Estimation of Production Function of Direct Health Care Services Delivered by Iranian Social Security Organization

Background and Objectives: Endometrial hyperplasia (EH) is an abnormal overgrowth of endometrium that may lead to endometrial cancer, especially when accompanied by atypia. The treatment of EH is challenging, and previous studies report conflicting results. Metformin (dimethyl biguanide) is an anti-diabetic and insulin sensitizer agent, which is supposed to have antiproliferative and anticancer effects and the potential to decrease cell growth in endometrium. While some studies have evaluated the anticancer effect of metformin, studies on its potential effect on endometrial hyperplasia are rare. To address this gap, in this comparative trial study, we evaluate the effect of additive metformin to progesterone in patients with EH. Methods: In this clinical trial, 64 women with EH were randomized in two groups. The progesterone-alone group received progesterone 20 mg daily (14 days/month, from the 14th menstrual day) based on the type of hyperplasia, and the progesterone-metformin group received metformin 1000 mg/day for 3 months in addition to progesterone. Duration of bleeding, hyperplasia, body mass index (BMI), and blood sugar (BS) of the patients were then compared between the two groups. Findings: NA mean age of 44.5 years, mean BMI of 29 kg/m2 and mean duration of bleeding of 8 days were calculated for the study sample. There was no significant difference in age, BMI, gravidity, bleeding duration, and duration of disease at baseline between the two groups. While all patients in the progesterone-metformin group showed bleeding and hyperplasia improvement, only 69% of the progesterone-alone patients showed such an improvement, with the difference between the two groups being significant (P = 0.001). Although the difference between two groups in the post treatment endometrial thickness was not significant (P = 0.55), post treatment BMI in the progesterone-metformin group was significantly lower than in the progesterone-alone group (P = 0.01). In addition, the BS reduction in the progesterone-metformin group was significantly larger than that in the progesterone-alone group (P = 0.001). Conclusions: Our results indicated that administration of progesterone 20 mg/day plus metformin 1000 mg/day can significantly decrease bleeding duration, hyperplasia, BMI and BS in women with EH.


Background and Objectives
Endometrial hyperplasia (EH) is an abnormal overgrowth of endometrium that may lead to endometrial cancer, especially when accompanied by atypia [1].
Although the effect appears only in 5% of asymptomatic patients, its prevalence in patients with PCOS and oligomenorrhea is about 20% [2].Body mass index (BMI) and nulliparity are two main risk factors for EH.Other risk factors include chronic anovulation, early menarche, late onset of menopause and diabetes [3], which are related to increased circulating estrogen [4].The treatment of EH is challenging and previous studies report conflicting results [5].Age, fertility, and severity of EH in histology are the most important factors determining the treatment option [5].Most studies have addressed hysterectomy in patients with atypical EH [5], particularly those with PCOS, and have led to conflicting results [5-11].

Evaluation of the Effect of Additive Metformin to Progesterone on Patients with Endometrial Hyperplasia
47 the urban population. 10While the health expenditures have jumped as high as 52.8% from 2014 to 2015, the corresponding resources have increased only 17%.This situation together with the accelerated pace of Iranian population aging is going to violate the balance between resources and demand in the SSO. 11Given the unique status of SSO in providing health care to the population, the above-mentioned situation requires immediate attention to keep SSO health care activities economically viable. 103][14][15][16] The average BOR of SSO hospitals is reported to be 76.1%, 11 close to that of OECD countries (77%), Belgium (78%) and France (75%), higher than that of the United States (65%,) and lower than that of Norway and Canada (90%) and the United Kingdom (85%), as reported in 2013. 13 the other hands, the ALS in SSO hospitals is reported to be 2.7 days which is extremely lower than that of the OECD countries (8.1 days) 11 and even below the minimum standard of 3.5 days required by the MOHME. 17This situation suggests that the relatively high BOR of SSO hospitals is achieved at the expense of compromised quality of health care represented by ALS.
While available data suggest that the SSO's health care organizations are already under extreme economic pressure to the extends that the quality of care is obviously scarified in the favor of reduced costs, the increasing gap between growth of expenditures and resources as revealed by recent statistics depict the possibility of financial crisis in these organizations in the upcoming years.The potentially critical situation ahead calls for application of scientific approaches to identify the current situation in detailed economic terms and seek for efficient solutions to rationalize the allocation of resources, improve quality of services, and attain higher efficiency. 18,191][22][23][24] These studies have shown that inefficiency of human resources can increase hospital costs due to the induced demand and total organizational costs.1][22][23][24] The useful insights obtained from these studies encourage further investigation of SSO hospitals' economy in quest to reach higher efficiency solutions.Thus, the present study was conducted to estimate the production function of direct health care services delivered by SSO hospitals and explore the contribution of input variables to an overall representative output, i.e. admission rate.Estimation of hospital production function would serve as a decision support tool to control costs, increase efficiency, and improve services quality.

