lysis has been carried out by applying Autoregressive Integrated Moving Averages (ARIMA) model examining the forecast of the future levels of neonatal, infant and under five mortality rates in India and its states. Along with under-five and infant mortalities, the trend in the level of neonatal mortality (mortality within first 28 days) is also examined in view of highest numbers of deaths occurring in India in the first four weeks of human life [10] . The study is carried out with a view to refine understanding of the future course of mortality among children evaluating country’s present status in achieving the future Sustainable Development Goal 3 (SDG-3).

2. Data & Methods

The time series data (1981-2013) from the Sample Registration System [4] (Registrar General, India)on neonatal, infant and under-five mortalities in rural and urban areas of India and its 16 major states, are used for the projection of future mortality in case of neonatal, infant and under-five. For the state of Jammu and Kashmir, systematic time series data are not available and hence projection is not done for the state. Three states namely, Chhattisgarh, Jharkhand and Uttaranchal are included in their mother states like, Madhya Pradesh, Bihar and Uttar Pradesh respectively to prepare the time series data for a long period of 33 years.

Since, the data are used for the analysis from a common source, which is SRS, we do not require any specific assumption about the behavior of data series, which are required, if data points belong to different sources. The other source of data for infant and child mortality in India is National Family Health Survey (NFHS) but with limited three rounds and the fourth round of survey is in vogue. The level and pattern of infant and child mortality in both the surveys are found to be similar [11] . The major challenge in time series modeling is posed by the fact that the error residuals are correlated with their own lagged values violating the standard assumption of regression theory that disturbances are not correlated. We adopt here autoregressive integrated moving average (ARIMA) time series model to forecast the neonatal, infant and under-five mortalities for the period of 2015-2030 based on the data values taken from SRS for the period 1981-2013. The ARIMA model takes care of this serial correlation [12] by taking into account the historical fluctuations, trends, seasonality, cycles, prediction errors and non-stationarity of the data. The model helps to improve accuracy in forecasting [13] . The ARIMA modeling approach is pioneered by Box and Jenkins [14] and has been widely used in forecasting of different social and economic real life variables. The ARIMA time series models are preferred over simple and intuitive methods to obtain estimates and future projections by smoothing of data followed by extrapolation. This is due to the fact that simple trend analysis assumes that the past trends uninterruptedly continue in the future which cannot be assumed while modeling the demographic indicators because of very high uncertainty [15] . Furthermore, a time series model could be either stationary or non-stationary. The stationary model assumes that the process remains in equilibrium with a constant mean whereas in real life, empirical time series do not have a fixed mean. Hence, models are developed to describe homogeneous non-stationary behavior by supposing some suitable differences of the process to be stationary [16] . This type of model is known as non-stationary model and denoted as ARIMA (p, d, q) where, p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively. Here, parameter “p” provides information concerning the order of structural dependence existent between adjacent observations, indicating the existence of autocorrelation. The parameter “d” denotes the number of times the series must be differentiated in order to become stationary and the parameter “q” indicates the number of moving average terms. Thus, we have to identify whether the applied model is autoregressive (AR), moving averages (MA), autoregressive moving averages (ARMA) or auto regressive integrated moving averages (ARIMA).

The SRS data on neonatal, infant and under-five mortalities for the period of 1981-2013 were found to be non-stationary. They were therefore converted to stationary series by first transforming by taking its natural logarithm and then by applying successive differencing of the transformed series. To obtain the predicted values, the projected values were derived by taking antilogarithm. To build up the model for each state and India, whether the series is stationary or not is judged by estimating sample autocorrelation function (ACF) and partial autocorrelation functions (PACF). Autocorrelation refers to the way the observations in a time series was related to each other and is measured by the simple correlation between current observation (Yt) and observations from “p” periods before the current one (Yt−p). Partial autocorrelations are used to measure the degree of association between data points Yt and Yt−p when the Y-effects at other time lags 1, 2, 3 … p − 1 are removed. The stationarity is verified by applying an Augmented Dickey Fuller test. So by differencing the data series and testing by ADF, stationary model is determined, selection of the model for any state or India may vary according to the nature of time series data included in the analysis.

