Background
Methods
Models
Parameter estimation
-
Let \(R_{i^{\prime }}\in (a_{i^{\prime }},b_{i^{\prime }}]\) be an interval for the occurrence of non-fatal events associated with subjects in routes 3 or 4. Let s1 be the smallest value among all \(b_{i^{\prime }}\)’s for subjects in the set \(\mathcal {B}_{3}\cup \mathcal {B}_{4}\). Let s2 be the smallest value among all \(b_{i^{\prime }}\)’s corresponding to subjects having \(a_{i^{\prime }}\) greater than or equal to s1. This process is repeated until we have no subjects with \(a_{i^{\prime }}\) greater than or equal to sm (m=1,2,…). Thus, we can have a refined set of time points$$\begin{array}{@{}rcl@{}} 0=s_{0}< s_{1}< s_{2}<\cdots< s_{l}< s_{l+1}=\infty. \end{array} $$
-
We can define the weight \(w_{i^{\prime }m}\) at time sm (m=1,2,…) for subject i′ in the set \(\mathcal {B}_{3}\cup \mathcal {B}_{4}:\)$$ {\begin{aligned} w_{i^{\prime}m} = \frac{d_{i^{\prime}m}\exp\left\{-H_{0}\left(e_{i^{\prime}},s_{m}|{\boldsymbol{w}}_{i^{\prime}}, {\boldsymbol{z}}_{i^{\prime}}, u_{i^{\prime}}\right)\right\}\lambda_{01}(s_{m}|{\boldsymbol{w}}_{i^{\prime}}, {\boldsymbol{z}}_{i^{\prime}}, u_{i^{\prime}})}{\sum_{m^{\prime}=1}^{l} d_{i^{\prime}m^{\prime}}\exp\left\{-H_{0}(e_{i^{\prime}},s_{m^{\prime}}|{\boldsymbol{w}}_{i^{\prime}}, {\boldsymbol{z}}_{i^{\prime}}, u_{i^{\prime}})\right\}\lambda_{01}(s_{m^{\prime}}|{\boldsymbol{w}}_{i^{\prime}}, {\boldsymbol{z}}_{i^{\prime}}, u_{i^{\prime}})}, \end{aligned}} $$(8)
Results
Simulation studies
-
Step 0: We may allow the total number of occurrences for non-fatal events to be 24 times in a 12-month period, such as 15,31,…,349,365 days. However, the actual visiting time of each subject can be different from the designated times. Hence, we add random numbers, generated from a normal distribution with a mean of zero and a variance of 9, to each designated time point. Subsequently, the actual observed time points will be defined as$$\begin{array}{@{}rcl@{}} 0= l_{0} < l_{1i} < \cdots < l_{23,i} < l_{24}=366. \end{array} $$Let u01i, u02i, and u03i be random numbers generated from a uniform distribution on the interval (0,1). Additionally, let Ri, Ti, and Li be, respectively, the roots s of the equations:$$\begin{array}{*{20}l} \Lambda_{01}(s|z_{i}, w_{i},u_{i}) + \log(1-u_{01i})&=0,\\ \Lambda_{02}(s|z_{i}, w_{i},u_{i}) + \log(1-u_{02i})&=0,\\ \text{and} \Lambda_{03}(s|z_{i}, w_{i},u_{i}) + \log(1-u_{03i})&=0, \end{array} $$where$$\begin{array}{@{}rcl@{}} \Lambda_{0j}(s|z_{i}, w_{i},u_{i}) = \eta_{i}\left[\left(\beta_{0j} z_{i}\right) s + \exp\{\alpha_{0j} w_{i}\} \theta_{0j} s^{\gamma_{0j}}\right]\ \text{for}\ j=1,2,3. \end{array} $$
-
Step 1: If C≤Ri∧Ti∧Li, then the ith subject is defined as being censored without experiencing a non-fatal event, i.e., \(i \in \mathcal {B}_{1}\). If Ti=Ri∧Ti∧Li, then the ith subject is defined as being dead without experiencing a non-fatal event, i.e., \(i \in \mathcal {B}_{2}\). However, if Ri=Ri∧Ti∧Li, proceed to Step 2, and if Li=Ri∧Ti∧Li, proceed to Step 3.
