Trend of Neonatal Mortality in Nigeria from 1990 to 2017 using Time Series Analysis

The study examined the incidence of the rate of Neonatal Mortality in Nigeria. The incidence tested with use of Time Series Analysis (ARIMA). The trend plot of the incidence shows that there has been steady decrease in the incidence rate over the years. The series was stationarity using the Augmented Dickey-Fuller (ADF) Test, the result found to be stationary. The Correlogram of the incidence also supports the stationarity of the series at 1% level of significance. The model that best describes the incidence was tested using the Box-Jenkins four step procedures, which involve identification, explanation, diagnostic and forecasting. ARMA (1, 1), and ARIMA (1, 1, 1) models were tested, and ARIMA (1, 1, 1) model happens to be the best model that best fits the series. The time series analysis shows that neonatal mortality rate has reduced by 17.8% from 51. 7% in the year 1990 to 33. 9% in the year 2017. DOI: https://dx.doi.org/10.4314/jasem.v23i5.15 Copyright: Copyright © 2019 Usman et al. This is an open access article distributed under the Creative Commons Attribution License (CCL), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Dates: Received: 10 December 2018; Revised: 21 May 2019; Accepted 23 May 2019

Neonatal mortality is a significant public health problem worldwide, and accounts for more than 60% of newborn deaths before their first birthday [UNICEF 2008], neonatal mortality rate is the number of neonates dying before reaching 28 days of age, per 1,000 live births in a given year. Previous studies have shown that about half of infant deaths occur in the neonatal period. Knowledge of the determinants of neonatal mortality are essential for the design of intervention programs that will enhance neonatal survival. Therefore, this study was conducted to investigate the trends and factors associated with neonatal mortality in Nigeria from 1990 to 2017. The neonatal mortality can be prevented or reduced through the following measures, Policy National Health Bill implementation will strengthen primary care and make funds available for implementation of Integrated Maternal Newborn and Child Health (IMNCH) Strategies, expansion and provision of Neonatal Intensive Care Unit (NICU) services and equipment in the tertiary. Centers, increase in training on ENC and Neonatal resuscitation in all hospitals, adequate staffing -doctors, nurses, facilitators, training and re training of staff., NGOs organizations and other bodies working on maternal and Newborn survival.

Method of Data Analysis:
The methods of data analysis that will be employed in this study is the Time Series Analysis using Autoregressive Integrated Moving Average (ARIMA). The statistical softwares that will be used in this study are; Minitab and Gretl.
Autoregressive (AR) Model: n statistics and sigma process, an autoregressive (AR) model is a type of random process which is often used to model and predict various types of natural phenomena. The autoregressive model is one of a group of linear prediction formulae that attempt to predict an output of a system based on the previous outputs. The AR(p) indicates an autoregressive model of the order p. the AR(p) model is defined as: Where β are the parameters of the model, β0 is a constant (often omitted for simplicity) and Ԑt is a white noise.
Some constraints are necessary on the values of the parameters of this model in order that the model remain wide sense stationary. For example, processes in the AR(i) model with |pi|z| are not stationary. More generally, for an AR(p) model to be wide sense stationary, the root of the polynomial must lie within the unit circle i.e. each root 2, must satisfy 2,1<1 An AR(i) process is given by: Where Ԑt is white noise process with zero mean and variance 1 i.e.

= β
Moving Average (MA) Process: In statistics, a moving average is a calculation to analyze data points by creating series of averages of different of the full data set. A moving average is commonly used with time series data to smooth out short-term fluctuations and high-light longer-term trends or cycles.
Mathematically, moving average can be expressed as: Where Xi is the individual observations and n = the number of moving average.
In time series analysis, the moving average model is a common approach for modeling univariate time series. The moving average model specifies that the output variable depends linearly on the current and past values of a stochastic term. The moving average process of order q denoted by:   PAC (k) = AC after controlling the effects of (Yt, ……. Yt-k+1), (Yt-k). At lag (1), the (1) = PAC (1) always. At lag (2), the AC (2) = (ρ0 -ρ12)/ (1 -ρ12) for lag (3) and lags greater than 3, the formula is more complex. PAC (k) can be obtain as the coefficient of Yt-k in the regression. Y 2 = 0 + 1Y 2 + 2Y 2 + ⋯ + k − 1Y 2 This implies that PAC (k) = k. The PAC is also used to tell the maximum order of an auto regression process and test of a Moving Average Process.

RESULTS AND DISCUSSIONS
The time plot in Figure 1 shows that Neonatal Mortality Rate in Nigeria exhibits a curvilinear trend pattern. From Figure 2, the mean absolute percentage error (MAPE) = 2.24 which implies that the forecast of the data is off by 2% which means that percentage of error for the series is 2%. Likewise, the mean absolute deviation (MAD) = 1.05 which indicates that the series of good fit, as the lower the MAD, the better the fit of the series.
Stationarity Test: A stationarity test employed in testing whether or not a time series variable possesses a unit root. The hypothesis for this work is H0: There is a unit root for the series. H1: There is no unit root for the series. The series is stationary.
Decision rule: if p-value is less than the significance level alpha=0.01, we reject H0 and conclude H1. We do not reject H0 if otherwise. Unit-root null hypothesis: a = 1 a is the differenced order; Since the computed P-value = 0.0029 is greater than the significance level α=0.01, we reject H0 and conclude that the series is stationary. From Table 2, the p-value of both the AR and MA = 0.000 which is less than the level of significance α = 0.01, we reject H0 and conclude that the series are serially correlated. Hence the series is not fit.  Table 3.3, the Modified Box-Pierce (Ljung-Box) Chi-Square Statistic, the P-value at lag 12 and lag 24 = 0.000 and 0.000 which are less than the significance level α = 0.01 we reject H0 and conclude that the series are correlated i.e. insignificant. From Table 4, it was discovered that the best model fit to model the neonatal mortality rate is ARIMA (1, 1, 1) because the P-value is greater than the level of significance α = 0.01 at MA (1). Since the p-value = 0.320 is greater than the significance level α = 0.01, we fail to reject H0 and conclude that the series is uncorrelated. i.e. it is a very good model. Also studying the MS, it is the model with the smallest MS and hence the best model.  Table 5, the Modified Box-Pierce (Ljung-Box) Chi-Square Statistic, the P-value at lag 12 and lag 24 = 0.174 and 0.035 which are greater than the significance level α = 0.01 which also confirms that the series are uncorrelated i.e. significant. The Quantile plot of neonatal mortality rate appears to exhibit a straight line, which also confirms the normality of the residuals.
Forecasting: A forecast made to predict the future occurrence of neonatal mortality in Nigeria. So that it can serve as a help to federal government and to the health sector, for control measures and awareness. A forecast of 20 years was made using a base year of 2017 between 2018 to 2037.
The forecast shows that there will be a consistent decline in neonatal mortality rate in Nigeria in years to come. It is expected that neonatal mortality rate will in the next 20 years drop to 17.75% as against the present 33.9%, which means a decline of about 16%.
Conclusion: This study critically accessed the incidence of Neonatal Mortality in Nigeria between 1990 to 2017, the time plot of the incidence of neonatal mortality exhibits a downward movement which shows that neonatal mortality is been conquered gradually, but over the period of this study, there has been a significant decrease in the incidence of neonatal mortality. Nigeria is gradually winning the war against child mortality, especially war against neonatal mortality. More measures needs be put in place to further help in fighting neonatal mortality.