Introduction
Factors such as economic development and improvement of health status, increase in life expectancy, decrease in births and increase in life expectancy have made the world population face the phenomenon of aging. Paying attention to the health/treatment needs of the elderly population and their costs is one of the challenges of societies [1]. Considering the rapid growth of the elderly population in Iran [2], it is necessary to pay attention to their problems, especially the problems related to the increase in medical expenses. Identifying factors affecting the increase in medical expenses for the elderly, who are generally considered to be the inactive population, can help health policymakers in making appropriate decisions in this field. This study aims to identify the factors related to the increase in hospitalization costs of the elderly people with circulatory system diseases using generalized gamma marginalized two-part model.
Methods
In this retrospective cohort study, 335 older adults were selected randomly from among the patients in Imam Khomeini and Golestan hospitals in Ahvaz, Iran. Since angina pectoris and heart failure were the prevalent diseases in Khuzestan province and even in the country, the older adults with these diseases were selected. The inclusion criteria were age ≥60 years and suffering from heart disease or circulatory system disease. The variables of age, season of the patient’s visit to the hospital, gender, marital status, number of hospitalization days, and hospitalization in the intensive care unit (ICU) were included in the study as predictor variables. The total hospitalization costs of the patients were considered as the response variable. Zero values in the response variable indicates zero cost. Examining the assumption of normality by applying the Shapiro-Wilk test for cost data showed that this variable is skewed to the right and does not follow a normal distribution. In this study, 89% of patients incurred medical costs and 11% incurred no medical costs. Therefore, due to the fact that 11% of the response variable values are zero, the marginalized two-part model was used to model the data. It was performed in SAS v. 9.4 software and NLMIXED program. The logistic regression model was used to model the first part, which is based on zero or non-zero costs, and the generalized gamma model was used for the second part, which is related to the total cost. To present the results, the odds ratio (OR) values of the factors that were significant (P<0.05) were interpreted.
Results
The mean age of the elderly was 70.71 ± 8.27; 54% were female and 46% were male. The mean hospitalization costs were about 20±35 million Rials. The high value of the dispersion measure was due to the presence of zero values in the cost data. Using the generalized gamma- marginalized two-model model, it was determined that in the discrete part, the variables of hospitalization in ICU, marital status, age, number of hospitalization days, and admission in the autumn season had a significant positive effect on the treatment costs (P<0.05). The value of OR in the discrete part of the model for the variable of hospitalization status in ICU showed that the likelihood of spending cost in older patients hospitalized in ICU was 3.59 times higher than that in other patients. Regarding the marital status variable, the likelihood of medical expenses in married older patients was 0.36 times more than that in single older patients. In other words, the likelihood of having medical expenses in single older patients was 2.77 times more than that in married older patients. Regarding the age variable, OR value indicated that the likelihood of spending medical costs increases by 0.96 for each year of increase in age, provided that other variables remain constant. Assuming that other variables are constant, the likelihood of having medical costs increases by 1.49 for each day of increase in hospital stay. The probability of having a cost for the variable of the season of admission to the hospital was significant only in the autumn season such that its likelihood in patients admitted in the autumn was 0.20 times higher than that in patients admitted in the summer. In other words, the likelihood of having medical expenses in the summer was 5 times higher than that in the autumn,
According to the results of the continuous part of the model, the variables of age, marital status, number of hospitalization days, gender, and hospitalization status in ICU had a significant relationship with the increase in the treatment costs of the elderly (P<0.05). The value of OR for the variable of hospitalization status in ICU showed that the likelihood of spending costs in older patients hospitalized in ICU was 3.70 times higher than that in patients not hospitalized in ICU. Regarding the gender variable, the likelihood of spending costs in older men was 1.67 higher than that in older women. The likelihood of having medical costs increases by 1.11 for each day of increase in hospital stay. Regarding the marital status variable, the likelihood of having medical expenses in single older patients was 2 times more than that in married older patients. Regarding the age variable, OR value indicated that the likelihood of spending medical costs increases by 0.96 for each year of increase in age (from the age 60).
Discussion
The burden of medical expenses is heavier on the younger elderly. Older men incur more hospital costs than older women, and single elderly people incur more hospital costs than married ones. The increase in the number of hospitalization days causes a significant increase in hospital costs, and these costs increase dramatically when the elderly need to hospitalize in ICU. Therefore, these factors can increase the average medical expenses of the elderly. The results of this study can be extended to the future years as long as macro health policies are stable in the country.

Ethical Considerations
Compliance with ethical guidelines
This study was approved by the ethics committee of Ahvaz Jondishapur University of Medical Sciences (Code: IR.AJUMS.REC.1398.405).

Funding
This research has been financially supported by Jundishapor University of Medical Sciences, Ahvaz, with project number U-98100.

Authors' contributions
Study design: Kambiz Ahmadi Angali and Mohammad Reza Akhund; Drafting of the article: Kambiz Ahmadi Angali and Mahan Bahman Ziari; Statistical analysis: Mohammad Reza Akhund, Payam Amini, Kambiz Ahmadi Angali and Mahan Bahman Ziari; Editing of the final version of the article: Payam Amini, Amin Torabipour, Kambiz Ahmadi Angali and Mahan Bahman Ziari; Data collection: Amin Torabipour.

Conflicts of interest
The authors declared no conflict of interest.

Acknowledgements
The authors of this article appreciate and thank all the participants in this study.


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