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Research article · 2018 · Full text

International Journal of Statistics and Applied Mathematics

Predicting infant mortality in India using time series models

Mritunjay Pal SinghRagini Singh

Volume 3(5) · Pages 33–42

Research areasIoT and GPS-based Vehicle Safety SystemsArtificial Intelligence and Decision Support SystemsForecasting Techniques and Applications

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Abstract

Author-written

Predicting infant mortality rate is an important aspect of study to prepare society and government for better or worst in future Many Programs might approach to fulfill the desired target in given time. In study an approach of time series models had used for prediction of infant mortality in India and some of its states. States had been selected by using the target sated in revised population policy 2017. In the study we found 13 states of India which does not have twenty eight per thousand infant mortality Rate in 2016 SRS data. We made our prediction using time series model named as Autoregressive Integrated Moving Average Method. This Chapter also compares these results to previous attempt to predict IMR Using ARIMA models.

Summary

Source-checked

Plain-language reading of the full paper, prepared with AI and checked against the text. Each point links to the authors' own words.

  1. Why it matters

    • Infant mortality rate (IMR) is used by global organizations like the WHO and UN as a key measure of a country's socio-economic development and social well-being. View evidence ↗

      Why it matters

      Infant mortality rate (IMR) is used by global organizations like the WHO and UN as a key measure of a country's socio-economic development and social well-being.

      In the paper's own words

      “The infant mortality is judged as a comprehensive indicator of socio-economic development.”

      Page 1

      Found in: Introduction

      Read it in the full textOpen PDF at page 1 ↗
    • The United Nations previously set a target to reduce the infant mortality rate by two-thirds between 1990 and 2015 as part of the Millennium Development Goals. View evidence ↗

      Why it matters

      The United Nations previously set a target to reduce the infant mortality rate by two-thirds between 1990 and 2015 as part of the Millennium Development Goals.

      In the paper's own words

      “Its target is to two third reduction in infant mortality rate (IMR) from 1990 to 2015 (United Nations, 2000).”

      Page 1

      Found in: Introduction

      Read it in the full textOpen PDF at page 1 ↗
    • India showed progress in reducing under-five child deaths, which dropped from 2.5 million in 2001 to 1.5 million in 2012. View evidence ↗

      Why it matters

      India showed progress in reducing under-five child deaths, which dropped from 2.5 million in 2001 to 1.5 million in 2012.

      In the paper's own words

      “India has made steady progress in reducing deaths in children younger than 5 years, with total deaths declining from 2.5 million in 2001 to 1.5 million in 2012 (UN, 2012) [10].”

      Page 1

      Found in: Introduction

      Read it in the full textOpen PDF at page 1 ↗
  2. The question

    • The study aims to predict the future infant mortality rate for India and several of its states using the Autoregressive Integrated Moving Average (ARIMA) model. View evidence ↗

      The question

      The study aims to predict the future infant mortality rate for India and several of its states using the Autoregressive Integrated Moving Average (ARIMA) model.

      In the paper's own words

      “This chapter is an attempt to predict infant mortality rate in India and some of its states up to sometime points in future Using ARIMA Model”

      Page 2

      Found in: Introduction

      Read it in the full textOpen PDF at page 2 ↗
  3. What they did

    • The study used Sample Registration System (SRS) data from 1980 to 2016, though for Chhattisgarh, Jharkhand, and Uttarakhand, data was only available from 2000 to 2016. View evidence ↗

      What they did

      The study used Sample Registration System (SRS) data from 1980 to 2016, though for Chhattisgarh, Jharkhand, and Uttarakhand, data was only available from 2000 to 2016.

      In the paper's own words

      “Data of SRS from 1980-2016 have been taken except for 3 states as Chhatisgarh, Jharkhand and Uttarakhand data is not available before 2000. Thus for these states data of IMR from 2000 to 2016 SRS is being considered.”

      Page 2

      Found in: Arima Model

      Read it in the full textOpen PDF at page 2 ↗
    • The ARIMA model parameters (p, d, q) were adopted from a previous study by De et al. (2016). View evidence ↗

      What they did

      The ARIMA model parameters (p, d, q) were adopted from a previous study by De et al. (2016).

      In the paper's own words

      “The estimated values of p,d,q are considered as the values of De et al. (2016) [8].”

      Page 2

      Found in: Arima Model

      Read it in the full textOpen PDF at page 2 ↗
  4. What they found

    • For Andhra Pradesh, the study predicted an IMR of 28 (95% CI: 27-30) by 2019, suggesting the state would meet the target that year. View evidence ↗

      What they found

      For Andhra Pradesh, the study predicted an IMR of 28 (95% CI: 27-30) by 2019, suggesting the state would meet the target that year.

      In the paper's own words

      “For year 2019 the predicted value in De et al. (2016) [8] is 33 whether in study the predicted value is 28 with confidence interval of 95% 27-30. This shows that the state achieve the target in year 2019.”

      Page 3

      Found in: Predicted Values for Andhra Pradesh

      Read it in the full textOpen PDF at page 3 ↗
    • Assam is predicted to reach the target IMR of 28 (95% CI: 23-31) in the year 2030. View evidence ↗

      What they found

      Assam is predicted to reach the target IMR of 28 (95% CI: 23-31) in the year 2030.

      In the paper's own words

      “Result shows that in 2030, De et al. (2016) [8] predicted value 36 our result shows the predicted value 28 with 95% confidence interval 23-31. This shows that the state achieve the target in year 2030.”

