1. INTRODUCTION
In the past decade, Universal Health Coverage (UHC) has arisen as a progressive goal that every nation ceaselessly desires to pursue to ensure their citizens access rights to good, sufficient medical care system, concurrently, keep them away from inequity and financial hardship. In 2013, Adam Wagstaff clarified a UHC must cover three dimensions: population coverage, health services coverage and financial protection (Wagstaff, 2013). Then, in 2014, Omanathan et al. (2014) stated that sustainable financial sources for moving toward Universal Health should be considered as the fourth objective in order to fully and correctly assess UHC in Vietnam (Somanathan et al., 2014). That inspires for the title “3 + 1 dimensions” of this paper.
In addition, the financial protection of UHC has made it a more crying need for Vietnam already, when their people are everyday suffering very high outofpocket (OOP) payments on medical care expenditures. It is believed to be literally not only the root of households’ financial hardship, but also invisible barriers for people to equally access to needed medical care services. Specifically, in 1998, OOP payments were reported to take accounts for 65% of households’ total health expenditure and finally reached its top at 72.5% in 2005 (Ministry of Health, 2010). In following years, the percentage of households spending at least 40% of their capacity for health care expenses was up to 5% and 17% in 2002 and 2008 respectively (Do et al., 2014).
Because of nonstop shifts in human wellbeing improvement technology, as well as diseases and population structure, UHC is somewhat a moving target rather than specific goals to complete then marked as ‘accomplished’. Thus, it is foremost to continuously have an uptodate monitoring framework, which will enable policymakers to reduce gaps in policies and keep solutions uptodate for current problems, or, at least adjust future expected goals in a rational way. Besides, forecasting accurately trends of factors to anticipate potential problems will also play an important role in providing the government with a probable perspective, from which there will be appropriate developing plans or preparation of beforehand solutions for possible challenges in future (World Health Organization, 2015). Moreover, people are usually confining their choices with Autoregressive integrated moving average (ARIMA) or Exponential smoothing themselves and the same others, which somehow cannot identify the significant forecasting values for future. For example, AnaMaria and Ghiorghe (2013) found it essential to analyze and forecast the evolution of the marine insurance market by the ARIMA method, but this technique still existed significant errors in forecasting. In a paper of Venezian (1985) A model of this process suggests that the rates set by such methods would create a quasicyclical pattern of underwriting profit margins. The details of the forecasting method determine the characteristics of the cylical pattern, so different lines may have different periods or different phases. Empirical data on major lines of property and liability insurance are consistent with the hypothesis that ratemaking methods contribute to the fluctuations of underwriting profit margins. Zhao and Chen (2007) introduced the method of building Auto Regressive Integrated Moving Average Model ARIMA(p, d, q) and reviews realizing, applies ARIMA Model to analyzing and forecasting Fujian's GDP, the satisfying results are obtained.
For those mentioned information, this paper is set to have the first purpose that is to develop an adequate managing framework to monitor Vietnam Universal Health Coverage. Also, data used for the system will be updated to the newest one and all are retrieved from reliable national information sources. Second one, several forecasting models in Grey Systems series such as Grey Model First Order One Variable GM (1, 1) Grey Verhulst Model, Discrete Grey Models DGM (1, 1) and DGM (2, 1) will be implemented to make prediction on some distinctive indices of Universal Health Coverage dimensions that are withdrawn from new managing framework found out. After that, Errors Inspection Tools such as MAPE, MAD, MSE and RMSE will be utilized to examine those models’ applicability and accuracy. These forecasting objectives are believed that forecasting is crucial over here to help national leaders in the field make good plans and policies for future development and solutions to the previous mentioned issues. The whole process is illustrated as in Figure 1.
2. LITERATURE REVIEW
2.1 Universal Health Coverage
Universal Health Coverage is a progressive goal that every nation ceaselessly desire to pursue, which nowadays consists of 4 dimensions: coverage in population, coverage in health service, financial protection and sustainable financial resources. In a succeed UHC environment, people will equally have access rights to medical care service as they need without any fears of facing financial hardship caused by high outofpocket payments.
2.2 Financing mechanisms for Universal Health Coverage and Social Health Insurance
Health financing is not all but an essential factor that let countries get closer to UHC. This decides whether a financial source is sustainable or not. Basically, whatever financing approaches toward Universal Health Coverage should include either tax – based (usually State budget) or social insurance – based financing (Health Insurance fund) or both. They have nature of public health financing mechanisms and can support each other (Reid, 2017).
