.3389/fpubh.2024.1375533 16A. Nahvijou, A., Hadian, M., & Mohamadkhani, N. (2024). Finding the PSA-based screening stopping age using prostate cancer risk. Elsevier BV. https://doi.org/10.1016/j.ctarc.2024.100791 17A. Yang, T.-K., Chuang, P.-C., Yen, A. M.-F., Chen, H.-H., & Chen, S. L.-S. (2019). Gene‒ProstateSpecific-Antigen-Guided Personalized Screening for Prostate Cancer. MDPI AG. https://doi.org/10.3390/genes10090641 18A. Callender, T., Emberton, M., Morris, S., Eeles, R., Kote-Jarai, Z., Pharoah, P. D. P., & Pashayan, N. (2019). Polygenic risk-tailored screening for prostate cancer: A benefit–harm and cost-effectiveness modelling study (S. D. Shapiro, Ed.). Public Library of Science (PLoS). https://doi.org/10.1371/journal.pmed.1002998 19A. Yen, A. M., Auvinen, A., Schleutker, J., Wu, Y., Fann, J. C., Tammela, T., … Chen, H. (2015). Prostate cancer screening using risk stratification based on a multi‐state model of genetic variants. Wiley. https://doi.org/10.1002/pros.22964 20A. Callender, T., Emberton, M., Morris, S., Pharoah, P. D. P., & Pashayan, N. (2021). Benefit, Harm, and Cost-effectiveness Associated With Magnetic Resonance Imaging Before Biopsy in Age-based and Risk-stratified Screening for Prostate Cancer. American Medical Association (AMA). https://doi.org/10.1001/jamanetworkopen.2020.37657 21A. Xia, R., Li, H., Shi, J., Liu, W., Cao, M., Sun, D., … Chen, W. (2022). Cost-effectiveness of riskstratified endoscopic screening for esophageal cancer in high-risk areas of China: a modeling study. Elsevier BV. https://doi.org/10.1016/j.gie.2021.08.008 22A. Qin, S., Wang, X., Li, S., Tan, C., Zeng, X., Luo, X., … Wan, X. (2022). Clinical Benefit and Cost Effectiveness of Risk-Stratified Gastric Cancer Screening Strategies in China: A Modeling Study. Springer Science and Business Media LLC. https://doi.org/10.1007/s40273-022-01160-8 23A. Callender, T., Emberton, M., Morris, S., Pharoah, P. D., & Pashayan, N. (2021). Benefit, harm, and cost-effectiveness associated with magnetic resonance imaging before biopsy in age-based and riskstratified screening for prostate cancer. JAMA Network Open, 4(3), e2037657-e2037657. Supplement 2: Numerical Example calculation of method Age group and size Incidence by stage, cases WA p.y. Incidence Rate Conditional Survival Probability Cumulative Cancerfree Survival St. 0 St. 1-4 St. 0 St. 1-4 St. 0 St. 1-4 St. 0 St. 1-4 j Nj C0j C1-4j I0j I1-4j q0j q1-4j S0j S1-4j 0 - 9 340,191 0 0 0.00% 0.00% 100.00% 100.00% 98.10% 86.26% Oct/19 372,442 0 0 0.00% 0.00% 100.00% 100.00% 98.10% 86.26% 20 - 29 382,265 1.9 22.6 0.00% 0.01% 100.00% 99.94% 98.10% 86.26% 30 - 39 429,841 28.5 203.9 0.01% 0.05% 99.93% 99.53% 98.10% 86.31% 40 - 49 429,095 130.5 796.3 0.03% 0.19% 99.70% 98.16% 98.17% 86.72% 50 - 59 461,210 246.4 1342.6 0.05% 0.29% 99.47% 97.13% 98.47% 88.35% 60 - 69 430,583 247.9 1553.3 0.06% 0.36% 99.43% 96.45% 98.99% 90.96% 70 - 79 325,830 101 1186.6 0.03% 0.36% 99.69% 96.42% 99.56% 94.31% 80-85 109,433 27.7 483.4 0.03% 0.44% 99.87% 97.81% 99.87% 97.81% Tot. 3,280,890 783.8 5588.8 Table 3: Example calculation of the pre-stratification at-risk groups, using national incidence data. The first step involves calculating the incidence rate, then the conditional cancer free survival probability, which leads to the cumulative cancer-free survival. Taking the remainder of these cumulative cancer-free survival rates gives the at-risk proportion of the specific age-group. The relevant formula for the calculation is shown in the bottom row. Age group and size Incidence by stage, p.y. Distribution of Incidence Conditional Survival Adjustment Conditional Transition Rate St. 0 St. 1 St. 0 St. 1 St. 0 St. 1 St. 0 St. 1 j Nj Ci C1j π0j π1j P0j P1j λ0j λ1j 0 - 9 340,191 0 0 0.00% 0.00% 100.00% 100.00% 0.00% 0.00% Oct/19 372,442 0 0 0.00% 0.00% 100.00% 100.00% 0.00% 0.00% 20 - 29 382,265 1.9 11.6 0.24% 0.42% 100.00% 100.00% 0.24% 0.42% 30 - 39 429,841 28.5 91.5 3.63% 3.34% 99.76% 99.58% 3.64% 3.35% 40 - 49 429,095 130.5 373.6 16.65% 13.63% 96.12% 96.24% 17.32% 14.17% 50 - 59 461,210 246.4 735.2 31.44% 26.83% 79.48% 82.61% 39.56% 32.48% 60 - 69 430,583 247.9 883.1 31.62% 32.23% 48.04% 55.77% 65.83% 57.79% 70 - 79 325,830 101 500.7 12.89% 18.27% 16.42% 23.54% 78.50% 77.61% 80-85 109,433 27.7 144.5 3.53% 5.27% 3.53% 5.27% 100.00% 100.00% Tot. 3,280,890 783.8 2740.1 Table 4: Example calculation of the conditional transition probability of the first transition from at-risk to cancer. The first step involves calculating the age-distribution of the incidence. Then the conditional cancer-free survival adjustment is calculated. This can be thought of as the proportion of the at-risk group that has yet to develop cancer. The conditional rate is then calculated as the division of the agedistribution by the survival adjustment. In simple terms, the portion of the at-risk group that is pre-predicted to get cancer at that specific age. Supplement 3: Markov Model Diagram Figure 1: Markov Model diagram of the complete model with 4 distinct risk-groups. Each group has a separate proportion of at-risk individuals (higher proportions in the elevated and high risk-groups) and individual levels of screening rates based on age and group.