      Page 3

      Found in: Predicted Values for Assam

      Read it in the full textOpen PDF at page 3 ↗
    • Bihar is predicted to achieve the target IMR in 2023, with a predicted value of 27 (95% CI: 23-31). View evidence ↗

      What they found

      Bihar is predicted to achieve the target IMR in 2023, with a predicted value of 27 (95% CI: 23-31).

      In the paper's own words

      “For 2023 the predicted value in De et al. (2016) [8] 31 and in study the predicted value is 27 with 95% confidence interval 23-31. This shows that the state achieve the target in year 2023.”

      Page 3

      Found in: Predicted Values for Bihar

      Read it in the full textOpen PDF at page 3 ↗
    • Chhattisgarh is predicted to reach the target IMR of 28 (95% CI: 25-31) in 2020, one year after the 2019 goal. View evidence ↗

      What they found

      Chhattisgarh is predicted to reach the target IMR of 28 (95% CI: 25-31) in 2020, one year after the 2019 goal.

      In the paper's own words

      “In 2020 in our result shows the predicted value is 28 with 95% confidence interval 25-31. This shows that the state achieve the target one year later than 2019.”

      Page 3

      Found in: Predicted Values for Chhatishgarh

      Read it in the full textOpen PDF at page 3 ↗
    • Madhya Pradesh is predicted to achieve the target IMR of 28 (95% CI: 26-29) in 2024. View evidence ↗

      What they found

      Madhya Pradesh is predicted to achieve the target IMR of 28 (95% CI: 26-29) in 2024.

      In the paper's own words

      “For year 2024 the predicted value in De et al. (2016) [8] is 40 whether in study the predicted value is 28 with confidence interval of 95% 26-29. This shows that the state achieve the target in year 2024.”

      Page 4

      Found in: Predicted Values for Madhya Pradesh

      Read it in the full textOpen PDF at page 4 ↗
    • Uttar Pradesh is predicted to meet the target IMR of 28 (95% CI: 26-31) in 2027. View evidence ↗

      What they found

      Uttar Pradesh is predicted to meet the target IMR of 28 (95% CI: 26-31) in 2027.

      In the paper's own words

      “In case of year 2027 the predicted values for De et al. (2016) [8] 30, in study predicted value is 28 with 95% confidence interval 26-31. This shows that the state achieve the target in year 2027.”

      Page 5

      Found in: Predicted Values for Uttar Pradesh

      Read it in the full textOpen PDF at page 5 ↗
    • Uttarakhand is predicted to achieve the target IMR of 28 in 2022. View evidence ↗

      What they found

      Uttarakhand is predicted to achieve the target IMR of 28 in 2022.

      In the paper's own words

      “In case of year 2022 the predicted values in study 28 with 95% confidence interval 23-23. This implies that the target will be achieved in 2022.”

      Page 5

      Found in: Predicted Values for Uttarakhand

      Read it in the full textOpen PDF at page 5 ↗
    • For India as a whole, the study predicts the target IMR of 28 (95% CI: 27-30) will be achieved in 2022. View evidence ↗

      What they found

      For India as a whole, the study predicts the target IMR of 28 (95% CI: 27-30) will be achieved in 2022.

      In the paper's own words

      “In case of year 2022 the predicted values for De et al. (2016) [8] 30, in study predicted value is 28 with 95% confidence interval 27-30. Which interprets that India will achieve the target in 2022.”

      Page 5

      Found in: Predicted Values for India

      Read it in the full textOpen PDF at page 5 ↗
  5. What it means

    • The authors conclude that India can reach its overall target if specific focus is placed on the states that are lagging. View evidence ↗

      What it means

      The authors conclude that India can reach its overall target if specific focus is placed on the states that are lagging.

      In the paper's own words

      “This reflect that India can achieve the target if special focus on some states is been made.”

      Page 5

      Found in: Discussions and Conclusion

      Read it in the full textOpen PDF at page 5 ↗
    • The authors recommend periodic updates to the data to ensure more accurate future planning. View evidence ↗

      What it means

      The authors recommend periodic updates to the data to ensure more accurate future planning.

      In the paper's own words

      “It also suggest that it is better to study the data time to time for better future planning.”

      Page 5

      Found in: Discussions and Conclusion

      Read it in the full textOpen PDF at page 5 ↗

Visual summary

3 visuals

Illustrations explain the paper; charts are replotted from the paper's own table values.

AI-generated illustration
AI-generated conceptual illustration (Infants in India). It explains the idea and does not show study data.↗ Enlarge
ARIMA Prediction Concept
AI-generated conceptual illustration (Infants in India). It explains the idea and does not show study data.

AI-generated conceptual illustration (Infants in India). It explains the idea and does not show study data.

Open full-size image ↗

ARIMA Prediction Concept

AI-generated conceptual illustration (Infants in India). It explains the idea and does not show study data.

View source evidence ↗
Replotted from source data
Replotted from Table 1 (page 7) of the original paper. Every bar is the paper's own table value.↗ Enlarge
2015: SRS values vs In Paper
Replotted from Table 1 (page 7) of the original paper. Every bar is the paper's own table value.

Replotted from Table 1 (page 7) of the original paper. Every bar is the paper's own table value.

Open full-size image ↗

2015: SRS values vs In Paper

Replotted from Table 1 (page 7) of the original paper. Every bar is the paper's own table value.