3. Results

In the present study, projection of NNMR, IMR and U5MR of major Indian states including India as a whole up to the year 2030 are presented. To identify the intra-state variations based on residence type, rural and urban areas of each state are projected separately along with the entire state under consideration. This projection exercise is done for a duration of 15 years, starting from 2015 and ending with 2030, which is actually the target year for SDG goals under Post-2015 Development Agenda. However, mortality projections are restricted for a small period because different important parameters related with socio-economic and demographic conditions in the country may change over time and affect the projected values. The Tables 1(a)-(c) are presented for infant mortality. Similarly, Tables 2(a)-(c) are included for under-five mortality. Lastly, Tables 3(a)-(c) are created for neonatal mortality. All the projected values in the tables are based on different fitted ARIMA (p, d, q) models. The predicted values from 2015 to 2030 of the Box-Jenkins results are illustrated in the tables. The forecasts and 95% forecast confidence intervals for IMR are shown in Figures 1(a)-(c) for the total, rural and urban areas of India respectively. Similar Figures 2(a)-(c) and Figures 3(a)-(c) are also presented for U5MR and NNMR respectively.

It has already been mentioned that SDG3 target has to be fixed to reach the child

(a) NOTE: ARIMA―Autoregressive integrated moving averages; LCL―lower confidence level; UCL―upper confidence level. The states Bihar, Uttar Pradesh and Madhya Pradesh include Jharkhand, Uttarakhand and Chhattisgarh respectively. ARIMA (p, d, q)―p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively (b) NOTE: ARIMA―Autoregressive integrated moving averages; LCL―lower confidence level; UCL―upper confidence level. The states Bihar, Uttar Pradesh and Madhya Pradesh include Jharkhand, Uttarakhand and Chhattisgarh respectively. ARIMA (p, d, q)―p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively (c) NOTE: ARIMA―Autoregressive integrated moving averages; LCL―lower confidence level; UCL―upper confidence level. The states Bihar, Uttar Pradesh and Madhya Pradesh include Jharkhand, Uttarakhand and Chhattisgarh respectively. ARIMA (p, d, q)―p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively

Table 1. (a) Predicted values of infant mortality rates (Total) and associated 95% confidence intervals using ARIMA model by states and India, 2015-2030; (b) Predicted values of infant mortality rates (Rural) and associated 95% confidence intervals using ARIMA model by states and India, 2015-2030; (c) Predicted values of infant mortality rates (Urban) and associated 95% confidence intervals using ARIMA model by states and India, 2015-2030.

(a) NOTE: ARIMA―Autoregressive integrated moving averages; LCL―lower confidence level; UCL―upper confidence level. The states Bihar, Uttar Pradesh and Madhya Pradesh include Jharkhand, Uttarakhand and Chhattisgarh respectively. ARIMA (p, d, q)―p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively (b) NOTE: ARIMA―Autoregressive integrated moving averages; LCL―lower confidence level; UCL―upper confidence level. The states Bihar, Uttar Pradesh and Madhya Pradesh include Jharkhand, Uttarakhand and Chhattisgarh respectively. ARIMA (p, d, q)―p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively (c) NOTE: ARIMA―Autoregressive integrated moving averages; LCL―lower confidence level; UCL―upper confidence level. The states Bihar, Uttar Pradesh and Madhya Pradesh include Jharkhand, Uttarakhand and Chhattisgarh respectively. ARIMA (p, d, q)―p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively

Table 2. (a) Predicted values of under-five mortality rates (Total) and associated 95% confidence intervals using ARIMA model by states and India, 2015-2030; (b) Predicted values of under-five mortality rates (Rural) and associated 95% confidence intervals using ARIMA model by states and India, 2015-2030; (c) Predicted values of under-five mortality rates (Urban) and associated 95% confidence intervals using ARIMA model by states and India, 2015-2030.

(a) NOTE: ARIMA―Autoregressive integrated moving averages; LCL―lower confidence level; UCL―upper confidence level. The states Bihar, Uttar Pradesh and Madhya Pradesh include Jharkhand, Uttarakhand and Chhattisgarh respectively. ARIMA (p, d, q)―p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively (b) NOTE: ARIMA―Autoregressive integrated moving averages; LCL―lower confidence level; UCL―upper confidence level. The states Bihar, Uttar Pradesh and Madhya Pradesh include Jharkhand, Uttarakhand and Chhattisgarh respectively. ARIMA (p, d, q)―p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively (c) NOTE: ARIMA―Autoregressive integrated moving averages; LCL―lower confidence level; UCL―upper confidence level. The states Bihar, Uttar Pradesh and Madhya Pradesh include Jharkhand, Uttarakhand and Chhattisgarh respectively. ARIMA (p, d, q)―p, d and q denote orders of auto-regression, integration (differencing) and moving average respectively

Table 3. (a) Predicted values of neonatal mortality rates (total) and associated 95% confidence intervals using ARIMA model by states and India, 2015-2030; (b) Predicted values of neonatal mortality rates (Rural) and associated 95% confidence intervals using ARIMA model by states and India, 2015-2030; (c) Predicted values of neonatal mortality rates (Urban) and associated 95% confidence intervals using ARIMA model by states and India, 2015-2030.

