# Projection of the Number of Elderly in Different Health States in Thailand in the Next Ten Years, 2020–2030

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Study Design and Development of Conceptual Framework

#### 2.2. Parameter Management

_{SH}[from social group to home group], Θ

_{SB}[from social group to bedridden group], Θ

_{HS}[from home group to social group], Θ

_{HB}[from home group to bedridden group], Θ

_{BS}[from bedridden group to social group], and Θ

_{BH}[from bedridden group to home group]). The final outputs were presented in terms of S(t), H(t), B(t), and D(t) which refer to the number of cases in social, home, bedridden, and dead groups at time t, respectively. The time step for the analysis was one year. The analysis commenced when people reached 60 years of age.

#### 2.2.1. Population Cohort in Each Time Frame (Λ)

_{D}denoted the mortality rate of new people who died before transferring to the following year; and second, π denoted the prevalence of people in each health status at any time (t − 1). This meant for the first cohort included in the model, π referred to the percentage of people in a particular health status when they were 59 years of age. The mortality rate of people who died before becoming 60 years old was calculated from the following formula: π

_{die before become 60-year-old}= (n. of people aged 60 years—n. of people in the same cohort at aged 59 years)/(n. of people in the same cohort at aged 59 years). We obtained the number of people in each specific age group from the Civil Registry website [17]; and we used use the mean mortality rate for each cohort year from the Civil Registry data between 1994 and 2019 [17]. The prevalence of the population in each health status (social, home, and bedridden) was based on the study by Charnduwit in 2017, which calculated the prevalence based on population aged between 60 and 64 years [14]. The equation used to estimate the number of population cohort was shown in Table 2.

#### 2.2.2. Transition Probabilities (Θ)

#### 2.2.3. Starting Population (Pop(t = 0))

#### 2.2.4. Mortality Rate (Δ)

#### 2.3. Model Prediction Error

#### 2.4. Model Validation

#### 2.5. Projection of the Amount of Bedridden Patients

#### 2.6. Sensitivity Analysis

#### 2.7. Statistical Software

^{®}(© 2020 RStudio, Boston, MA, USA), and Microsoft Excel (Microsoft (Thailand) Ltd., Bangkok, Thailand).

## 3. Results

#### 3.1. Parameter Identification

#### 3.1.1. Population Cohort in Each Time Frame (Λ)

^{0.0359(t)}, where t started from the calendar year of 1994. The coefficient of determination (R

^{2}) was 0.9442. Parameters that were used to indicate the number of incoming populations were π

_{S}= 0.9922, π

_{H}= 0.0029 (0.000031), π

_{B}= 0.0049 (0.000041) and π

_{D}= 0.0131 (0.0054).

#### 3.1.2. Transition Probabilities (Θ)

_{SH}, Θ

_{SB}, Θ

_{HS}, Θ

_{HB}, Θ

_{BS}, and Θ

_{BH}equated 0.0169, 0.0071, 0.1257, 0.0782, 0.0470, and 0.0688, respectively. The value of these parameters after adjusting with the actual data was 0.0049, 0.0002, 0.1259, 0.0782, 0.0470, and 0.0709, in consecutive order. After adjustment, the model error reduced from 38.67% to 1.40%.

#### 3.1.3. Starting Population

#### 3.1.4. Mortality Rate (Δ)

#### 3.2. Model Validation

#### 3.3. Projected Amount of Bedridden Patients

#### 3.4. Sensitivity Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Ethical Consideration

## References

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**Figure 5.**Number of bedridden patients given different degrees of uncertainty of the transition probabilities (scenarios with 5%, 10%, 15%, and 20% changes).

**Table 1.**Summary of the liner difference equations used to estimate volume of patients in social, home, bedridden, and dead groups.

