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Section Computer Science

Prediction of Kidney Failure and Cancer Insurance Claims with Bayesian MCMC

Prediksi Klaim Asuransi Gagal Ginjal dan Kanker dengan Bayesian MCMC
Vol. 10 No. 2 (2025): December:
DOI : https://doi.org/10.21070/acopen.10.2025.11480
Published : Jul 14, 2025

Nirmala Ayuningtyas (1), Abdullah Ahmad Dzikrullah (2)

(1) Program Studi Statistika, Universitas Islam Indonesia , Indonesia
(2) Program Studi Statistika, Universitas Islam Indonesia , Indonesia
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Abstract:

General Background: Health insurance plays a crucial role in mitigating the financial risks of catastrophic illnesses. Specific Background: In Indonesia, chronic kidney disease (CKD) and cancer contribute significantly to the burden of BPJS Health claims, with rising costs reported in recent years. Knowledge Gap: Existing claim estimation models often fail to capture the uncertainty and variability inherent in real-world data. Aims: This study aims to develop a Bayesian model with a Markov Chain Monte Carlo (MCMC) approach to accurately estimate insurance claims for CKD and cancer. Results: Using 2021–2024 data from RSUP Dr. Soeradji Tirtonegoro Klaten, the model successfully estimated outpatient CKD claims at 1649.29 (SD = 19.82) and outpatient cancer claims at 147.68 (SD = 10.18). All model diagnostics indicate strong convergence and accuracy (R-hat = 1.0, ESS > 5000). Novelty: This research applies MCMC-based Bayesian inference with various prior settings (informative to non-informative) and demonstrates robust posterior prediction under different assumptions. Implications: The model provides a credible framework for insurance risk management, improving claim prediction and fiscal planning for health providers and insurers, particularly in managing high-cost diseases within the national health system.
Highlight :



  • The Bayesian MCMC model produced accurate and stable estimates of kidney failure and cancer claims (R-hat = 1.0, ESS > 5000).

  • Sensitivity analysis showed the results remained stable despite different priors, indicating a robust model.

  • The best prediction in outpatient CKD (MAPE 5.15%), but less accurate in outpatient cancer (MAPE 50.26%).


Keywords : Bayes, Claims, MCMC, PyMC, Python

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References

Y. Yan et al., “Machine Learning Models Predict the Progression of Long-Term Renal Insufficiency in Patients With Renal Cancer After Radical Nephrectomy,” BMC Nephrology, vol. 25, no. 1, p. 450, Dec. 2024, doi: 10.1186/s12882-024-03907-1.

M.-P. Côté, C. Genest, and D. A. Stephens, “A Bayesian Approach to Modeling Multivariate Multilevel Insurance Claims in the Presence of Unsettled Claims,” Bayesian Analysis, vol. 17, no. 1, Mar. 2022, doi: 10.1214/20-BA1243.

L. Hong and R. Martin, “Valid Model-Free Prediction of Future Insurance Claims,” North American Actuarial Journal, vol. 25, no. 4, pp. 473–483, Oct. 2021, doi: 10.1080/10920277.2020.1802599.

W. Niemiro, “Bayesian Prediction With an Asymmetric Criterion in a Nonparametric Model of Insurance Risk,” Statistics (Berlin), vol. 40, no. 4, pp. 353–363, Aug. 2006, doi: 10.1080/02331880600618996.

L. Hong and R. Martin, “A Flexible Bayesian Nonparametric Model for Predicting Future Insurance Claims,” North American Actuarial Journal, vol. 21, no. 2, pp. 228–241, Apr. 2017, doi: 10.1080/10920277.2016.1247720.

J. Gyarmati-Szabó and L. Márkus, “A Hierarchical Bayesian Model to Predict Belatedly Reported Claims in Insurances,” in Recent Advances in Stochastic Modeling and Data Analysis, World Scientific, Nov. 2007, pp. 137–144, doi: 10.1142/9789812709691_0017.

Y. Zhang, L. Ji, G. Aivaliotis, and C. Taylor, “Bayesian CART Models for Insurance Claims Frequency,” Insurance: Mathematics and Economics, vol. 114, pp. 108–131, Jan. 2024, doi: 10.1016/j.insmatheco.2023.11.005.