Every nation has their own most suitable approaches to get along concerns related to moving toward Universal Health Coverage (WHO, 2018). Turkey, for instance, has been focusing on enhancement of equity and implementing Health Transformation Program as an effective approach to achieve UHC (Atun et al., 2013), whereas China has been making their efforts to protect inhabitants’ finance by establishing simultaneously 3 programs: New Rural Cooperative Medical Scheme (NRCMS), Urban Resident Basic Health Insurance (URBHI), and Medical Financial Assistance (MFA) (Marten et al., 2014).
To Vietnam, the government’s commitment is to ensure equity among citizens through implementing public health financing “universal health insurance”. That was clearly stated in the 6th meeting of Vietnam 12th Central Committee with Resolution No. 20/NQTW (Central Committee, 2017). Social Health Insurance with its united fund, to which people “prepaid” their healthcare expenses based on their capacity through paying premiums, is indeed a very important financing mechanism for UHC activities in Vietnam. In addition, SHI fund is the only scheme for citizens to join, which decides degree of financial protection they will benefit. In particular, those are in the scheme will receive same services from same sources, meanwhile those are outside will pay more outof pocket expenses (Lieberman and Wagstaff, 2009).
Somanathan et al. (2014) debated in 2014 that because Social Health Insurance (SHI) is a key tactic to attain UHC in Vietnam, then consequently, it is worth noting that “any assessment of Vietnam’s path to UHC must inevitably assess the implementation of SHI in Vietnam, and provide recommendations for strengthening this mechanism” (Somanathan et al., 2014). Framework of monitoring UHC developed by Ministry of Health in 2013 considered SHI’s development as an important indicator (Ministry of Health and Health Partnership Group, 2013). Yet, they miss the most recent problem with this mechanism, which is about deficit probability of SHI fund. Therefore, it is essential that not only Social Health Insurance progress but also the chance that its fund’s expenditure exceeds revenue should be assessed in the monitoring framework of UHC.
2.3 Develop Adequate Monitoring Framework
The monitoring framework, in other words, can be considered as navigation for governments to follow and ensure they will not misdirect their objectives of strategies or policies to UHC dimensions. According to WHO and World Bank, implementing UHC of a nation can be scrutinized and evaluated by 2 globallyused frameworks that are distinguished by health services coverage assessments basis based on Millennium Development Goals (MDGs) and Sustainable Development Goals (SDGs) (World Health Organization, 2015; World Health Organization, 2005). This research takes reference from 3 sources: the 2 bases recommended by WHO, Ministry of Health’s report and expected goals of Vietnam government mentioned in Resolution No. 20/NQTW Central Committee (2017), to develop a new system that is uptodate with recent matters (Ministry of Health, 2018a and 2018b). This new framework contains 45 indicators evaluating 11 different sections within 4 dimensions of UHC. Some of these indicators are going to be forecasted in later sections and are merely fundamentals of forecasting variables of the research.
2.4 Forecasting UHC Dimensions
In 1982, Deng was the one who initially developed Grey System Theory which includes other subsystems such as Grey Prediction, Grey Model, Grey Relational Analysis, etc. In recent times, Grey Systems and its basic model GM (1, 1) are applied widely in numerous scientific and socialrelated fields, for example, natural disasters, agriculture, geology (An et al., 2012) and electric power (Wang and Wu, 2008), economics (Nguyen and Tran, 2015), economic development, tourism (Nguyen and Tran, 2017), education and finance (Lin et al., 2004) and medical (Yang et al., 2018).
Recently, there have been studies related to health sectors that use Grey Forecasting Models such as research of Yang et al. (2018) about applying GM (1, 1) to make prediction on trends of typhoid and paratyphoid fevers in Wuhan City, China (Yang et al., 2018). Or, also in 2018, “demand prediction in health sector” research of Ceyda and Ferhan used both GM (1, 1) and TFGM (1, 1) to conduct forecasting then compared two models by using MAPE, MAD and MSE metrics (Zor and Çebi, 2018). It is obvious that Grey Model is becoming popular and applied in many fields. In academic research, some papers have raised interesting topics about forecasting demands and test results in some fields e.g., economics, tourism, consumption and so on (Nguyen and Tran, 2015, 2017, 2019).
3. METHODOLOGY DEVELOPMENT AND DATA COLLECTION
3.1 Methodology Development
3.1.1 Forecasting UHC Dimensions
“Grey Model First Order One Variable” or GM (1,1) in short is used to forecast only nonnegative data occurring in sequences of time (Julong, 1989). It is defined as following:
from which, then the first–order Accumulated Generated Operation sequence (1AGO) is
where (1) ${x}^{(1)}(k)={\displaystyle {\sum}_{i=1}^{k}{x}^{0}(i);with\hspace{0.17em}k=1,\hspace{0.17em}2,\hspace{0.17em}\dots ,\hspace{0.17em}n}$ Then we have GM (1, 1) original equation:
if the sequence of mean generation of adjacent neighbour from sequence X^{(1)} is
where ${z}^{(1)}(k)=\frac{1}{2}\left({x}^{(1)}(k)+{x}^{(1)}(k1)\right);with\hspace{0.17em}k=2,\hspace{0.17em}3,\hspace{0.17em}\dots \hspace{0.17em}n.$
Definition 3. Equation (2) can be solved by least square estimate.
When ${X}^{(0)},\hspace{0.17em}{X}^{(1)},\hspace{0.17em}and\hspace{0.17em}{Z}^{(1)}$ are defined as Definition 1 and 2 and if $\widehat{a}={\left[a,b\right]}^{T}$ is the parameters of this model, and
then the equation (2) satisfies $\widehat{a}={\left[a,b\right]}^{T}={({B}^{T}B)}^{1}{B}^{T}Y$.

