Trend analysis of mortality rates and causes of death in children under 5 years old in Beijing, China from 1992 to 2015 and forecast of mortality into the future: an entire population-based epidemiological study

Objectives To analyse trends in mortality and causes of death among children aged under 5 years in Beijing, China between 1992 and 2015 and to forecast under-5 mortality rates (U5MRs) for the period 2016–2020. Methods An entire population-based epidemiological study was conducted. Data collection was based on the Child Death Reporting Card of the Beijing Under-5 Mortality Rate Surveillance Network. Trends in mortality and leading causes of death were analysed using the χ2 test and SPSS 19.0 software. An autoregressive integrated moving average (ARIMA) model was fitted to forecast U5MRs between 2016 and 2020 using the EViews 8.0 software. Results Mortality in neonates, infants and children aged under 5 years decreased by 84.06%, 80.04% and 80.17% from 1992 to 2015, respectively. However, the U5MR increased by 7.20% from 2013 to 2015. Birth asphyxia, congenital heart disease, preterm/low birth weight and other congenital abnormalities comprised the top five causes of death. The greatest, most rapid reduction was that of pneumonia by 92.26%, with an annual average rate of reduction of 10.53%. The distribution of causes of death differed among children of different ages. Accidental asphyxia and sepsis were among the top five causes of death in children aged 28 days to 1 year and accident was among the top five causes in children aged 1–4 years. The U5MRs in Beijing are projected to be 2.88‰, 2.87‰, 2.90‰, 2.97‰ and 3.09‰ for the period 2016–2020, based on the predictive model. Conclusion Beijing has made considerable progress in reducing U5MRs from 1992 to 2015. However, U5MRs could show a slight upward trend from 2016 to 2020. Future considerations for child healthcare include the management of birth asphyxia, congenital heart disease, preterm/low birth weight and other congenital abnormalities. Specific preventative measures should be implemented for children of various age groups.

Mortality in 2015 could not be interpreted as the results of "Selective Two child policy" implemented in 2014. Furthermore, the alleged reason (the aged mother) is only attributable for neonatal mortality not for infant and U5 Mortality in this mechanism. However, increasing in neonatal morality (+0.08) is relatively smaller than the other two mortalities (+0.16, +0.20). Removing the "Selective Two child policy" attribution is suggested. If this should be the main research question, the method should be more solid rather than this secular trend analysis. Otherwise, the authors need to take out this research question.
(in results section). Page 7 line 15-19. It is a bit confusing in the text. U5 death included Infant death or not? Similarly, infant death include neonate death or not? According to the text, it looks that they are not included to the others (mutually exclusive). However, next sentence "death in neonates accounted for more than 50% of all death among for under-5 children" made audience to think they not mutually exclusive to each other (U5 death include infant death; and infant death include neonate death). Which one is correct? Please be consistent or make it not confusing. New raw for total death next to 2015 will make audience less confusing as well.
Page 8. Line 38. "mortality rates for leading cause of death…overall decreasing…" sounds very illogical. Some mortality rates, which were leading cause of death in 1992, can be decreasing since then. However, general decreasing of leading cause of deaths sounds very inappropriate expression. Other cause became major leading causes? Or Same rank of cause of death but all decreasing in terms of mortality per se? Even the latter is right, this section is not the decomposition of all cause mortality, but cause of death distribution mostly based on rank order description. So in this sense, the expression is not suitable to the section heading. Page 10, line 3. The percentages looks confusing? What do they mean?
Upward trend forecasting may be model misspecification due to adapting the function of "y=aX squre+bX+c". Inverse root X function or logarithmic function would predict differently.
Page 14. Line 34-42. It sounds too redundant. Same color should be consistent across A-D so that no confusion rises to the audience. Purple represented pneumonia in A-D consistently. However, yellow color was for birth asphyxia in A-B but in C, it meant septicemia; in D, it meant leukemia. By this way, chart looks not succinctly show the mortality composition change but making confusion. Please use different color different cause of death.

GENERAL COMMENTS
General comment: Trend analysis in mortality rates and causes of death for under-5 children in Beijing, China from 1992 to 2015 and forecasting mortality into the future: an entire population based epidemiological study.