mortality by 2030 to half its level in 2010. Now, based on the previous SRS data of 2010, we would expect more specifically, by 2030, India should aiming to reduce neonatal mortality to 16.3 per 1000 live births, infant mortality to 23.5 per 1000 live birth and under-5 mortality to at least as low as 29.5 per 1000 live births. The Table 1(a) shows that, the projected IMR value would be 24 per thousand live birth on 2030 more or less fulfilling the target mentioned above. However, in rural area the projected rate is slightly higher (26) for India as a whole [Table 1(b)], but in urban area this rate would be 17 only [Table 1(c)]. Thus, India as a whole will meet the desired goal of IMR. Similarly, in case of U5MR [presented in Tables 2(a)-(c)], the projected mortality rate of 25 per thousand live birth easily reaching the 2030’s target mentioned above. For rural and urban areas of India, we would expect 28 and 16 under-five mortality rates respectively. Here also, there exists a wide gap in the projected values between rural and ur-

Figure 1. (a) Forecast of IMR of India (total) for the years 2015-2030; (b) Forecast of IMR of India (rural) for the years 2015-2030; (c) Forecast of IMR of India (urban) for the years 2015-2030.

Figure 2. (a) Forecast of U5MR (total) for the years 2015-2030; (b) Forecast of U5MR of India (rural) for the years 2015-2030; (c) Forecast of U5MR of India (urban) for the years 2015-2030.

Figure 3. (a) Forecast of NNMR of India (total) for the years 2015-2030; (b) Forecast of NNMR of India (rural) for the years 2015-2030; (c) Forecast of NNMR of India (urban) for the years 2015-2030.

ban areas of India. Now, the value of projected neonatal mortality (17) for India in the year 2030 is slightly higher than the targeted rate of 16.3. But these figures will be 20 and 9 respectively for rural and urban areas of India again indicating rural-urban divergence. Overall, in India with respect to Sustainable Development Goal-3, there is no or negligible shortfall of reaching the targets of NNMR, IMR and U5MR.The projected data in all the tables show that, India as a whole would be able to achieve the targets by 2030. But if we consider the world target of NNMR (12 per thousand live birth) and U5MR (25 per thousand live birth) mentioned earlier in the introduction section then, India will be only fulfilling the under-five mortality target.

Now, from past SRS data and projected figures [Figures 1(a)-3(c)] it may be observed, infant and under-five mortality rates are initially declining at a faster rate over time, but the rate of decline became slower from 1990’s onwards. Again, reduction of IMR over time is much slower than reduction in U5MR. Moreover, the gap between the IMR and NNMR either remains same or reduced very slowly over time. Also, the NNMR itself has been declining very slowly over time. Thus it can be said that, decline in the infant mortality rate was largely due to reduction in post-neonatal mortality, with neonatal mortality rate not contributing substantially. This indicates that deaths of infants within the first four weeks have relatively greater significance in determining the level of infant and under-five mortality rates in India. As a result, currently almost two-thirds of the IMR is being contributed by the neonatal mortality rate in India. A closer look into the NNMR and U5MR projected data [Tables 2(a)-(c) and Tables 3(a)-(c)] show that, share of neonatal death among under-five death is increasing steadily over the future projected years. This indicates slower decline in the neonatal mortality rate than the mortality rate for older children. Moreover, projected neonatal rates indicate higher proportion of neonatal death in rural areas of India.

Let us concentrate on individual state projected values for different mortality rates. Even though India as a whole is predicted to attain SDG-3 targets, at least eight, four and six states are not predicted to attain the targeted rates for IMR, U5MR and NNMR respectively. Detailed analysis of the major states show that, Andhra Pradesh, Bihar, Gujarat, Haryana, Himachal Pradesh, Karnataka, Kerala, Maharashtra, Punjab, Rajasthan, Tamil Nadu, and West Bengal have the possibility of achieving the SDG3 goal for U5MR. In case of IMR, Gujarat, Himachal Pradesh, Karnataka, Kerala, Maharashtra, Punjab, Tamil Nadu, and West Bengal states have the prospect of attaining the target. Major shortfall of 8 points and above is observed for the states like, Assam, Madhya Pradesh and Orissa in under-five target mortality rates. Shortfall of 3 points is seen for Uttar Pradesh state. Similar observations may be mentioned here for IMR in the selected states under study. In year 2030, the states like, Gujarat, Karnataka, Kerala, Maharashtra, Punjab, Tamil Nadu and West Bengal can achieve all the NNMR, IMR and U5MR targets of sustainable Development Goal 3. According to the previous report of Millennium Development Goals by India (Country Report 2014), the major States like, Bihar, Jharkhand, Madhya Pradesh, Chhattisgarh, Orissa, Uttar Pradesh and Uttarakhand, which are also the more populated states, are among the lagging states in reducing the poverty and not possibly able to achieve their target of halving the poverty ratio of 1990 by 2015 [1] . These States along with Maharashtra had about 193.5 million of people below poverty line in 2004-05 (64% of total below poverty line (BPL) population) and are expected to have nearly 198 million people below poverty line in 2015 (71% of total projected BPL population) [17] . So these heartland states of India along with Assam, Orissa and Rajasthan are also behind in effectively reducing neonatal, infant and under-five mortality rates. It is to be noted that during the projected years (Table 3(a)) the possibility of reducing neonatal deaths is very minimum in the backward states. Particularly in these backward states rural-urban differential of neonatal death will be very high compare to other states under consideration.