-
Step 2: Let u12i be a random number generated from a uniform distribution on the interval (1− exp{Λ12(Ri|zi,wi,ui)},1), where$$\begin{array}{@{}rcl@{}} \Lambda_{12}(s|z_{i},w_{i},u_{i})=\eta_{i}\left[(\beta_{12} z_{i}) s + \exp\{\alpha_{12}w_{i}\} \theta_{12}s^{\gamma_{12}}\right]. \end{array} $$Redefine Ti as the root s of the equation,$$\begin{array}{@{}rcl@{}} \Lambda_{12}(s|z_{i},w_{i},u_{i}) + \log(1-u_{12i})=0. \end{array} $$If C≤Ti, then the ith subject is defined as being censored after experiencing a non-fatal event, i.e., \(i \in \mathcal {B}_{3}\). Otherwise, the ith subject is defined as being dead at time Ti after experiencing a non-fatal event, i.e., \(i \in \mathcal {B}_{4}\). Moreover,- If Ri∈(0,l1i), let ai=0 and bi=l1i. If Ri∈(lk−1,i,lki), let ai=lk−1,i and bi=lki for k=2,3,…,23.- However, if Ri∈(l23,i,C), the type of path should be redefined because a non-fatal event for the subject did not occur before the time of the last observation. Thus, if C≤Ti, the ith subject is defined as being censored without experiencing a non-fatal event, i.e., \(i \in \mathcal {B}_{1}\). Otherwise, the ith subject is defined as being dead at time Ti without experiencing a non-fatal event, i.e., \(i \in \mathcal {B}_{2}\).
-
Step 3: Let u32i and u34i be random numbers generated from uniform distributions on the intervals (1− exp{Λ32(Li|zi,wi,ui)},1) and (1− exp{Λ34(Li|zi,wi,ui)},1), respectively, where$$\begin{array}{@{}rcl@{}} \Lambda_{3j}(s|z_{i},w_{i},u_{i})=\eta_{i}\left[(\beta_{3j} z_{i}) s + \exp\{\alpha_{3j}w_{i}\} \theta_{3j}s^{\gamma_{3j}}\right],\ \text{for}\ j=2,4. \end{array} $$Now redefine Ri and Ti as the roots s of the equations:$$\begin{array}{*{20}l} \Lambda_{32}(s|z_{i},w_{i},u_{i}) + \log(1-u_{32i})&=0 \\ \text{and} \Lambda_{34}(s|z_{i},w_{i},u_{i}) + \log(1-u_{34i})&=0, \end{array} $$respectively. If C≤Ri∧Ti, the ith subject is defined as being censored without experiencing a non-fatal event after LTF, i.e., \(i \in \mathcal {B}_{5}\). If Ti≤Ri, then the ith subject is defined as being dead without experiencing a non-fatal event after LTF, i.e., \(i \in \mathcal {B}_{6}\). However, if Ri<Ti, move to Step 4.
-
Step 4: Let u42i be a random number generated from a uniform distribution on the interval (1− exp{Λ42(Ri|zi,wi,ui)},1), where$$\begin{array}{@{}rcl@{}} \Lambda_{42}(s|z_{i},w_{i},u_{i})=\eta_{i}\left[(\beta_{42} z_{i}) s + \exp\{\alpha_{42}w_{i}\} \theta_{42}s^{\gamma_{42}}\right]. \end{array} $$Redefine Ti as the root s of the equation,$$\begin{array}{@{}rcl@{}} \Lambda_{42}(s|z_{i},w_{i},u_{i}) + \log(1-u_{42i})=0. \end{array} $$If C≤Ti, then the ith subject is defined as being censored at time C after experiencing LTF and a non-fatal event, i.e., \(i \in \mathcal {B}_{5}\). Otherwise, the ith subject is defined as being dead at time Ti after experiencing LTF and a non-fatal event, i.e., \(i \in \mathcal {B}_{6}\).
