Pemodelan Dependensi Risiko Penyakit Diabetes Melitus dan Kardiovaskular pada Program Jaminan Kesehatan Nasional dengan Copula Elliptical dan Archimedean

Ahnafi Syahri Giovanni Feistyano, Danang Teguh Qoyyimi, M.Sc., Ph.D.

2026 | Skripsi | S1 ILMU AKTUARIA

Penyakit kardiovaskular merupakan penyakit katastropik dengan beban klaim terbesar dalam Program Jaminan Kesehatan Nasional (JKN) dan sering muncul bersamaan dengan diabetes melitus. Keterkaitan tersebut dapat mengindikasikan dependensi antara besar klaim kedua penyakit, sehingga pengabaiannya berpotensi menyebabkan underestimation ataupun overestimation terhadap risiko klaim agregat. Penelitian ini memodelkan dependensi antara besar klaim penyakit kardiovaskular dan diabetes melitus serta mengevaluasi dampaknya terhadap pengukuran risiko agregat dalam Program JKN. Analisis dilakukan pada 38.168 peserta JKN yang memiliki besar klaim positif untuk kedua penyakit menggunakan pendekatan parametrik Inference Functions for Margins (IFM) dan semiparametrik Maximum Pseudo-Likelihood (MPL). Dependensi empiris diukur menggunakan Kendall's tau dan Spearman's rho, sedangkan kandidat copula dievaluasi melalui uji goodness-of-fit, AIC, dan BIC. Risiko agregat dievaluasi menggunakan variansi, Value-at-Risk (VaR) 99%, dan Conditional Tail Expectation (CTE) 99%. Berdasarkan pemodelan, distribusi Lognormal terpilih sebagai distribusi marginal kedua penyakit. Kendall's tau dan Spearman's rho empiris masing-masing sebesar 0,0561 dan 0,0716 menunjukkan dependensi positif yang lemah. Copula Gumbel dengan pendekatan semiparametrik MPL memberikan kecocokan terbaik, dengan Kendall's tau sebesar 0,0561. Dibandingkan dengan asumsi independen, model tersebut meningkatkan variansi agregat sekitar 12%, serta VaR 99?n CTE 99% masing-masing sekitar 3%. Hasil ini menunjukkan bahwa dependensi yang relatif lemah tetap memengaruhi pengukuran risiko agregat. Dengan demikian, pemodelan dependensi memberikan representasi risiko klaim kesehatan yang lebih sesuai dan dapat mendukung pengelolaan risiko finansial dalam Program JKN.

Cardiovascular disease is the catastrophic disease with the largest claim burden in Indonesia's National Health Insurance Program (JKN) and frequently coexists with diabetes mellitus. This association may indicate dependence between the claim amounts of the two diseases, such that ignoring this dependence may lead to underestimation or overestimation of aggregate claim risk. This study models the dependence between cardiovascular disease and diabetes mellitus claim amounts and evaluates its impact on aggregate risk measurement within the JKN Program. The analysis was conducted on 38,168 JKN participants with positive claim amounts for both diseases using the parametric Inference Functions for Margins (IFM) approach and the semiparametric Maximum Pseudo-Likelihood (MPL) approach. Empirical dependence was measured using Kendall's tau and Spearman's rho, while candidate copulas were evaluated using goodness-of-fit tests, AIC, and BIC. Aggregate risk was evaluated using variance, 99% Value-at-Risk (VaR), and 99% Conditional Tail Expectation (CTE). Based on the modeling results, the Lognormal distribution was selected as the marginal distribution for both diseases. The empirical Kendall's tau and Spearman's rho were 0.0561 and 0.0716, respectively, indicating weak positive dependence. The Gumbel copula estimated using the semiparametric MPL approach provided the best fit, with a Kendall's tau of 0.0561. Compared with the independence assumption, the model resulted in approximately 12% higher aggregate variance, while the 99% VaR and 99% CTE were each approximately 3% higher. These findings indicate that relatively weak dependence still affects aggregate risk measurement. Therefore, explicitly modeling the dependence structure provides a more representative assessment of health insurance claim risk and may support financial risk management within the JKN Program.

Kata Kunci : Dependensi, copula, risiko, diabetes melitus, kardiovaskular