Microeconometric Model
We used stochastic frontier approach (SFA) [25][26][27][28][29] to estimate production function.SFA is a parametric technique with relatively low sensitivity to outliers and high capability to distinguish random error from inefficiency, making it more suitable for hospital-specific data as compared with non-parametric methods such as data envelopment analysis. 30

Model Selection
SFA requires assumptions about the form of the production function and the distribution of the error terms.Cobb-Douglas and Transcendental functions are the 2 popular models frequently used to estimate hospital production. 31ile the Cobb-Douglas function is easy to estimate, its main drawback is that it assumes constant input elasticities and technical substitution rates.Alternatively, the Transcendental production function, which is an extension of the Cobb-Douglas model, allows for variable production elasticity. 32test was used to select between Cobb-Douglas (restricted) and transcendental (non-restricted) functions.
F-value was calculated to be 7.175 which is significantly higher than the tabular F value of 2.89 (df = 6196 and P = .01).Thus, the restricted model (Cobb-Douglas function) was found to be more suitable to capture our data.

Results
Table 1 shows the results of Cobb-Douglas function estimated based on our data.Of the coefficients of 6 major variables included in the model, the absolute largest value is related to active beds, followed by bed restoration interval, and physicians.The smallest absolute coefficient is obtained for other staff, and the only minus coefficients is related to bed restoration interval and paraclinical staff.All model coefficients except for those of paraclinical staff and other staff are statistically significant.

The Parameters and Efficiency Scores
Figure 1 shows the average technical efficiency of direct healthcare services provided by SSO hospitals during 2008-2014.As seen, the technical efficiency shows an increasing trend over the recent 7-year period.Although the increase of efficiency is marginal and limited to total of 1.4% from 2008 to 2014, the efficiency during this period is acceptable.Consistently, the coefficient η was calculated to be 0.015, indicating that inefficiency has decreased over time.The coefficient γ was calculated to be 0.581 which indicates that the role of inefficiency is greater than that of random factors.

The Return to Scale, Marginal Productivity and MRTS
The total input elasticity in 2-sided logarithmic model represents the status of return to the scale.The sum of inputs coefficients was calculated to be 1.1368 (> 1), indicative of an increasing return to scale for direct healthcare services.
Table 2 presents the estimated marginal production.
The by far highest marginal production input is represented by active beds, followed by physicians and nurses.Ac-  Table 3 shows the marginal rate of technical substitution (MRTS) of production factors.While the largest MRTS was related to nurse-physician ratio, the nurse-bed ratio represents the smallest value.The positive sign of the marginal rates of substitution between the three produc-