View source evidence ↗
Replotted from source data
Replotted from Table 1 (page 7) of the original paper. Every bar is the paper's own table value.↗ Enlarge
2016: SRS values vs In Paper
Replotted from Table 1 (page 7) of the original paper. Every bar is the paper's own table value.

Replotted from Table 1 (page 7) of the original paper. Every bar is the paper's own table value.

Open full-size image ↗

2016: SRS values vs In Paper

Replotted from Table 1 (page 7) of the original paper. Every bar is the paper's own table value.

View source evidence ↗

Figures & tables

From the original paper
Trend Line of Infant Mortality in IndiaFigure 1Page 5Trend Line of Infant Mortality in IndiaFigure 1Page 6Correlogram of Infant Mortality in IndiaFigure 3Page 6Partial Correlogram of Infant Mortality in IndiaFigure 4Page 6Observed and Predicted Values of IMR in Andhra PradeshTable 1Page 7Observed and Predicted Values of IMR in AssamTable 2Page 7Observed and Predicted Values of IMR in BiharTable 3Page 7Observed and Predicted Values of IMR in ChhatisgarhTable 4Page 7Observed and Predicted Values of IMR in GujratTable 5Page 7Observed and Predicted Values of IMR in HaryanaTable 6Page 8Observed and Predicted Values of IMR in JharkhandTable 7Page 8Observed and Predicted Values of IMR in Madhya PradeshTable 8Page 8Observed and Predicted Values of IMR in MeghalayaTable 9Page 8Observed and Predicted Values of IMR in OdishaTable 10Page 8Observed and Predicted Values of IMR in RajasthanTable 11Page 9Observed and Predicted Values of IMR in Uttar PradeshTable 12Page 9Observed and Predicted Values of IMR in UttarakhandTable 13Page 9Observed and Predicted Values of IMR in IndiaTable 14Page 9
FULL TEXT Original article · reflowed for reading

Introduction

The infant mortality is judged as a comprehensive indicator of socio-economic development. Policy-making bodies like World Health Organization (WHO), United Nations (UN) have been using it as an important indicator to measure the socio-economic development of a country. It as often used as an indicator to understand the equity of distribution of resources and investment in health and social services (WHO, 2001) [12] . The UN currently uses IMR as a measure of social well-being and considers the trends of IMR as one of the indicators to achieve the Millennium Development Goals (MDG). Its target is to two third reduction in infant mortality rate (IMR) from 1990 to 2015 (United Nations, 2000). Thus study of underfive mortality trends and the possible explanations for such trends are of prime importance to understand socio-economic progress and investment in public health (De, 2011) visualized in sustainable development goals too. The International Conference on Primary health car held in Alma Ata in 1978 was the first global forum to consider how child and infant mortality could be reduced by the systematic development of primary health care system (WHO, 1978) [11] . Ahmad et al. (2000) [6] suggested that rapid rate of decline observed earlier was not sustainable given the slow rate of economic development and infusion of a very narrowly defined set of sophisticated technology-driven public health inventions. India has made steady progress in reducing deaths in children younger than 5 years, with total deaths declining from 2.5 million in 2001 to 1.5 million in 2012 (UN, 2012) [10] . Neonatal and 1-59 month mortality vary substantially between subregions of India as a result of the underlying differences in social and economic status, child nutrition status, health services, work culture, gender bias, and other factors that affect child mortality. The National Rural Health Mission recommends district-based planning for maternal child health programs and, indeed, for other disease-specific initiatives (Bhan, 2013) [4] . Benicio et al. (1985) [5] studied the declining trend of the infant mortality rate in Sao-Paulo during the 1980 in relation to the improvement of social conditions, especially the increased numbers of households with mains water, the schooling levels of parents, and the expanded reach of health services as reflected in vaccination coverage and hospital attendance. Concurrent with the improving profile of infant mortality in the city, the rise in mortality associated with perinatal events and nutritional deficiencies in the poorest areas reflected increasing social inequalities (Monteiro, et al. 1995) [1] .

Proposing and planning the programs related to infant mortality are based on the present conditions to improve future. That initiates the curiosity that what will be future if no new programs or plans are included in population at present. Which turns to idea of future prediction. General future predictions are made by the base of some past data. Sample registration system data is being used for past study. To predicting the infant Mortality various methods are available. In recent times the time series models are considered quite useful in predicting the demographic phenomenon. These methods are Simple moving average (SMA), Exponential Smoothing System (SES), Autoregressive integrated moving Average method (ARIMA), Neral Network (NN) and Crosten. Tripathi et al. (2018) [9] proposed the Baysian Approach of ARIMA model in Indian Context to predict the total fertility rate. De et al. (2016) [8] Suggested to use the ARIMA model to predict Child mortality in some states of India for the duration of 2015-2030. He also suggested that if a predicted values in future vary from original values that might effect whole other predicted values. This chapter is an attempt to predict infant mortality rate in India and some of its states up to sometime points in future Using ARIMA Model using De et al. (2016) [8] results with its corresponding diagnostics and also being compared to results of those states whose infant mortality had predicted by De et al. (2016) [8] because observed infant mortality of 2014, 2015 and 2016 are different from predicted values in De et al. (2016) [8] . Now for better studies we move to data and methodology section.

Data and Methodology

Data and Methodology

Arima Model Assumptions

The main Assumption is that ARIMA models is of stationarity of process over time or a process whose Unconditional joint probability distribution does not change when shifted in time if not it will transformed into it before applying ARIMA. (Box and Jenkins(1970)).