Model Equation | Formula |
---|---|

1 | S(t + 1) = S(t) + Λ_{S}(t) + H(t) × Θ_{HS} + B(t) × Θ_{BS} − S(t) × Θ_{SH} − S(t) × Θ_{SB} − S(t) × Δ_{S} |

2 | H(t + 1) = H(t) + Λ_{H}(t) + S(t) × Θ_{SH} + B(t) × Θ_{BH} − H(t) × Θ_{HS} − H(t) × Θ_{HB} − H(t) × Δ_{H} |

3 | B(t + 1) = B(t) + Λ_{B}(t) + H(t) × Θ_{HB} + S(t) × Θ_{SB} − B(t) × Θ_{BS} − B(t) × Θ_{BH} − B_{G}(t) × Δ_{B} |

4 | D(t + 1) = D(t) + S(t) × Δ_{S} + H(t) × Δ_{H} + B(t) × Δ_{B} |

Equation | Formula | Description |
---|---|---|

1 | Λ_{D} = π_{die before becoming 60-year-old} × Λ | Number of deaths at time t − 1 |

2 | Λ′ = Λ − Λ_{D} | Number of the elders entering time t |

3 | Λ_{S} = π_{S} × Λ′ | Number of social group entering time t |

4 | Λ_{H} = π_{H} × Λ′ | Number of home group entering time t |

5 | Λ_{B} = π_{B} × Λ′ | Number of bedridden group entering time t |

**Table 3.**Summary of the equations used to estimate the volume of population at the start of the analysis (initial reservoirs).

Equation | Formula | Description |
---|---|---|

1 | Pop(0) = S(0) + H(0) + B(0) + D(0) | Total volume of population aged ≥60 years consisted of people aged ≥60 years in the social group, the home group, the bedridden group, and the death group at time 0. |

2 | S(0) = Pop(0) × Π_{S} | Volume of people aged ≥60 years in the social group resulted from population aged ≥60 years multiplied by prevalence of social group. |

3 | H(0) = Pop(0) × Π_{H} | Volume of people aged ≥60 years in the home group resulted from population aged ≥60 years multiplied by prevalence of home group. |

4 | B(0) = Pop(0) × Π_{B} | Volume of people aged ≥60 years in the bedridden group resulted from population aged ≥60 years multiplied by prevalence of bedridden group. |

5 | D(0) = 0 | Volume of dead people in the model. We assumed there was no death at the beginning of the analysis. |

Equation | Formula | Description |
---|---|---|

1 | $\Delta =\frac{{\Pi}_{s}{\Delta}_{S}{+\Pi}_{H}{\Delta}_{H}{+\Pi}_{B}{\Delta}_{B}}{{\Pi}_{S}+{\Pi}_{H}+{\Pi}_{B}}$ | Crude mortality rate was a prevalence weight average of group-specific mortality. |

2 | Δ_{S} = ${\mathsf{\gamma}}_{s}$ × Δ | Social group mortality rate was social group specific severity factors multiply by crude mortality. |

3 | Δ_{H} = ${\mathsf{\gamma}}_{H}$ × Δ | Home group mortality rate was home group specific severity factors multiply by crude mortality. |

4 | Δ_{B} = ${\mathsf{\gamma}}_{B}$ × Δ | Bedridden group mortality rate was bedridden group specific severity factors multiply by crude mortality. |

5 | ${R}_{H}=\frac{{\Delta}_{H}}{{\Delta}_{S}}=\frac{\Delta \times {\mathsf{\gamma}}_{H}}{\Delta \times {\mathsf{\gamma}}_{s}}$ | Relative risk of home mortality was calculated from home group mortality rate over social group mortality rate. |

6 | ${R}_{B}=\frac{{\Delta}_{B}}{{\Delta}_{S}}=\frac{\Delta \times {\mathsf{\gamma}}_{B}}{\Delta \times {\mathsf{\gamma}}_{s}}$ | Relative risk of bedridden mortality was calculated from bedridden group mortality rate over social group mortality rate. |

7 | ${\mathsf{\gamma}}_{s}=\frac{1}{{\Pi}_{S}{+\Pi}_{H}{R}_{H}{+\Pi}_{B}{R}_{B}}$ | Social group mortality was calculated from group specific prevalence and relative risk. This equation was rewritten form of equations 1–6. |