Discussion
This study was conducted to update the estimation of production function of SSO hospitals in terms of direct health care services.Our results predict that the increase of active beds by a factor of 10% would increase the hospital admissions up to 8.35% when all other factors remain constant.4][35][36][37][38] At the same time, the marginal product of active bed input showed that production in the direct healthcare services is capital-intensive.Therefore, inefficient use of active beds increases the ratio of cost to income in healthcare services, resulting in the financial imbalance.The annual cost of beds may reach up to be 1.5 times as much as the annual revenue in inefficient hospitals. 39In addition, since recruitment in the health sector should be based on the number of the beds, the unused bed capacity will also increase the costs of human resources.Based on the latest statistics (2014), the BOR of SSO hospitals is 76.1% 11 which shows the room for considerable improvement when compared with the corresponding rate in Norway and Canada (90%) and the United Kingdom (85%). 13The very high contribution of active beds in production of SSO hospitals, hence, encourages focused planning to achieve higher BOR as a potential strategy to narrow the increasing gap between the resources and the costs derived by the escalating demand.
Based on our results 10% increase in the number of physicians would increase hospital admissions by a factor of 0.73%.This finding is consistent with the studies of Jensen and Morrisey, 33 Hamidi, 34 Hadian et al, 36 Karami-Matin et al, 37 and Rezaei et al. 38 The present payment system and induced demand has led to the fact that the wage of physicians is responsible for a majority of the human resources cost in the Iranian health sector. 40,41The share of physician payment to the healthcare costs has increased recently due to the government-led health system reform, according to which healthcare tariffs have grown by over 250%, the burden of which being transferred largely to the insurance sector of SSO. 42On the other hands, MRTS revealed that for the same level of patient admission each unite of physician could be substituted by 1.8 unit of nurse.
Given the significantly lower wage of nurses as compared with the doctors, the SSO, thus, can reduce this burden by employing nurses in medical procedures they can perform instead of physicians.
[35][36][37][38] The bed restoration interval is an indicator of effective use of beds.Our results showed that 10% increase in the restoration interval will reduce hospital admission by nearly 2%.In the structure of the Iran's health system economy most revenue of hospital admissions is achieved by within 72 hours after admission. 43This fact, together with limited capacity of public hospitals has led to the optimal ALS to be targeted at 3.5 days in Iran. 17While this value is incomparably lower than the corresponding value in OECD countries (8.1 days), there is little evidence to show that factors contributing to quality of health care were considered in this targeting.The reported ALS in the direct healthcare services of the SSO is even lower (2.7 days) suggesting the unsatisfactory status of health care quality.
At the same time, the negative contribution of bed restoration interval (BRI) to production points to the economic challenges associated with improving quality by targeting higher ALS.
Input coefficients for paraclinical staff and other staff were insignificant.While these two inputs were also reported to be insignificant in relevant studies conducted by Ghaderi et al 35 and Mehraban, 24 Jensen and Morrisey, 33 Hadian et al, 36 Karami-Matin et al, 37 Rezaei et al 38 found positive significant effect for them.Nonetheless, the minus coefficient of paracinical staff indicates that the number of patient admissions reduces with the increase in paraclinical personnel.This can be explained by the notion that complete pre-admission checkup of patients in paraclinical/outpatient department may help to reduce nonemergency inpatient admissions.Inversely, the insignificant yet positive coefficient personnel's input is in line with the positive impact of adequate hospital staffing for admission, discharge, accounting, and other processes on hospital admission capacity.

Conclusions
Our results showed that health care services production in SSO is capital-intensive and highly dependent on active beds.The share of inefficiency component in the production process was found to be higher than that of random components, indicating the possibility of enhancing performance despite the very low rate of technical efficiency increase.The MRTS between physicians and nurses indicated that the growing burden of physicians' wage can

A
mathematical description of Cobb-Douglas production function is given in Additional File 1.The Data, Output, and Inputs Seven-year time series (2008-2015) were collected from the statistical yearbooks of SSO published in 2015.All Iranian provinces in which SSO owns medical centers were involved.Data were collected at provincial level and each province was considered as a single decision-making unit.The annual rate of patient admission was specified as the only output variables because of the limited information on other output indicators.Five input variables were incorporated into the model, including active beds (representing capital goods), the number of physicians, nurses, paraclinical staff, and personnel (representing the human resources), and the bed restoring interval (representing efficiency of bed utilization).Thus the output variable was assumed to follow the input variables as the following: Annual admissions = f (hospital beds, nurses, doctors, paraclinical staff, other staff, and the bed restoration interval) The Cobb-Douglas production was estimated using Int J Hosp Res 2016, 5(2):46-51 maximum likelihood estimation (MLE).Calculation was carried out using Frontier version 4.1 software.
Int J Hosp Res 2016, 5(2):46-51 be alleviated by employing nurses in the services they can deliver instead of physicians.Bed restoration interval showed significant negative contribution to production, pointing towards the challenges associated with improving quality by increasing ALS.The problem of inconsistency between quality services and high production, thus, persist indicating the need for in-depth reform in the structure of health care delivery.

Table 1 .
Maximum Likelihood Estimates of the Cobb-Douglas Regression Coefficients

Table 2 .
Marginal Production of Active Beds, Physicians, and Nurses Estimation of Production Function of Direct Heath Care Services Int J Hosp Res 2016, 5(2):46-51

Table 3 .
Marginal Rates of Technical Substitution between Active Beds, Physicians, and Nurses