A recursive model of residual life prediction for human beings with health information from activities of daily living and memory

Figures & data

Table 1. Sample statistics.

		Life	Age at the first survey	Survey times
Type	Number	Mean (Median)
Complete	1746	74.3 (75)	66.05 (64.36)	2.536 (3)
Censored	9240		61.40 (59.01)	2.643 (3)
Total	10,986		62.14 (59.74)	2.626 (3)

Table 2. ADL.

(i) Activity type	PCA
1 Running a kilometre	0.131
2 Walking a kilometre	0.244
3 Walking 200 metres	0.258
4 Walking across a room	0.237
5 Sitting continuously for two hours	0.175
6 Standing up after sitting for a long time	0.218
7 Climbing one staircase	0.251
8 Climbing a few stairs without stopping	0.238
9 Lifting or raising a 5-kilogram bag (such as a bag of flour, rice, or other miscellaneous items)	0.226
10 Squatting down, kneeling, or bending over	0.219
11 Putting on your clothes	0.232
12 Combing your hair	0.215
13 Using the toilet	0.240
14 Bathing yourself	0.250
15 Eating by yourself	0.191
16 Shop (buying food, clothes, etc.) without others’ help	0.255
17 Cook without others’ help	0.244
18 Use public transportation to go places where it is too far to walk	0.223
19 Manage your money (record your income and expenses, etc.)	0.211
20 Use the telephone without others’ help	0.163

Table 3. Memory.

(i) Question	Answers	PCA
1 How is your memory?	1 very good, 2 good, 3 OK, 4 bad, 5 very bad	0.418
2 In the past twelve months, how has your memory changed?	1 improved, 2 stayed the same, 3 deteriorated	0.296
3 Memorize and repeat ten words	The number of correct words repeated	−0.540
4 Please count backward from 20 to 1	1 correct the first time, 2 correct the second time, 3 incorrect both times	0.409
5 Repeat the same ten words again after counting	The number of correct words repeated	0.528

Figure 1. Variances of principal components.

Table 4. Parameter estimated.

Parameter set	Parameters
1	$\alpha$, $\text{β}$
2	$c_s$, $d_s$, $c_m$, $d_m$
3	$a$, $b$

Figure 2. Comparison of the predicted residual life distribution based on the fitted model and the initial distribution. (Note: the distribution curves of the fourth and fifth predictions are too centralized to be shown in the plot, so the last two curves are interrupted; the following figures also have the similar situations).

Figure 3. Comparison of the predicted residual life distribution based on the fitted model with Weibull distribution and the fitted model with exponential distribution.

Figure 4. Comparison of the predicted residual life distributions from the proposed model and multiple linear regression.

Figure 5. Comparison of the predicted residual life distribution based on the fitted model with Weibull distribution and the fitted model with exponential distribution.

Table 5. Life table of Chinese population in 2010.

Age	Expected residual life
61	20.76
65	17.62
68	15.39
72	12.72
74	11.50