Prediction of China’s Population Mortality under Limited Data
Abstract
:1. Introduction
2. Materials and Methods
- Model classical algorithm Establish a logarithmic center mortality model and estimate the model parameters through past data. The basic formula of the model is:We let be the central rate of death at age x and in year t. where and are age-specific parameters, x is a time-varying index, and is a random item with zero means and finite variances, the variances is .Since there are numerous groups that meet the requirements of the equation, Lee and Carter have standardized the parameters to estimate the above parameters, we let , , , .where t is the total number of calendar years included in the mortality data to be estimated. is the mean of logarithmic center mortality for age. indicates the intensity of mortality at year. Derived from both sides of Equation (1).We obtain . That is, represents the sensitivity of logarithmic mortality change when the mortality intensity changes.
- Maximum likelihood estimation is used to estimate the parameters in Lee-Carter model. The method assumes that the number of deaths follows the Poisson distribution with parameter , that is:In Equation (3), is the annual mortality of the population aged x in year t, and is the death risk exposure of the population in the year of death. In practical application, it is often replaced by the number of people in this year . By maximizing the following likelihood function, we can obtain an estimate of the sum.After the above iterative process, is small enough, Likelihood formula approaches maximum,where .
- In the second stage, is modeled and fitted according to the time series method. The model is very simple [34,35]. It only needs endogenous variables without the help of other exogenous variables. In most studies, ARIMA (p, d, q) process is used to model series. ARIMA’s prediction model can be expressed as:
3. Results
3.1. Data Description
3.1.1. Data Source and Processing
- 1.
- In order to keep the number of deaths and the overall population in each year roughly in order of magnitude, divide the census data by 1000, and divide the 1% spot check data by 10. According to the mortality data of different ages, the death toll of each age is adjusted based on 1 million;
- 2.
- It is assumed that both 1% population sampling and variable sampling methods have good random sampling characteristics;
- 3.
- The data for most years are from 0 to 89 years old, and the data for 2000, 2005, 2010, and 2015 are from 0 to 99 years old. This paper uses kannisto method to fit the missing data of 90–100 years old in the data;
- 4.
- When the death toll data is zero or missing, the cubic spline interpolation method for the year is used to fill in.
3.1.2. Descriptive
3.2. Parameter Estimation
- Parameter of male:The weighted least square method (WLS) is used to estimate the parameter age effect factors , and time factor of Lee-Carter model, as shown in Figure 2 below:
- Parameter of female:The weighted least square method (WLS) is used to estimate the parameter age effect factors , and time factor of Lee-Carter model, as shown in Figure 3 below:
- Forecast value of .is a time series model, the unit root AR(1) model is usually employed in the studying of longevity risk, which is a random walk process with drift term. But in this paper, by fitting the ARIMA model, using AIC criteria and t-test statistics, the optimal ARIMA model is selected. Both men and women are ARIMA (1, 2, 1).
3.3. Age Factor Expansion
3.4. Mortality Prediction
3.5. Model Evaluation
3.5.1. Residual Plot Test
3.5.2. MAPE Value Test
3.6. Conclusion
Impact on Life Expectancy
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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(Year) | Male | Female |
---|---|---|
1997 | 39.71694 | 49.62551 |
1998 | 39.37878 | 44.25081 |
1999 | 26.90062 | 44.27759 |
2000 | 33.22122 | 41.42727 |