The topic is an important one and covers a timely and important subject of great medical interest: Future death rates are extremely important to governmental and non-governmental organizations as forecasts of mortality rates used to plan social security and health care programs. The paper is well written and the conclusions drawn more or less supported by the data used. The limitations of the study were stated fairly though the strength was overstated. Latest advances in predicting mortality increasingly include Bayesian inference and they account for the distribution of the age at death in order to capture detailed patterns of mortality. In addition, some recent studies used rates of improvement or rate changes rather than death rates to forecast mortality changes better. Whether you use classical or Bayesian approach, to address the objectives in your paper more efficiently: 1) It would be better to use forecasting models which accounts for different age groups (infants, neonates,…).
2) It would be better to forecast mortality for each major cause of death.
3) It would be better to use forecasting models which accounts for other related impact factors.

VERSION 1 -AUTHOR RESPONSE
Reviewer: 1 1. Mortality in 2015 could not be interpreted as the results of "Selective Two child policy" implemented in 2014. Furthermore, the alleged reason (the aged mother) is only attributable for neonatal mortality not for infant and U5 Mortality in this mechanism. However, increasing in neonatal morality (+0.08) is relatively smaller than the other two mortalities (+0.16, +0.20). Removing the "Selective Two child policy" attribution is suggested. If this should be the main research question, the method should be more solid rather than this secular trend analysis. Otherwise, the authors need to take out this research question. Reply: Thanks for your comments.
We agree with reviewer's comments. Since we only collected 2-year data (2014 and 2015) after the "Selective Two Child Policy" (2014), the representativeness of the changing trend and solid statistical analysis was limited. Therefore, our results could not detect the effect of "Selective Two Child Policy" directly. We just suggest that the policy regulation may affect slight upward trend in mortalities to rise healthcare workers' attention about this potential problem (as we discussing in "Limitations", Page 3, Line 17-20 and Page 15, Line 15-19). It seems we haven't explained clearly the three mortalities, so we clarify the definition of "neonatal mortality rate (NMR)", "infant mortality rate (IMR)" and "under-5 mortality rate (U5MR)" in methods section (Page 6, Line 2-6). That is to say, U5MR included IMR, and IMR included NMR. Therefore, increasing in NMR (+0.08) must be smaller than IMR (+0.16) and U5MR (+0.20). However, increasing in mortalities in neonates (<28 days) and children aged 28 days to 1 year were bigger than children aged 1-4 years indeed after we calculated mortalities in different age groups. Increasing in mortalities in neonates and children aged 28 days to 1 year and 1-4 years were 0.08, 0.08 and 0.04 (from 1.50‰, 0.83‰ and 0.56‰ in 2014 to 1.58‰, 0.91‰ and 0.60‰ in 2015). They coincided with the aged mother being attributable for mortalities in children within 1 year.
2. Page 7 line 15-19. It is a bit confusing in the text. U5 death included Infant death or not? Similarly, infant death include neonate death or not? According to the text, it looks that they are not included to the others (mutually exclusive). However, next sentence "death in neonates accounted for more than 50% of all death among for under-5 children" made audience to think they not mutually exclusive to each other (U5 death include infant death; and infant death include neonate death). Which one is correct? Please be consistent or make it not confusing. New raw for total death next to 2015 will make audience less confusing as well.
Reply: Thanks for your comments. This comment is similar to the previous comment. We clarified the definition of "neonatal mortality rate (NMR)", "infant mortality rate (IMR)" and "under-5 mortality rate (U5MR)" in methods section (Page 6, Line 2-6). That is to say, U5MR included IMR, and IMR included NMR. What's more, the section in Page 6, Line 20-21 has been corrected into neonatal deaths, infant deaths and under-5 children deaths. We hope that it is not confusing any more this time.