It has already been mentioned that, along with overall India and state wise projections of IMR, U5MR and NNMR, the present study also projected the same for rural and urban areas of each state separately. The U5MR, IMR and NNMR rates are quite very high in rural areas compared to urban areas over the years. The rural-urban differential of under-five and infant mortalities has decreased very rapidly till 1990, but after that the gap is more or less constant till 2008 and then has started to decline very slowly over the years. The rural-urban differential reduced over time may be due to the intervention of different health care and developmental programmes in different states of India. However, still there exists a constant difference due to more socio-economic and infrastructural benefits enjoyed by the urban sector compared to the rural sector in the country.

In case of under-five mortality, the states of Assam, Bihar, Madhya Pradesh, Orissa and Uttar Pradesh future projected values of ‘total’ and ‘rural’ areas are mostly coinciding throughout the projected period indicating the importance of rural child death in total death. For the states like, Punjab, Tamil Nadu, Karnataka and West Bengal, the future values for “total”, “rural” and “urban” are converging rapidly over the future years. These states were also the achiever of MDG4 target in the year 2015. However, Bihar shows convergence over the projected years. So we can expect rapid improvement of U5MR in future years for this state. In both the cases of NNMR and U5MR for Assam, Madhya Pradesh, Orissa and Rajasthan, a high difference in values has been observed between the rural and urban areas over the projected years.

4. Discussion

It may be concluded from the foregoing results that without appropriate intervention, most of the India’s backward and heartland states will not be able to reach the SDG3 target by 2030. Achievement of the targeted level will require further acceleration in the reduction of the U5MR and NNMR particularly in the highest burden states like, Assam, Madhya Pradesh (with Chhattisgarh), Orissa, Rajasthan and Uttar Pradesh (with Uttarakhand).

Particularly in the backward states extra efforts and resources will be needed to achieve reductions in under-five as well as neonatal mortality levels. However, further reductions in under-five mortality rates, to a large extent, depend on reducing the neonatal mortality. The focus now should be on neonatal mortality that has experienced hardly any improvement over the years. New tools and resources are needed to prevent these deaths. Thus, appropriate explanation and also intervention strategies are needed to overcome such a situation, which obstruct the policy maker in achieving the targeted goals. To address the issues of higher neonatal and early neonatal mortality, facility based newborn care services at health facilities should be established with high priority. Infrastructure strengthening, logistics and capacity building of Health workers must be ensured at the earliest for immediate intervention [1] . It has already been mentioned that, the rates for the components of under-five mortality are quite high in rural areas compared to urban areas over the years and the gap is consistent and continued over the years. Effective health care and developmental programmes are needed in the rural sector to reduce the gap in socio-economic and infrastructural benefits enjoyed by the urban sector compared to the rural sector in economy.

The relatively unfavorable international standing of India with respect to attainment of MDGs and SDGs in terms of under-five and neonatal mortalities mainly originates from the existence of substantial disparity in child survival and associated socioeconomic inequality in the country [18] . Factors contributing to the apparent stagnation and thereafter slowing decline of under-five mortality and its components include the lower socio-economic, cultural and health status of women and children in India [19] . Inequality in the use of health care services among the states also creates large differentials in U5MR components. Therefore, the implication of the present research is that government and other national and international organizations need to increase their efforts in reducing NNMR and U5MR, which calls for adjustments in planning and funding immediately. Thus, for the present 12th Five-year plan, strategic planning and effective implementation to the matter is needed. Particularly in the heartland states immediate mass investments in building basic health infrastructure are needed in rural areas to meet up with the goals. These states are extremely lacking in reproductive and child health services in the remote village areas. Finally, poverty eradication which is also a goal among the other SDGs needs appropriate household mapping and targeting irrespective of caste and community to reduce the burden of child death.

