Universal Journal of Public Health 10(5): 547-553, 2022
DOI: 10.13189/ujph.2022.100512
http://www.hrpub.org
Critical Illness Insurance Model for Breast Cancer
Patients Based on Chemotherapy Responses
M. Ivan Ariful Fathoni
1,2,*
, Gunardi
1
, Fajar Adi-Kusumo
1
, Susanna Hilda Hutajulu
3
,
Ibnu Purwanto
3
1
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia
2
Department of Mathematics Education, Universitas Nahdlatul Ulama Sunan Giri, Bojonegoro, Indonesia
3
Department of Internal Medicine, Universitas Gadjah Mada, Yogyakarta, Indonesia
*
Corresponding Author: fathoni@unugiri.ac.id
Received July 10, 2022; Revised September 29, 2022; Accepted October 11, 2022
Cite This Paper in the following Citation Styles
(a): [1] M. Ivan Ariful Fathoni, Gunardi, Fajar Adi-Kusumo, Susanna Hilda Hutajulu, Ibnu Purwanto, ”Critical Illness Insurance Model for Breast Cancer
Patients Based on Chemotherapy Responses,” Universal Journal of Public Health, Vol.10, No.5, pp. 547-553, 2022. DOI: 10.13189/ujph.2022.100512
(b): M. Ivan Ariful Fathoni, Gunardi, Fajar Adi-Kusumo, Susanna Hilda Hutajulu, Ibnu Purwanto (2022). Critical Illness Insurance Model for Breast Cancer
Patients Based on Chemotherapy Responses. Universal Journal of Public Health, 10(5), 547-553. DOI: 10.13189/ujph.2022.100512
Copyright ©2022 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of
the Creative Commons Attribution-NonCommercial International License 4.0
Abstract The insurance model in the form of Critical
Illness (CI) is generally structured by a multi-state model
that allows us to describe changes in insurance policies based
on status changes experienced. The model in this study
discusses the Markov process, which describes the critical
illness insurance policy in each state for a continuous-time.
Critical illness of breast cancer is modeled by several states
consisting of A is healthy or disease-free, B is early cancer,
C is cancer increase after chemo, and Y is dead from cancer.
This condition is based on the response to treatment after
chemotherapy. The first steps in this study are to assign a
function to the transition intensity from state to state and
the transition probability. The transition probability of the
multi-state model is the solution of the Kolmogorov forward
differential equation. The following discussion is to create
a formula for calculating the pure premium rate based on
age intervals. A case study based on medical record data at
dr.Sardjito Hospital is applied to calculate insurance premiums
based on policies and age groups. A case study based on med-
ical record data at dr.Sardjito Hospital is applied to calculate
insurance premiums based on policies and age groups. The
premium generated in this study is assumed to only depend on
the number and time of state transfers. This insurance model
can be an alternative to a more accurate insurance calculation
based on the incidence of displacement of critically ill patients,
especially breast cancer patients.
Keywords Critical Illness Insurance, Multi State Model,
Breast Cancer, Pure Premium Rate, Chemotherapy
1 Introduction
There are various types of health insurance products in the
world, and there are many traditions of actuarial calculations
that are used. The insurance model in the form of Critical Ill-
ness (CI) or Long Term Care (LTC) is generally structured by
a multi-state model that allows us to describe changes in insur-
ance policies provided based on status changes experienced.
The multi-state model is a model in a continuous stochastic
process that discusses the movement of a person in a limited
number of states. Status can be in the form of health, illness,
or death. This change or transfer of state is called a transition
or event.
The complexity of the multi-state model depends very much
on the number of states and the transition probability. Transi-
tion opportunities from one state to another are formed from
the transition intensity. The transition intensity provides the
rate of change from one state to another per unit time. The
Markov model in the multi-state model is widely used as a ba-
sis for the analysis and development of a transitional oppor-
tunity model. A person’s chance to transition from healthy to
sick status or vice versa in the future depends only on his cur-
rent state.
Several studies on critical illness insurance models have
been conducted. Gui and Macdonald [1] have researched the
epidemiology of Early-Onset Alzheimer’s Disease (EOAD) for
life insurance and critical illness insurance. Gutierrez and