Arima Model

Given a time series of data 𝑋 𝑡 where t is an integer index and the 𝑋 𝑡 are real numbers, an ARIMA (𝑝, 𝑞) model is given by

Where 𝐿 is the lag operator, the 𝛼 𝑖 are the parameters of the autoregressive part of the model, the 𝜃 𝑖 are the parameters of the moving average part and the 𝜀 𝑡 are error terms. Standard Form of ARIMA Consists with three Values (p,d,q) where p is autoregressive term, d is the difference, and q is moving average estimate, to evaluate value of (p,d,q) different graphs have been used over time. In this chapter the values of IMR have been predicted for above states and India to obtain that when the target of 28/1000 achieved by India and these states and How many years the states are behind or forward to achieve the target than India. The estimated values of p,d,q are considered as the values of De et al. (2016) [8] . Data of SRS from 1980-2016 have been taken except for 3 states as Chhatisgarh, Jharkhand and Uttarakhand data is not available before 2000. Thus for these states data of IMR from 2000 to 2016 SRS is being considered.The data of Telangana is not available before 2015 so prediction for Telangana not been made.

Results

When we study diagnostic of model we found that the model satisfies the value of Arima (0, 1, 1) for India which is same as the values considered in De et al. (2016) [8] . So using these results we go for the predicted values for states considered.

Predicted Values for Andhra Pradesh

Result shows the predicted values for Andhra Pradesh as in 2015 SRS value is 37, in De et al. (2016) [8] the predicted value was 37 our result shows the predicted value 36 with 95% confidence interval 35-37. For year 2016 SRS value is 34 De et al. (2016) [8] predicted values 36, in study this value is 34 with 95% confidence interval 33-35. In case of year 2017 the predicted values for De et al. (2016) [8] 35, in study predicted value is 32 with 95% confidence interval 31-33. For 2018 the predicted value in De et al.

(2016) [8] 34 and in study the predicted value is 30 with 95% confidence interval 29-31. For year 2019 the predicted value in De et al. (2016) [8] is 33 whether in study the predicted value is 28 with confidence interval of 95% 27-30. This shows that the state achieve the target in year 2019.

Predicted Values for Assam

Result shows the predicted values for Assam as in 2015 SRS value is 47, in De et al. (2016) [8] the predicted value was 52 our result shows the predicted value 49 with 95% confidence interval 47-50. For year 2016 SRS value is 44 De et al. (2016) [8] predicted values 51, in study this value is 47 with 95% confidence interval 45-49. In case of year 2017 the predicted values for De et al. (2016) [8] 50, in study predicted value is 45 with 95% confidence interval 43-47. For 2018 the predicted value in De et al.

(2016) [8] 49 and in study the predicted value is 43 with 95% confidence interval 41-45. For year 2019 the predicted value in De et al. (2016) [8] is 48 whether in study the predicted value is 41 with confidence interval of 95% 39-44. This shows that the state does not achieve the target in year 2019. Result also shows for Assam in 2020, in De et al. (2016) [8] the predicted value was 47 our result shows the predicted value 40 with 95% confidence interval 37-42. For year 2021, De et al. (2016) [8] predicted values 46, in study this value is 38 with 95% confidence interval 35-41. In case of year 2022 the predicted values for De et al. (2016) [8] 45, in study predicted value is 37 with 95% confidence interval 34-39. For 2023 the predicted value in De et al. (2016) [8] 44 and in study the predicted value is 36 with 95% confidence interval 33-39. For year 2024 the predicted value in De et al. (2016) [8] is 43 whether in study the predicted value is 35 with confidence interval of 95% 32-38. Result suggest that the predicted values for Assam as in 2025, in De et al. (2016) [8] the predicted value was 42, our result shows the predicted value 34 with 95% confidence interval 31-37. For year 2026, De et al. (2016) [8] predicted value 41, in study this value is 33 with 95% confidence interval 30-35.

In case of year 2027 the predicted values for De et al. (2016) [8] is 40, in study predicted value is 32 with 95% confidence interval 29-36. For 2028 the predicted value in De et al. (2016) [8] is 39 and in study the predicted value is 31 with 95% confidence interval 27-34. For year 2029 the predicted value in De et al. (2016) [8] is 38 whether in study the predicted value is 29 with confidence interval of 95% 25-33. Result shows that in 2030, De et al. (2016) [8] predicted value 36 our result shows the predicted value 28 with 95% confidence interval 23-31. This shows that the state achieve the target in year 2030.

Predicted Values for Bihar

Result shows the predicted values for Bihar as in 2015 SRS value is 42, in De et al. (2016) [8] the predicted value was 39, our result shows that predicted value 41 with 95% confidence interval 38-43. For year 2016 SRS value is 38 De et al. (2016) [8] predicted values 38, in study this value is 39 with 95% confidence interval 36-41. In case of year 2017 the predicted values for De et al. (2016) [8] 37, in study predicted value is 37 with 95% confidence interval 35-40. For 2018 the predicted value in De et al.

(2016) [8] is 36 and in study the predicted value is 36 with 95% confidence interval 33-39. For year 2019 the predicted value in De et al. (2016) [8] is 35 whether in study the predicted value is 35 with confidence interval of 95% 31-37. This shows that the state does not achieve the target in year 2019. Result also shows the predicted values for Bihar as in 2020 De et al. (2016) [8] the predicted value was 34 our result shows the predicted value 32 with 95% confidence interval 29-36. For year 2021 De et al.