Equation | Formula | Description |
---|---|---|

1 | $Erro{r}_{j}=\frac{1}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\frac{\left|Observer{d}_{ij}-Predicte{d}_{ij}\right|}{Observer{d}_{ij}}$ | Mean absolute percentage error (MAPE) of group j was the summation of absolute difference divided by observed value. |

2 | $Modelerror=\frac{1}{K}{\displaystyle {\displaystyle \sum}_{j=1}^{K}}Erro{r}_{j}$ | Model error was mean average of all group-specific errors combined. |

No | Group of Variables | Parameters | Mean | SD | Reference (Ref) |
---|---|---|---|---|---|

1 | New population | Λ | Λ = 302,880 × e^{0.0359(t)} | Bureau of Registration administration [17] | |

2 | Prevalence of specific group who age equal 59-year-old | π_{S} | 0.9922 | - | Model calibration from Bureau of Registration administration [17] |

3 | π_{H} | 0.0029 | 0.000031 | Charnduwit [14] | |

4 | π_{B} | 0.0049 | 0.000041 | ||

5 | π_{D} | 0.0131 | 0.0054 | Model calibration from Bureau of Registration administration [17] | |

6 | Mortality rate | Δ | 0.0307 | 0.0011 | Bureau of Registration administration and Strategy and Planning Division [17,20] |

7 | Relative mortality rate | R_{H} | 1.45 | 0.0010 (SE of ln RR) | Ryg [21] |

8 | R_{B} | 2.27 | 0.0010 (SE of ln RR) | ||

9 | Prevalence of specific group in elderly | Π_{S} | 0.9683 | - | Model calibration from Charnduwit [14] |

10 | Π_{H} | 0.0199 | 0.000046 | Charnduwit [14] | |

11 | Π_{B} | 0.0118 | 0.000036 | ||

12 | Mortality rate in specific group | Δ_{S} | 0.0494 | - | Model calibration from Bureau of Registration administration, Strategy and Planning Division, and Ryg [17,20,21] |

13 | Δ_{H} | 0.1465 | - | ||

14 | Δ_{B} | 0.2050 | - | ||

15 | Transit probability from social group | Θ_{SH} | 0.0169 | - | Model calibration from Rickayzen [9] |

16 | Θ_{SB} | 0.0071 | - | ||

17 | Transit probability from home group | Θ_{HS} | 0.1257 | - | |

18 | Θ_{HB} | 0.0782 | - | ||

19 | Transit probability from bedridden group | Θ_{BS} | 0.0470 | - | |

20 | Θ_{BH} | 0.0688 | - | ||

21 | Initial Total population | Pop(t = 0) | 11,136,059 | - | Bureau of Registration administration [17] |

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**MDPI and ACS Style**

Tantirat, P.; Suphanchaimat, R.; Rattanathumsakul, T.; Noree, T.
Projection of the Number of Elderly in Different Health States in Thailand in the Next Ten Years, 2020–2030. *Int. J. Environ. Res. Public Health* **2020**, *17*, 8703.
https://doi.org/10.3390/ijerph17228703

**AMA Style**

Tantirat P, Suphanchaimat R, Rattanathumsakul T, Noree T.
Projection of the Number of Elderly in Different Health States in Thailand in the Next Ten Years, 2020–2030. *International Journal of Environmental Research and Public Health*. 2020; 17(22):8703.
https://doi.org/10.3390/ijerph17228703

**Chicago/Turabian Style**

Tantirat, Panupong, Repeepong Suphanchaimat, Thanit Rattanathumsakul, and Thinakorn Noree.
2020. "Projection of the Number of Elderly in Different Health States in Thailand in the Next Ten Years, 2020–2030" *International Journal of Environmental Research and Public Health* 17, no. 22: 8703.
https://doi.org/10.3390/ijerph17228703