Pemodelan Tingkat Klaim Asuransi Kesehatan Menggunakan Generalized Linear Model (GLM) Dengan Efek Spasial Berbasis Analisis Klaster Getis-Ord GI*

Hidayat, Mohammad Faryansyah (2026) Pemodelan Tingkat Klaim Asuransi Kesehatan Menggunakan Generalized Linear Model (GLM) Dengan Efek Spasial Berbasis Analisis Klaster Getis-Ord GI*. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Penerapan sistem iuran berbasis *community rating* pada Program Jaminan Kesehatan Nasional (JKN) berpotensi mengabaikan heterogenitas risiko yang tercermin dari perbedaan tingkat klaim kesehatan antarwilayah. Penelitian ini bertujuan memodelkan tingkat klaim asuransi kesehatan berbasis risiko regional pada tiga kategori penyakit (katastropik, skrining, dan lainnya) dengan menambahkan efek spasial melalui dua pendekatan estimasi, yaitu pendekatan *frequency-severity* (memodelkan frekuensi klaim berbobot dan besar klaim berbobot secara terpisah) serta pendekatan agregat (memodelkan tingkat klaim secara langsung). Unit analisis adalah 38 kabupaten/kota di Provinsi Jawa Timur tahun 2023. Pembobotan spasial berbasis kernel Gaussian digunakan untuk menghitung *Global Moran's I* pada sepuluh kovariat risiko kesehatan, yang menunjukkan enam kovariat, yaitu rasio penduduk miskin (x₂), prevalensi balita gizi buruk (x₄), persentase penduduk berkeluhan penyakit (x₆), persentase rumah bersanitasi layak (x₈), rata-rata konsumsi rokok (x₉), dan rata-rata lama rawat inap (x₁₀), memiliki autokorelasi spasial positif yang signifikan (α = 0,05). Keenam kovariat tersebut dianalisis lebih lanjut menggunakan *Getis-Ord Gi* untuk membentuk klaster *hot spot* dan *cold spot* sebagai variabel dummy spasial. Pemilihan distribusi GLM dilakukan secara empiris berdasarkan AIC *null model*, dengan distribusi Tweedie sebagai kandidat khusus pada pendekatan agregat. Penambahan dummy spasial terbukti menurunkan nilai AIC secara konsisten dan signifikan (uji *Likelihood Ratio Test*, p < 0,05) pada seluruh sembilan kombinasi model. Model terbaik menggunakan distribusi Gaussian, Inverse Gaussian, dan Tweedie untuk ketiga komponen kategori katastropik; Gamma untuk seluruh komponen kategori skrining; serta Gamma dan Inverse Gaussian untuk komponen kategori lainnya. Rasio penduduk miskin (x₂) secara konsisten berpengaruh negatif terhadap frekuensi dan tingkat klaim, mengindikasikan adanya hambatan akses nonfinansial di wilayah miskin, sedangkan rata-rata lama rawat inap (x₁₀) berpengaruh positif pada seluruh komponen kategori katastropik. Evaluasi akurasi menunjukkan tidak ada satu pendekatan yang secara konsisten unggul; pendekatan agregat memberikan hasil lebih baik pada kategori katastropik (MAPE 48,21% dibandingkan 50,61%) dan kategori lainnya (21,01% dibandingkan 24,22%), sedangkan pendekatan *frequency-severity* lebih unggul pada kategori skrining (47,98% dibandingkan 57,93%). Nilai MAPE yang masih tinggi pada kategori katastropik dan skrining mencerminkan keterbatasan GLM standar dalam merepresentasikan klaim *heavy-tailed* dengan jumlah observasi yang terbatas.
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The implementation of a *community rating* contribution system in Indonesia's National Health Insurance Program (JKN) has the potential to overlook risk heterogeneity reflected in differences in health claim rates across regions. This study aims to model regional risk-based health insurance claim rates for three disease categories (catastrophic, screening, and other) by incorporating spatial effects using two estimation approaches: the *frequency-severity* approach, which models weighted claim frequency and weighted claim severity separately, and the aggregate approach, which models claim rates directly. The unit of analysis consists of 38 regencies and cities in East Java Province in 2023. A Gaussian kernel-based spatial weight matrix was employed to compute *Global Moran's I* for ten health risk covariates, revealing that six covariates—poverty ratio (x₂), prevalence of malnourished children under five (x₄), percentage of residents with health complaints (x₆), percentage of houses with adequate sanitation (x₈), average cigarette consumption (x₉), and average length of inpatient stay (x₁₀)—exhibited significant positive spatial autocorrelation (α = 0.05). These six covariates were further analyzed using *Getis-Ord Gi* to identify *hot spot* and *cold spot* clusters, which were subsequently incorporated as spatial dummy variables. GLM distribution selection was performed empirically based on the *null-model* AIC, with the Tweedie distribution considered exclusively for the aggregate approach. The inclusion of spatial dummy variables consistently and significantly reduced AIC values (*Likelihood Ratio Test*, p < 0.05) across all nine model combinations. The best-performing models employed Gaussian, Inverse Gaussian, and Tweedie distributions for the three catastrophic-category components; Gamma distributions for all screening-category components; and Gamma and Inverse Gaussian distributions for the other-category components. Poverty ratio (x₂) consistently showed a significant negative effect on both claim frequency and claim rate, indicating the presence of non-financial barriers to healthcare access in poorer regions, while average length of inpatient stay (x₁₀) had a significant positive effect across all catastrophic-category components. Accuracy evaluation indicated that no single approach consistently outperformed the other: the aggregate approach achieved better performance for the catastrophic (MAPE 48.21% vs. 50.61%) and other (21.01% vs. 24.22%) categories, whereas the *frequency-severity* approach performed better for the screening category (47.98% vs. 57.93%). The relatively high MAPE values observed in the catastrophic and screening categories reflect the limitations of standard GLMs in modeling heavy-tailed claim distributions with a limited number of observations.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Autokorelasi Spasial, Generalized Linear Model, Getis-Ord Gi*, Global Moran’s I, Tingkat Klaim Claim Level, Generalized Linear Model, Getis-Ord Gi*, Global Moran’s I, Spatial Autocorrelation
Subjects:	H Social Sciences > HG Finance > HG8051 Insurance Q Science > QA Mathematics > QA278.3 Structural equation modeling.
Divisions:	Faculty of Mathematics, Computation, and Data Science > Actuaria > 94203-(S1) Undergraduate Thesis
Depositing User:	Mohammad Faryansyah Hidayat
Date Deposited:	22 Jul 2026 01:10
Last Modified:	23 Jul 2026 09:05
URI:	http://repository.its.ac.id/id/eprint/136463

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