G. Q. Yu, “Hierarchical Bayesian Modeling,” pp. 336–358, 2002, doi: 10.1002/9780470317105.ch14.

Y. Huang and S. Meng, “A Bayesian Nonparametric Model and Its Application in Insurance Loss Prediction,” Insurance: Mathematics and Economics, vol. 93, pp. 84–94, Jul. 2020, doi: 10.1016/j.insmatheco.2020.04.010.

A. Lestia and M. Idris, “Pendekatan Bayesian Markov Chain Monte Carlo (MCMC) Metropolis-Hastings Pada Pemodelan Klaim Asuransi Kesehatan,” Epsilon: Jurnal Matematika Murni dan Terapan, vol. 18, p. 165, Nov. 2024, doi: 10.20527/epsilon.v18i2.13872.

E. Ozkok, G. Streftaris, H. R. Waters, and A. D. Wilkie, “Bayesian Modelling of the Time Delay Between Diagnosis and Settlement for Critical Illness Insurance Using a Burr Generalised-Linear-Type Model,” Insurance: Mathematics and Economics, vol. 50, no. 2, pp. 266–279, Mar. 2012, doi: 10.1016/j.insmatheco.2011.12.001.

A. Kapoor, E. Nukala, and R. Chandra, “Bayesian Neuroevolution Using Distributed Swarm Optimization and Tempered MCMC,” Applied Soft Computing, vol. 129, p. 109528, 2022, doi: 10.1016/j.asoc.2022.109528.

H. Yotsui, K. Matsuoka, and K. Kaito, “Dual Sampling Method for Evaluating Uncertainty When Updating a Bayesian Estimation Model of a High-Risk Infrastructure,” Structural Safety, vol. 93, p. 102188, 2021, doi: 10.1016/j.strusafe.2021.102188.

D. Gamerman and H. F. Lopes, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, 2nd ed. Boca Raton: CRC Press, 2006.

S. Brooks, A. Gelman, G. L. Jones, and X. L. Meng, Handbook of Markov Chain Monte Carlo. Boca Raton: CRC Press, 2011.

R. M. Neal, “MCMC Using Hamiltonian Dynamics,” in Handbook of Markov Chain Monte Carlo, S. Brooks, A. Gelman, G. L. Jones, and X. L. Meng, Eds. Boca Raton: CRC Press, 2011, pp. 113–162.

H. H. Bock, Likelihood, Prior and Posterior: The Concept of Bayesian Inference, 2003.

M. West and J. Harrison, Bayesian Forecasting and Dynamic Models, 2nd ed. New York: Springer, 1997.

A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis, 3rd ed. Boca Raton: CRC Press, 2013.

M. K. Cowles and B. P. Carlin, “Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review,” Journal of the American Statistical Association, vol. 91, no. 434, pp. 883–904, Jun. 1996, doi: 10.1080/01621459.1996.10476956.

P. Congdon, Bayesian Statistical Modelling, 2nd ed. Wiley, 2006.

H. Jeffreys, Theory of Probability, 3rd ed. Oxford: Oxford University Press, 1961.

J. Aitchison and S. D. Silvey, “The Generalization of Probit Analysis to the Case of Multiple Responses,” Biometrika, vol. 44, no. 1/2, pp. 131–140, 1957.

W. M. Bolstad and J. M. Curran, Introduction to Bayesian Statistics, 3rd ed. Hoboken, NJ: Wiley, 2016.

A. J. Dobson and A. G. Barnett, An Introduction to Generalized Linear Models, 4th ed. CRC Press, 2018.

G. Casella and R. L. Berger, Statistical Inference, 2nd ed. Belmont, CA: Duxbury Press, 2001.

C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd ed. Springer, 2004.

R. J. B. Garthwaite, J. B. Kadane, and A. O’Hagan, “Statistical Methods for Eliciting Probability Distributions,” Journal of the American Statistical Association, vol. 100, no. 470, pp. 680–701, 2005.

M. D. Hoffman and A. Gelman, “The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo,” Journal of Machine Learning Research, vol. 15, no. 1, pp. 1593–1623, 2014.