2001 | 28.28746 | 23.72562 |
2002 | 23.76912 | 25.18467 |
2003 | 21.81028 | 33.53104 |
2004 | 16.12240 | 23.64792 |
2005 | −18.00578 | −28.60565 |
2006 | 4.64959 | 5.93254 |
2007 | 0.74380 | 1.80809 |
2008 | 13.01404 | 2.12542 |
2009 | −7.32940 | −9.68799 |
2010 | −22.27087 | −5.76496 |
2011 | −5.84174 | −10.94736 |
2012 | −7.58277 | −20.49683 |
2013 | −9.67512 | −18.16568 |
2014 | −11.03544 | −17.79088 |
2015 | −52.66777 | −41.73031 |
2016 | −34.43803 | −42.25345 |
2017 | −28.12194 | −39.70408 |
2018 | −30.28050 | −33.61352 |
2019 | −20.36489 | −26.77579 |
2020 | −27.36053 | −33.40219 |
2021 | −28.92028 | −36.01515 |
2022 | −32.22732 | −39.82445 |
2023 | −34.97272 | −43.27714 |
2024 | −37.89865 | −46.83612 |
2025 | −40.76655 | −50.36343 |
2026 | −43.65310 | −53.90017 |
2027 | −46.53366 | −57.43410 |
2028 | −49.41614 | −60.96887 |
2029 | −52.29801 | −64.50340 |
2030 | −55.18007 | −68.03799 |
2031 | −58.06208 | −71.57256 |
2032 | −60.94410 | −75.10714 |
2033 | −63.82611 | −78.64172 |
2034 | −66.70813 | −82.17630 |
2035 | −69.59014 | −85.71088 |
2036 | −72.47216 | −89.24546 |
2037 | −75.35418 | −92.78003 |
2038 | −78.23619 | −96.31461 |
2039 | −81.11821 | −99.84919 |
Prediction | 2025 Male | 2030 Male | 2025 Female | 2030 Female |
---|---|---|---|---|
0 | 0.002815632 | 0.001864309 | 0.002279284 | 0.001372894 |
1 | 0.000529425 | 0.000404437 | 0.000421002 | 0.000309032 |
2 | 0.000259631 | 0.000182212 | 0.000151838 | 0.000094000 |
3 | 0.000193766 | 0.000131181 | 0.000270073 | 0.000205789 |
4 | 0.000140375 | 0.000089400 | 0.000137687 | 0.000093800 |
5 | 0.000090700 | 0.000094500 | 0.000063300 | 0.000134991 |
6 | 0.000152940 | 0.000114613 | 0.000106773 | 0.000082200 |
7 | 0.000168450 | 0.000131642 | 0.000093800 | 0.000069200 |
8 | 0.000232580 | 0.000187947 | 0.000115986 | 0.000088100 |
9 | 0.000309759 | 0.000289486 | 0.000126814 | 0.000108278 |
10 | 0.000189158 | 0.000151044 | 0.000160350 | 0.000134703 |
11 | 0.000175596 | 0.000149353 | 0.000248531 | 0.000220986 |
12 | 0.000221387 | 0.000185156 | 0.000156758 | 0.000136913 |
13 | 0.000230460 | 0.000187790 | 0.000085925 | 0.000060314 |
14 | 0.000262990 | 0.000221228 | 0.000188295 | 0.000171488 |
15 | 0.000282440 | 0.000237320 | 0.000089595 | 0.000060976 |
16 | 0.000175137 | 0.000121344 | 0.000096146 | 0.000072854 |
17 | 0.000319452 | 0.000255342 | 0.000054329 | 0.000034126 |
18 | 0.000349785 | 0.000278339 | 0.000140665 | 0.000101496 |
19 | 0.000295161 | 0.000217803 | 0.000134585 | 0.000092890 |
20 | 0.000420180 | 0.000318750 | 0.000116659 | 0.000082486 |
... | ... | ... | ... | ... |
Male | Female | |
---|---|---|
MAPE | 0.49198 | 0.43572 |
2018 | 2019 | ... | 2023 | 2024 | 2025 | ... | |
---|---|---|---|---|---|---|---|
male | 74.878 | 75.227 | ... | 76.729 | 77.024 | 77.308 | ... |
true (male) | 73.64 | 74.7 | ... | — | — | — | ... |
female | 78.717 | 79.694 | ... | 82.23 | 82.17 | 82.24 | ... |
true (female) | 79.43 | 80.5 | ... | — | — | — | ... |
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Cheng, Z.; Si, W.; Xu, Z.; Xiang, K. Prediction of China’s Population Mortality under Limited Data. Int. J. Environ. Res. Public Health 2022, 19, 12371. https://doi.org/10.3390/ijerph191912371
Cheng Z, Si W, Xu Z, Xiang K. Prediction of China’s Population Mortality under Limited Data. International Journal of Environmental Research and Public Health. 2022; 19(19):12371. https://doi.org/10.3390/ijerph191912371
Chicago/Turabian StyleCheng, Zhenmin, Wanwan Si, Zhiwei Xu, and Kaibiao Xiang. 2022. "Prediction of China’s Population Mortality under Limited Data" International Journal of Environmental Research and Public Health 19, no. 19: 12371. https://doi.org/10.3390/ijerph191912371
APA StyleCheng, Z., Si, W., Xu, Z., & Xiang, K. (2022). Prediction of China’s Population Mortality under Limited Data. International Journal of Environmental Research and Public Health, 19(19), 12371. https://doi.org/10.3390/ijerph191912371