(2016) [8] predicted values 33, in study this value is 31 with 95% confidence interval 27-34. In case of year 2022 the predicted values for De et al. (2016) [8] 32, in study predicted value is 29 with 95% confidence interval 25-33. For 2023 the predicted value in De et al. (2016) [8] 31 and in study the predicted value is 27 with 95% confidence interval 23-31. This shows that the state achieve the target in year 2023.

Predicted Values for Chhatishgarh

Result shows the predicted values for Chhatisgarh as in 2015 SRS value is 41, our result shows the predicted value 40 with 95% confidence interval 38-42. For year 2016 SRS value is 39, in study this value is 37 with 95% confidence interval 35-39. In case of year 2017 predicted value is 35 with 95% confidence interval 33-37. For 2018 the predicted value is 33 with 95% confidence interval 30-35. For year 2019 the predicted value in study is 30 with confidence interval of 95% 28-30. This shows that the state does not achieve the target in year 2019. In 2020 in our result shows the predicted value is 28 with 95% confidence interval 25-31. This shows that the state achieve the target one year later than 2019.

Predicted Values for Gujrat

Result shows the predicted values for Gujrat as in 2015 SRS value is 33, in De et al. (2016) [8] the predicted value was 34 our result shows the predicted value 33 with 95% confidence interval 32-35. For year 2016 SRS value is 30 De et al. (2016) [8] predicted values 32, in study this value is 31 with 95% confidence interval 30-33. In case of year 2017 the predicted values for De et al. (2016) [8] 31, in study predicted value is 29 with 95% confidence interval 28-31. For 2018 the predicted value in De et al.

(2016) [8] 30 and in study the predicted value is 27 with 95% confidence interval 26-29. This shows that the state achieve the target in year 2019.

Predicted Values for Haryana

Result shows the predicted values for Haryana as in 2015 SRS value is 39, in De et al. (2016) [8] the predicted value was 34 our result shows the predicted value 36 with 95% confidence interval 35-38. For year 2016 SRS value is 33 De et al. (2016) [8] predicted values 32, in study this value is 34 with 95% confidence interval 33-36. In case of year 2017 the predicted values for De et al. (2016) [8] 31, in study predicted value is 32 with 95% confidence interval 30-34. For 2018 the predicted value in De et al.

(2016) [8] 30 and in study the predicted value is 30 with 95% confidence interval 28-32. For year 2019 the predicted value in De et al. (2016) [8] is 29 whether in study the predicted value is 28 with confidence interval of 95% 26-30. This shows that the state achieve the target in year 2019.

Predicted Values for Jharkhand

Result shows the predicted values for Jharkhand as in 2015 SRS value is 32, result shows the predicted value 31 with 95% confidence interval 29-33. For year 2016 SRS value is 29, in study this value is 29 with 95% confidence interval 26-32. In case of year 2017 the predicted values in study is 27 with 95% confidence interval 24-30. This shows that the state achieve the target before year 2019.

Predicted Values for Madhya Pradesh

Result shows the predicted values for Madhya Pradesh as in 2015 SRS value is 50, in De et al. (2016) [8] the predicted value was 51 our result shows the predicted value 49 with 95% confidence interval 47-50. For year 2016 SRS value is 47 De et al. (2016) [8] predicted values 50, in study this value is 47 with 95% confidence interval 46-48. In case of year 2017 the predicted values for De et al. (2016) [8] is 49, in study predicted value is 44 with 95% confidence interval 43-45. For 2018 the predicted value in De et al.

(2016) [8] 47 and in study the predicted value is 41 with 95% confidence interval 40-43. For year 2019 the predicted value in De et al. (2016) [8] is 46 whether in study the predicted value is 39 with confidence interval of 95% 38-40. This shows that the state does not achieve the target in year 2019. Result also shows in 2020, in De et al. (2016) [8] the predicted value was 45 our result shows the predicted value 36 with 95% confidence interval 35-37. For year 2021, De et al. (2016) [8] predicted values 43, in study this value is 33 with 95% confidence interval 32-35. In case of year 2022 the predicted values for De et al. (2016) [8] is 42, in study predicted value is 31 with 95% confidence interval 29-32. For 2023 the predicted value in De et al. (2016) [8] is 41 and in study the predicted value is 30 with 95% confidence interval 28-31. For year 2024 the predicted value in De et al. (2016) [8] is 40 whether in study the predicted value is 28 with confidence interval of 95% 26-29. This shows that the state achieve the target in year 2024.

Predicted Values for Meghalaya

Result shows the predicted values for Meghalaya as 2015 SRS value is 42, our result shows the predicted value 45 with 95% confidence interval 40-50. For year 2016 SRS value is 39, in study this value is 38 with 95% confidence interval 36-49. In case of year 2017 predicted value is 37 with 95% confidence interval 34-48. For 2018 predicted value is 36 with 95% confidence interval 33-48. For year 2019 in study the predicted value is 35 with confidence interval of 95% 31-47. This shows that the state does not achieve the target in year 2019. Result also shows the predicted values in our study for 2020 is 32 with 95% confidence interval 30-47. For year 2021, in study this value is 31 with 95% confidence interval 19-44. In case of year 2022 the predicted values, in study predicted value is 30 with 95% confidence interval 17-44. For 2023 the predicted value, in study is 29 with 95% confidence interval 16-43. For year 2024 the predicted value in study is 28 with confidence interval of 95% 14-43. This shows that the state achieve the target in year 2024.