3. Page 8 line 38. "mortality rates for leading cause of death…overall decreasing…" sounds very illogical. Some mortality rates, which were leading cause of death in 1992, can be decreasing since then. However, general decreasing of leading cause of deaths sounds very inappropriate expression. Other cause became major leading causes? Or Same rank of cause of death but all decreasing in terms of mortality per se? Even the latter is right, this section is not the decomposition of all cause mortality, but cause of death distribution mostly based on rank order description. So in this sense, the expression is not suitable to the section heading. Reply: Thanks for your comments. We corrected the section heading (Page 7, Line 12), because this section mainly describes the distribution of leading causes of death. The change in rank order and reduction in mortality rates for leading causes of death are described in Table 2, Page 7, Line 13-18 and Page 8, Line 1-5. We hope that it is not confusing any more this time. . These results indicated that the cause-specific mortalities in congenital heart disease, other congenital abnormalities and accidental asphyxia had obvious fluctuation, which is different from the trends in other age groups (Figure 2).
5. Upward trend forecasting may be model misspecification due to adapting the function of "y=aX squre+bX+c". Inverse root X function or logarithmic function would predict differently. Reply: Thanks for your comments.
In the present study, we used ARIMA model to forecast the U5MRs using surveillance data. Since U5MR has many aspects of influencing factors such as population, policy, economy and environment and has continuity in time traditional statistical analysis such as regression analysis methods are unsuitable. As it clarifying in the section of "Statistical analysis" (Page 6, Line 11-13), ARIMA model can use time to replace kinds of influencing factors and can be established on the base of past values of series and previous error for forecasting. It has been reported that ARIMA model can be applied to forecast incidence of hand-foot-mouth disease [1], influenza H5N1 [2] and injury [3]. The forecasting model ARIMA(1, 1, 1) is: "x" _"t" "=-0.445+1.509" "x" _"t-1" "-0.509" "x" _"t-2" "+" "α" _"t" "+0.999" "α" _"t-1" . It is established on the base of past values of series (xt-1, xt-2) and previous error ("α" _"t" ,"α" _"t-1" ), not the formula of "y=a" "x" ^"2" "+bx+c" which you mentioned before. Therefore, the forecasting mortalities are predicted according to the previous trend and don't adapt the function any more.
In the model we established, R2=0.982, AIC=2.15, BIC=2.30 and MAPE=4.76%. Therefore, it is appropriate to forecast U5MRs by ARIMA model. Reviewer: 2 1. Latest advances in predicting mortality increasingly include Bayesian inference and they account for the distribution of the age at death in order to capture detailed patterns of mortality. In addition, some recent studies used rates of improvement or rate changes rather than death rates to forecast mortality changes better. Whether you use classical or Bayesian approach, to address the objectives in your paper more efficiently: 1) It would be better to use forecasting models which accounts for different age groups (infants, neonates,…).
2) It would be better to forecast mortality for each major cause of death.
3) It would be better to use forecasting models which accounts for other related impact factors. Reply: Thanks for your comments. It is very constructive. As the review mentioned above, Bayesian inference is really an excellent method and can be used in many fields. The present study used the surveillance data between 1992 and 2015 from Beijing Under-5 mortality rate Surveillance Network and aimed to analyze the dynamic changes in U5MR. The index of U5MR is an important indicator which reflects children's health and the development of economy and culture in a country or area. U5MR is different from cause-specific mortality rate, which is affected by many aspects of influencing factors such as population, policy, economy and environment. In addition, we can only acquire death data (case group) from the surveillance network and lack of healthy children data (control group). Therefore, using traditional regression analysis methods which consider related impact factors to predict is limited. ARIMA model can use time to replace kinds of influencing factors and can be established on the base of past values of series and previous error for forecasting. It has been applied to forecast incidence of hand-foot-mouth disease [1], influenza H5N1 [2] and injury [3]. What's more, U5MR has continuity in time. In the model we established, R2=0.982, AIC=2.15, BIC=2.30 and MAPE=4.76%. Therefore, it is appropriate to forecast U5MRs by ARIMA model. Bayesian inference can use apriori information and sample information to establish steadier forecasting model to capture detailed patterns of mortality. Bayesian inference and ARIMA model both have advantages and disadvantages in prediction. We intend to process another further study to compare the effect of Bayesian inference and ARIMA model in predicting U5MRs. Furthermore, in the present study, we only intended to observe the long-term and prospective changing trend in mortality rates in entire under-5 children through the forecasting model, so we didn't consider to accounts for different age groups and specific diseases. At the same time, considering the length of the article, we are going to consider the suggestions in the future.