The present comprehensive analysis of the past trends, present status, and future course of mortality among children are not only vital for developing effective maternal and child health programs and policies but is crucial in the formulation of overall national health planning. In the present study a systematic effort has been done to bring together a discussion of long-term trends and differentials in child mortality in rural and urban areas of the country based on the available time series data of different states in India. However, the present mortality forecast model particularly for the children may be improved by in-depth understanding of the various causes and predictors of mortality. This may be done by inclusion of important dependent variables like, education, gender, poverty level etc. in the analysis. This can improve the accuracy of the projection. However, the inclusion of number of variables should not be large so that confusion and complications arise in using the mortality projections. To reduce this gap in future years much attention is needed in the rural sector for states which will improve the neonatal and under-five mortalities. This implies burden in neonatal mortality is mostly borne by the rural sectors in these states and needs appropriate attention.

At the end it may be mentioned that we have included the latest data of neonatal mortality (NNMR), infant mortality (IMR) and under-five mortality (U5MR) rates from India’s Sample Registration System (SRS). Hence, our interpretation relied completely on the quality of SRS data. An evaluation of SRS data exhibited omission rates of 1.8% for births and 2.5% for deaths [20] . Towards the method, there have been some research indicating that ARIMA time series modeling may be more suitable than the simple trend fitting approach, which suffers from model specification error [21] . Particularly, researchers have shown that the forecasting methodology can be improved by incorporating the ARIMA method [22] . However, use of ARIMA model for future forecasting and interpretation of the results requires caution because stationary time series system, which passes through different stages of development during the period under study, may also experience variations in coverage which can affect the quality of time series.

5. Conclusions

It may be concluded from the foregoing analysis that without immediate intervention, India's majority backward and heartland states would not be able to achieve the SDG3 target by 2030. Achievement of the targeted level will require further acceleration in the reduction of the U5MR and NNMR particularly in the highest burden states like, Assam, Madhya Pradesh (with Chhattisgarh), Orissa, Rajasthan, Uttar Pradesh (with Uttarakhand), and Bihar (with Jharkhand).

Further reductions in infant and under-five mortality rates, to a large extent, depend on reducing the neonatal mortality. Hence, focus should be on neonatal mortality that has hardly shown any improvement so far. New tools and resources are needed to prevent these deaths. Appropriate intervention strategies are needed to overcome such a situation, which obstruct the policy maker to achieve the targeted goals. To address the issues of higher neonatal and early neonatal mortality, facility based newborn care services at health facilities should be established with high priority. Infrastructure strengthening, logistics and capacity building of Health workers must be ensured at the earliest for immediate intervention. Effective health care and developmental programmes are needed in the rural sector to reduce the gap in socio-economic and infrastructural benefits enjoyed by the urban sector compared to the rural sector in economy.

The current comprehensive analysis of the past trends, present status, and future course of mortality among children is not only vital for developing effective maternal and child health programmes and policies but also crucial in the formulation of overall national health planning.

6. Strengths and Limitations of This Study

6.1. Strengths

・ The child mortality is a key element of achieving new targets for SDGs for India and its states.

・ It is prudent to forecast the child mortality and its components assessing the recent interventions in reducing such deaths.

・ The present paper has used autoregressive integrated moving average (ARIMA) time series model to forecast the neonatal, infant and under-five mortalities in India for the period of 2015-2030 by using data from the Sample Registration System (SRS) for the period 1981-2013.

・ The projection showed that India as a whole would be able to achieve the SDG targets of NNMR, IMR and U5MR by 2030.

6.2. Limitation

・ The ARIMA model, as all forecasting methods, is essentially ‘’backward looking‟, such that, the long term forecast eventually goes to be straight line at predicting series with turning points.

Competing Interests

The authors declare that they have no competing interests.

Author’s Contributions

PD, AP, DS and BKG conceived and design the study, PD and AKS contributed in the development of method and analysis of data, PM, RGM and NC drafted the manuscript. All authors contributed to the interpretation of results and critical review towards finalization of manuscript.

Data Sharing Statement

Data from Sample Registration System is available in public domain (www.censusindia.gov.in).

Cite this paper
De, P. , Sahu, D. , Pandey, A. , Gulati, B. , Chandhiok, N. , Shukla, A. , Mohan, P. and Mitra, R. (2016) Post Millennium Development Goals Prospect on Child Mortality in India: An Analysis Using Autoregressive Integrated Moving Averages (ARIMA) Model. Health, 8, 1845-1872. doi: 10.4236/health.2016.815176.
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