Definition 5. Let $B,\hspace{0.17em}Y,\hspace{0.17em}\widehat{a}$ be defined the same as in Definition 3, (2) satisfies $\widehat{a}={(a,b)}^{T}={({B}^{T}B)}^{1}{B}^{T}Y$. Then, we have:

1/ The solution of (4) is called time response function and given by

2/ The time response sequence of (Eq.4) is
From (Eq.7) forecasting values of X^{(0)} can be obtained.
3.1.2 Grey Verhulst Model
Verhulst model was named after a biologist Pierre Franois Verhulst, which derives from the initial Grey Model GM (1, 1). It is noticeable that exponential data that shows monotonic trends can be operated well with GM (1, 1), whereas increasing non–monotonic processes is believed to be managed well with Verhulst model. This model is constructed as below:

Definition 1. Verhulst: When ${X}^{(0)},\hspace{0.17em}{X}^{(1)},\hspace{0.17em}and\hspace{0.17em}{Z}^{(1)}$ are defined as Definition 1 and Definition 2 of GM (1,1) above, then
is called the GM (1,1) power model, and
is the whitenization equation of GM(1,1) power model.

Definition 2. Then the solution of equation (9) is

Definition 3. When α = 2 , equation (8) becomes grey Verhulst model:
then

Definition 6. The solution of equation (13) is
Then time response sequence of the grey Verhulst model is:
3.1.3 Discrete Grey Model
Discrete Grey Model (DGM) basically has the form as following:
Which can be considered as a discretization of the GM (1, 1) model. Further theoretical information about this can be obtained in Liu and Lin’s book in 2010 (Liu et al., 2012).
3.2 Data Collection and Description
Chosen forecasting indicators for analyzing are extracted from some conspicuous indicators of the new framework, which do not draw whole but adequate parts of dimensions of UHC an are ultimately expected by the government that are stated clearly in recent Resolution 20/NQTW about Health Care. However, each indicator is a component of different other variables, we cannot directly make projections on them. Hence, to forecast indicators, we firstly make prediction on related variables, then through relationship formulas, forecasted indicators can thereof indirectly be found out (Table 1).
Besides, data used for the analysis are secondary data updated to the most recent ones (ranging from 2009 to 2017) from reliable national sources such as General Statistics Office of Vietnam (GSO, 2018), Health Statistics Year Book (HSYB) – Ministry of Health (MoH) or World Health Organization (WHO)’s data bank.
4. DATA ANALYSIS AND RESULTS
4.1 Forecast Variables and Errors Inspection
Figures 2 to 5 show process of implementing 4 forecasting models: GM (1, 1), Verhulst, DGM (1, 1) and DGM (2, 1) to predict variables of UHC indicators. Then, errors will be identified and only results from most appropriate accurate forecasting model are used to calculate forecasting values of indicators.
There are numerous tools for assessing accuracy of a forecasting model. Among which, Mean Absolute Percentage Error (MAPE) is commonly used and can be calculated by the formula:
n: number of forecasting steps
Ability to forecast of a single model can be accessed through MAPE results as following (Goodwin and Lawton, 1999;Nguyen and Tran, 2015):

•MAPE that is under 10%: “Excellent”

•MAPE that is between 10% to 20% can be interpreted as “Good”

•MAPE that is between 20% to 50% can be considered as “Reasonable”