Predicted Values for Odisha

Result shows the predicted values for Odisha as in 2015 SRS value is 46, in De et al. (2016) [8] the predicted value was 48 our result shows the predicted value 45 with 95% confidence interval 44-47. For year 2016 SRS value is 44, De et al. (2016) [8] predicted values 46, in study this value is 42 with 95% confidence interval 41-44. In case of year 2017 the predicted values for De et al. (2016) [8] 45, in study predicted value is 41 with 95% confidence interval 40-43. For 2018 the predicted value in De et al.

(2016) [8] 44 and in study the predicted value is 39 with 95% confidence interval 38-40. For year 2019 the predicted value in De et al. (2016) [8] is 42 whether in study the predicted value is 36 with confidence interval of 95% 34-37. This shows that the state does not achieve the target in year 2019. Result also shows for 2020, in De et al. (2016) [8] the predicted value was 41 our result shows the predicted value 34 with 95% confidence interval 32-35. For year 2021, De et al. (2016) [8] predicted value 40, in study this value is 33 with 95% confidence interval 31-34. In case of year 2022 the predicted values for De et al. (2016) [8] 39, in study predicted value is 31 with 95% confidence interval 30-32. For 2023 the predicted value in De et al. (2016) [8] is 37 and in study the predicted value is 30 with 95% confidence interval 28-41. For year 2024 the predicted value in De et al. (2016) [8] is 36 whether in study the predicted value is 29 with confidence interval of 95% 27-30. Result shows the predicted values for state, in 2025, in De et al. (2016) [8] was 35 our result shows the predicted value 28 with 95% confidence interval 24-30. This shows that the state achieve the target in year 2025.

Predicted Values for Rajasthan

Result shows the predicted values for Rajasthan as in 2015 SRS value is 43, in De et al. (2016) [8] the predicted value was 38 our result shows the predicted value 43 with 95% confidence interval 41-44. For year 2016 SRS value is 41 De et al. (2016) [8] predicted values 36, in study this value is 40 with 95% confidence interval 39-42. In case of year 2017 the predicted values for De et al. (2016) [8] 35, in study predicted value is 38 with 95% confidence interval 36-39. For 2018 the predicted value in De et al.

(2016) [8] 33 and in study the predicted value is 35 with 95% confidence interval 33-37. For year 2019 the predicted value in De et al. (2016) [8] is 32 whether in study the predicted value is 33 with confidence interval of 95% 31-35. This shows that Country does not achieve the target in year 2019. In 2020, in De et al. (2016) [8] the predicted value was 30 our result shows the predicted value 30 with 95% confidence interval 28-32. For year 2021 De et al. (2016) [8] predicted values 29, in study this value is 28 with 95% confidence interval 25-30. Which interprets that Rajasthan will achieve the target in 2021.

Predicted Values for Uttar Pradesh

Result shows the predicted values for Uttar Pradesh as in 2015 SRS value is 46, in De et al. (2016) [8] the predicted value was 46 our result shows the predicted value 46 with 95% confidence interval 45-48. For year 2016 SRS value is 43 De et al. (2016) [8] predicted value 45, in study this value is 44 with 95% confidence interval 44-45. In case of year 2017 the predicted values for De et al. (2016) [8] 43, in study predicted value is 43 with 95% confidence interval 41-44. For 2018 the predicted value in De et al.

(2016) [8] 42 and in study the predicted value is 42 with 95% confidence interval 29-31. For year 2019 the predicted value in De et al. (2016) [8] is 40 whether in study the predicted value is 41 with confidence interval of 95% 40-43. This shows that the state does not achieve the target in year 2019.Result also shows the predicted values for Uttar Pradesh as in 2020, in De et al. (2016) [8] the predicted value was 39 our result shows the predicted value 39 with 95% confidence interval 37-40. For year 2021 De et al.

(2016) [8] predicted values 37, in study this value is 38 with 95% confidence interval 37-39. In case of year 2022 the predicted values for De et al. (2016) [8] 36, in study predicted value is 36 with 95% confidence interval 34-38. For 2023 the predicted value in De et al. (2016) [8] 34 and in study the predicted value is 34 with 95% confidence interval 32-35. For year 2024 the predicted value in De et al. (2016) [8] is 34 whether in study the predicted value is 32 with confidence interval of 95% 30-34. Result suggest that the predicted values for Uttar Pradesh as in 2025, in De et al. (2016) [8] the predicted value was 33 our result shows the predicted value 31 with 95% confidence interval 29-33. For year 2026, De et al. (2016) [8] predicted values 31, in study this value is 30 with 95% confidence interval 28-32. In case of year 2027 the predicted values for De et al. (2016) [8] 30, in study predicted value is 28 with 95% confidence interval 26-31. This shows that the state achieve the target in year 2027.

Predicted Values for Uttarakhand

Result shows the predicted values for Uttarakhand as in 2015 SRS value is 34, our result shows the predicted value 34 with 95% confidence interval 32-37. For year 2016 SRS value is 33, in study this value is 33 with 95% confidence interval 30-36. In case of year 2017 the predicted value is 32 with 95% confidence interval 29-35. For 2018 the predicted value in study is 31 with 95% confidence interval 28-35. For year 2019 the predicted value in study is 30 with confidence interval of 95% 27-34. This shows that the state does not achieve the target in year 2019. In 2020, our result shows the predicted value 30 with 95% confidence interval 26-33. For year 2021, in study this value is 29 with 95% confidence interval 24-33. In case of year 2022 the predicted values in study 28 with 95% confidence interval 23-23. This implies that the target will be achieved in 2022.