•MAPE that is larger than 50% will be evaluated as “Poor”
Besides, we measure average of differences between forecasting values and actual values, which is called Mean Absolute Deviation or MAD in short with formula:
The smaller or lower value we get from MAD, the more precise forecasting model is. This helps compare accuracy of different forecasting models implemented.
Finally, in this section we also calculate Mean Squared Error and development of it – Root Mean Squared Error (RMSE), respectively through those two formulas:
In general, all four models are seen to have very high ability to forecast those variable, due to generating significantly small errors. It seems that GM (1, 1) as well as either Verhulst or DGM (1, 1) were all born to forecast Vietnam population when they have extremely small errors (0.0066%, 0.0068% and 0.0065% MAPE respectively). However, only results from the best model are chosen to calculate indicators. Therefore, in this case, results from DGM (1, 1) in application to forecast total population. Besides, results of GM (1, 1) from variable total number of doctors and those of Verhulst from nurse quantity will be utilized.
From calculations in the figures, it is obvious that DGM (2, 1) is not suitable for making prediction variables “Total number of pharmacists” (HW3) and “Total number of hospital beds” (I4) with extremely high MAPEs (2012.577% and 67.339% respectively). And in application to forecast the quantity of public hospitals (I5), although this model generates small errors, it is still not as good as the others. Meanwhile, Verhulst releases perfect results for variable HW3 or I5 and DGM (1, 1) is best for I4 with 6.711%, 4.958% and 0.116% MAPE respectively.
It can be seen that DGM (2, 1) also performs badly in the case of forecasting “Total number of under 1yearold children” individual with 2076.41% MAPE and Total number of those who are fully vaccinated with 2500.04% MAPE. Contrarily, in application to three variables above, Verhulst perform best for all with only 3.406%, 3.497% and 1.31% MAPE, thus, results from the model will be obtained to calculate indicators of UHC.
The figures show that, compared to the other 3 models, Verhulst once again, has excellent ability to forecast. Especially, when applied to make prediction on total health expenses and total number of people get malaria, the model generates percentage of MAPE that is less than a half of the other models that have good ability, which is 6.05% and 3.3% MAPE, whilst GM (1, 1) has 15.41% and 7.6% MAPE. Or, in another comparison, DGM (2, 1) is just assessed “Reasonable” with 22.91% MAPE in application to predict quantity of smear positive pulmonary, whereas, Verhults’s MAPE is only 0.791%.
In this section, it is conspicuous that best models for each variable are different. In particular, Verhulst is best matched to make projection on total Outofpocket expenses with 3.96% MAPE), forecasting results of total SHI fund revenue variable obtained from GM (1, 1) are generally the closest to actual values when its MAPE is 4.58%, or, there are no other models can be as suitable to forecast Total SHI expenditure as DGM (1, 1) with 4.87% MAPE.
We can see that, it is a disaster to apply DGM (2, 1) to forecast total government budget on paying health expenses with 23295.77% MAPE. Also, DGM (2, 1) has only “Reasonable” ability to forecast total SHI scheme. Or, in application to forecast total number of health insured people, it generates 5 times higher percentage of MAPE (5.39%) when compared to the others. Meanwhile, forecasting results for SHI scheme and total number of the health insured from Verhulst model has smallest errors in both cases, which are 6.91% and 1.723% MAPE respectively, so they will be used in next calculation. However, there is one thing should be noticed that the Verhulst forecast result for total number of the health insured in 2019 is 102.646 million people, which is higher than any Vietnamese population forecast results from any models. Hence, in this circumstance, Verhulst should only be applied for variable Total SHI scheme, and DGM (1, 1), which is at second place, will be applied for forecasting variable total health insured people number.
In implementing forecasting to the total amount of government budget, the differences between GM (1, 1)’s and DGM (1, 1)’s errors are not much, which are 6.95% and 6.97%. However, only results from best model are kept, and GM (1, 1) seems to be a little bit better than DGM (1, 1), thus, we will make use of GM (1, 1)’s results to calculate related indicators of this variable.
4.2 Calculating Forecasted Values of UHC Indicators
In this part, as mentioned above, we will utilize forecasting results of variables from best models analysed in section 4.1 to indirectly find out forecasting values of UHC indicators. Relationship between variables and their indicators is illustrated through formulas presented in Table 2 below:
5. CONCLUSION AND DISCUSSION
In brief, this research attempts to develop a system that is capable to keep track of most typical, conspicuous current issues or expected goals of governments distributed evenly entire 3 + 1 dimensions of UHC. In which, development of SHI financing mechanism and its fund’s deficit probability are included in the new framework. Those are also the most significant findings of this research within its first mission: “to develop a new adequate monitoring framework for Vietnam UHC”.
On the second mission: to present several forecasting models of Grey System Theory in application to make projection on variables of UHC indicators, analyse results with supports from errors inspection tools such as MAPE, MAD, MSE and RMSE indicates that Grey Model (1, 1), Grey Verhulst Model and Discrete Grey Model (1, 1) have higher ability to forecast and generate less errors in most of the cases. In contrast, Discrete Grey Model (2, 1) is incompatible with making prediction on most circumstances, some even have very high errors.
Forecasting results of UHC indicators shows that Vietnam has done well on preventive health care for children with the forecasting percentage of fully vaccinated newborn children is 96.5%. Concurrently, the Ministry of Health’s efforts on control communicable are also highly appreciated. Rates of the infected with those three deadly epidemics (HIV/AIDS, tuberculosis and malaria) are decreasing, especially malariaepidemic is predicted to be eradicated gradually (3.3% in 2019). In another facet, the increase in health workforces and infrastructure are not enough to adapt the change in population. Consequently, number of doctors (8.5 and 8.7), pharmacists (3.5) and nurses (11.5 and 11.4) per 10,000 populationare reported to remain unchanged.
About financing mechanism, SHI enrolment rate is projected to be 89.7%, however, the proportion of total SHI scheme and proportion of total government scheme over total health expenses are seen to remain unchanged in 2018 and 2019. That could be because growing speeds of those two schemes are not as fast as medical care expenses’. Yet, there is still a good side that outofpocket payments is under control (44.5% of total health expenses). The government should have some immediate policies and concrete actions to consolidate the strategic role of this national health insurance system or to make use government budget effectively. This is even on emergency, when it is foreseen that the SHI fund, which supports people to pay health expenses and supports other national health programs, will end up deficits with a balance of minus 326.53 and 703.65 million USD in the end of 2018 and 2019.
In overview, it is critical that health workforces as well as infrastructure should be invested more to adapt well with Vietnam current population development speed. Also, administration on SHI process in general, and, on using SHI fund in particular is recommended to be strengthened and there should be seriously strict punishments for individuals and organizations who dare to abuse SHI fund, avoid paying premiums, or commit illegal actions that do harm to the fund.