Predicted Values for India

Result shows the predicted values for India as in 2015 SRS value is 37, in De et al. (2016) [8] the predicted value was 38 our result shows the predicted value 37 with 95% confidence interval 36-38. For year 2016 SRS value is 34 De et al. (2016) [8] predicted values 36, in study this value is 36 with 95% confidence interval 35-40. In case of year 2017 the predicted values for De et al.

(2016) [8] 35, in study predicted value is 35 with 95% confidence interval 33-36. For 2018 the predicted value in De et al. (2016) [8] 34 and in study the predicted value is 33 with 95% confidence interval 32-35. For year 2019 the predicted value in De et al.

(2016) [8] is 33 whether in study the predicted value is 32 with confidence interval of 95% 31-34. This shows that Country does not achieve the target in year 2019. In 2020, in De et al. (2016) [8] the predicted value was 32 our result shows the predicted value 31 with 95% confidence interval 30-33. For year 2021 De et al. (2016) [8] predicted values 31, in study this value is 30 with 95% confidence interval 29-32. In case of year 2022 the predicted values for De et al. (2016) [8] 30, in study predicted value is 28 with 95% confidence interval 27-30. Which interprets that India will achieve the target in 2022.

Discussions and Conclusion

A thorough attempt of study on those states which cover the target of infant mortality of twenty eight per thousand at time point of end of year 2016 is made. Prediction are made up to different time years for different states as they can cover the set target in new national population policy (2017) of 28 infant death per thousand live births up to 2019. results shows that the states which can achieve the target in time of before that are Andhra Pradesh, Gujrat, Haryana, Jharkhand. Assam is 11 years behind the target time points. Bihar shows 4 year behind the target up to set time point. Chhatisgarh is 1 year behind the target of 2019. Result of Madhya Pradesh shows that this state is 5 year behind the target. Odisha is 7 year behind the target time point. Rajasthan shows its 2 year backwardness to target time point to achieve target. Uttar pradesh lies at 8 year behind the target in respect of the time point. Uttarakhad provides that it is 3 year behind the target. Study shows of all over India, The country itself 3 year behind the target of twenty eight infant deaths per thousand live births. This reflect that India can achieve the target if special focus on some states is been made. Results also reflects that the assumption in previous studies that if some new actual values are different from previously predicted values then whole other predicted values will be changed. It can be seen that when we include data of 2014 to 2016 Sample registration system for infant mortality is introduced the whole predicted values are changed from the prediction of previous study for the same methods. It also suggest that it is better to study the data time to time for better future planning.

Figures and tables from the paper

Figure 1. Trend Line of Infant Mortality in India
Trend Line of Infant Mortality in India↗ Enlarge
Figure 1
Trend Line of Infant Mortality in India

Trend Line of Infant Mortality in India

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Figure 1. Trend Line of Infant Mortality in India
Trend Line of Infant Mortality in India↗ Enlarge
Figure 1
Trend Line of Infant Mortality in India

Trend Line of Infant Mortality in India

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Figure 3. Correlogram of Infant Mortality in India
Correlogram of Infant Mortality in India↗ Enlarge
Figure 3
Correlogram of Infant Mortality in India

Correlogram of Infant Mortality in India

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Figure 4. Partial Correlogram of Infant Mortality in India
Partial Correlogram of Infant Mortality in India↗ Enlarge
Figure 4
Partial Correlogram of Infant Mortality in India

Partial Correlogram of Infant Mortality in India

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Original paper figureSource PDF · page 6 ↗
Table 1. Observed and Predicted Values of IMR in Andhra Pradesh
Andhra Pradesh—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20153737363537
20163436343335
201735323133
201834302931
201933282730

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Observed and Predicted Values of IMR in Andhra Pradesh↗ Enlarge
Table 1
Observed and Predicted Values of IMR in Andhra Pradesh

Observed and Predicted Values of IMR in Andhra Pradesh

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Table 2. Observed and Predicted Values of IMR in Assam
Assam—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20154752494750
20164451474549
201750454347
201849434145
201948413944
202047403742
202146383541
202245373439
202344363339
202443353238
202542343137
202641333035
202740322936
202839312734
202938292533
203036282331

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Table 2
Observed and Predicted Values of IMR in Assam

Observed and Predicted Values of IMR in Assam

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Table 3. Observed and Predicted Values of IMR in Bihar
Bihar—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20154239413843
20163838393641
201737373540
201836363339
201935343137
202034322936
202133312734
202232292533
202331272331

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Table 3
Observed and Predicted Values of IMR in Bihar

Observed and Predicted Values of IMR in Bihar

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Table 4. Observed and Predicted Values of IMR in Chhatisgarh
ChhatisgarhPredicted Values—95% Confidence interval—
YearSRS valuesIn PaperLowerUpper
201541403842
201639373539
2017353337
2018333035
2019302833
2020282531

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Table 4
Observed and Predicted Values of IMR in Chhatisgarh

Observed and Predicted Values of IMR in Chhatisgarh

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Table 5. Observed and Predicted Values of IMR in Gujrat
Gujrat—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20153334333235
20163032313033
201731292831
201830272629

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Table 5
Observed and Predicted Values of IMR in Gujrat

Observed and Predicted Values of IMR in Gujrat

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Table 6. Observed and Predicted Values of IMR in Haryana
Haryana—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20153934363538
20163332343336
201731323034
201830302832
201929282630

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Table 6
Observed and Predicted Values of IMR in Haryana

Observed and Predicted Values of IMR in Haryana

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Table 7. Observed and Predicted Values of IMR in Jharkhand
Jharkhand——95% Confidence Interval—
YearSRS valuesPredicted ValuesLowerUpper
201532312933
201629292632
2017272430

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Observed and Predicted Values of IMR in Jharkhand↗ Enlarge
Table 7
Observed and Predicted Values of IMR in Jharkhand

Observed and Predicted Values of IMR in Jharkhand

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Table 8. Observed and Predicted Values of IMR in Madhya Pradesh
Madhya Pradesh—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20155051494750
20164750474648
201749444345
201847414043
201946393840
202045363537
202143333235
202242312932
202341302831
202440282629

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Table 8
Observed and Predicted Values of IMR in Madhya Pradesh

Observed and Predicted Values of IMR in Madhya Pradesh

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Table 9. Observed and Predicted Values of IMR in Meghalaya
Meghalaya——95% Confidence Interval—
YearSRS valuesPredicted ValuesLowerUpper
201542454050
201639383649
2017373448
2018363348
2019353147
2020323047
2021311944
2022301744
2023291643
2024281443

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Table 9
Observed and Predicted Values of IMR in Meghalaya

Observed and Predicted Values of IMR in Meghalaya

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Table 10. Observed and Predicted Values of IMR in Odisha
Odisha—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20154648454447
20164446424144
201745414043
201844393840
201942363437
202041343235
202140333134
202239313032
202337302831
202436292730
202535282430

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Observed and Predicted Values of IMR in Odisha↗ Enlarge
Table 10
Observed and Predicted Values of IMR in Odisha

Observed and Predicted Values of IMR in Odisha

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Table 11. Observed and Predicted Values of IMR in Rajasthan
Rajasthan—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20154338434144
20164136403942
201735383639
201833353337
201932333135
202030302832
202129282530

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Observed and Predicted Values of IMR in Rajasthan↗ Enlarge
Table 11
Observed and Predicted Values of IMR in Rajasthan

Observed and Predicted Values of IMR in Rajasthan

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Table 12. Observed and Predicted Values of IMR in Uttar Pradesh
Uttar Pradesh—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20154646464548
20164345444245
201743434144
201842424043
201940414043
202039393740
202137383739
202236363438
202335343235
202434323034
202533312933
202631302832
202730282631

Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.

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Observed and Predicted Values of IMR in Uttar Pradesh↗ Enlarge
Table 12
Observed and Predicted Values of IMR in Uttar Pradesh

Observed and Predicted Values of IMR in Uttar Pradesh

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Table 13. Observed and Predicted Values of IMR in Uttarakhand
Uttarakhand——95% Confidence Interval—
YearSRS valuesPredicted ValuesLowerUpper
201534343237
201633333036
2017322935
2018312835
2019302734
2020302633
2021292433
2022282332

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Observed and Predicted Values of IMR in Uttarakhand↗ Enlarge
Table 13
Observed and Predicted Values of IMR in Uttarakhand

Observed and Predicted Values of IMR in Uttarakhand

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Original paper tableSource PDF · page 9 ↗
Table 14. Observed and Predicted Values of IMR in India
India—Predicted values—95% Confidence Interval—
YearSRS valuesDe et al. (2016)In PaperLowerUpper
20153738373638
20163436363540
201735353436
201834333235
201933323134
202032313033
202131302932
202230282730

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Observed and Predicted Values of IMR in India↗ Enlarge
Table 14
Observed and Predicted Values of IMR in India

Observed and Predicted Values of IMR in India

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Original paper tableSource PDF · page 9 ↗

References

12 in the original paper
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  2. Box GE, Jenkins GM, Reinsel GC, Ljung GM. Time series analysis: forecasting and control. John Wiley & Sons, 2015.
  3. Besag JE. Discussion of the paper by grenander and miller. Journal of the Royal Statistical Society, Series B. 1994; 56:591592.
  4. Bhan MK. Accelerated progress to reduce under-5 mortality in India. Open Access. 2013; 13:70076-70077.
  5. Benicio M, Monteiro C, de Souza JM, Castilho E, Reis I. Multivariate analysis of risk factors for low birth weight in live births in the municipality of São Paulo, SP (Brazil). Revista de saúde pública. 1985; 19:311-20.
  6. Ahmad OB, Lopez AD, Inoue M. The decline in child morality:. a repprasial bulletin of World Health Orgnization. 2000; 78(10):1175-1191.
  7. De P. A Temporal and Spatial Dimension of Under Five Mortality with Emphasis on Impact of National Health Programme: For the Period 1976-2004. PhD thesis, Jadhavpur University, 2011.
  8. De P, Sahu D, Pandey A, Gulati BK, Chandhiok N, Shukla A et al. Post Millennium Development Goals Prospect on Child Mortality in India: An Analysis Using Autoregressive Integrated Moving Averages (ARIMA) Model. Health. 2016; 08:18451872.
  9. Tripathi PK, Mishra RK. Upadhyay SK. Bayes and Classical Prediction of Total Fertility Rate of India Using Autoregressive Integrated Moving Average Model, J Stat. Appl. Pro. 2018; 7(2):233-244 233.
  10. UN. World population prospects: the revision, 2012.
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  12. WHO. World health chart. In Karolinka Institute/ Lund University SIDA, 2001.

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