Low (LTF(%)=22.6) | Moderate (LTF(%)=34.2) | High (LTF(%)=47.3) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Parameter | True value | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) |
Imputed-by-the-right-endpoint method
| |||||||||||||
α
01
| 0.01 | 81.7 | 15026 | 15104 | 96.8 | 73.3 | 15105 | 14975 | 95.2 | 20.6 | 14450 | 15186 | 96.2 |
α
02
| 0.01 | 176.2 | 22297 | 22961 | 95.4 | 324.5 | 24408 | 24066 | 94.8 | 28.8 | 27643 | 27426 | 95.4 |
α
03
| 0.01 | 133.2 | 27006 | 26429 | 95.4 | 86.1 | 16223 | 17086 | 96.2 | 75.3 | 13291 | 13250 | 95.2 |
α
12
| 0.01 | -145.7 | 28481 | 25849 | 95.2 | -113.4 | 29996 | 26279 | 93.6 | 74.1 | 27309 | 25620 | 96.2 |
α
32
| 0.01 | 109.7 | 65489 | 55615 | 93.2 | 77.1 | 36087 | 33747 | 96.8 | 50.8 | 26680 | 25219 | 94.8 |
β
01
| 0.004 | -10.1 | 81 | 87 | 93.8 | -9.4 | 80 | 88 | 91.6 | -8.6 | 87 | 88 | 92.6 |
β
02
| 0.004 | 1.1 | 92 | 92 | 94.6 | -1.4 | 97 | 96 | 94.4 | -0.4 | 103 | 101 | 94.0 |
β
03
| 0.004 | -7.2 | 87 | 86 | 91.2 | -6.4 | 105 | 105 | 93.4 | -9.3 | 136 | 133 | 91.6 |
β
12
| 0.004 | 3.5 | 115 | 115 | 97.0 | 5.7 | 112 | 116 | 95.6 | 3.4 | 116 | 115 | 95.8 |
β
32
| 0.004 | -0.3 | 217 | 199 | 96.8 | 7.6 | 174 | 173 | 96.4 | 5.3 | 148 | 152 | 97.2 |
σ
2
| 0.01 | 904.5 | 8164 | 8782 | 93.8 | 815.5 | 7848 | 8084 | 92.4 | 771.6 | 7626 | 7076 | 90.4 |
Proposed method
| |||||||||||||
α
01
| 0.01 | 32.2 | 15236 | 15136 | 96.2 | 64.8 | 15344 | 15084 | 95.0 | 20.7 | 14496 | 15279 | 96.2 |
α
02
| 0.01 | 70.2 | 22692 | 22951 | 95.0 | 286.1 | 24010 | 24133 | 95.2 | 100.4 | 28030 | 27569 | 95.2 |
α
03
| 0.01 | 289.4 | 27525 | 26349 | 95.0 | 121.3 | 16740 | 17161 | 95.0 | 86.3 | 13465 | 13391 | 95.0 |
α
12
| 0.01 | -24.6 | 26718 | 25661 | 95.8 | -83.4 | 29355 | 26230 | 94.0 | -37.0 | 27102 | 25736 | 96.2 |
α
32
| 0.01 | 123.2 | 67188 | 56122 | 93.6 | 93.4 | 36291 | 33577 | 95.6 | 54.0 | 26591 | 25204 | 94.2 |
β
01
| 0.004 | -5.5 | 89 | 90 | 95.0 | -5.0 | 85 | 91 | 93.8 | -5.3 | 88 | 91 | 94.4 |
β
02
| 0.004 | 5.9 | 95 | 97 | 96.2 | 4.0 | 99 | 100 | 94.2 | 4.8 | 107 | 106 | 94.8 |
β
03
| 0.004 | -1.7 | 92 | 91 | 93.2 | -1.7 | 107 | 110 | 95.6 | -3.3 | 141 | 139 | 93.4 |
β
12
| 0.004 | -1.9 | 109 | 110 | 96.4 | 0.9 | 108 | 112 | 95.2 | 0.1 | 110 | 111 | 96.0 |
β
32
| 0.004 | 1.0 | 214 | 199 | 96.6 | 8.4 | 179 | 175 | 96.2 | 4.4 | 150 | 153 | 97.0 |
σ
2
| 0.01 | 1016.2 | 9069 | 9074 | 92.2 | 897.8 | 7743 | 8198 | 91.0 | 874.1 | 7616 | 7423 | 87.2 |
Low (LTF(%)=19.4) | Moderate (LTF(%)=31.4) | High (LTF(%)=43.5) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Parameter | True value | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) |
Imputed-by-the-right-endpoint method
| |||||||||||||
α
01
| 0.01 | 36.6 | 15548 | 14973 | 93.8 | -110.5 | 15890 | 15137 | 94.2 | -97.0 | 15327 | 15425 | 94.6 |
α
02
| 0.02 | -8.8 | 23990 | 22697 | 96.0 | 2.5 | 23708 | 25122 | 97.0 | 44.4 | 29732 | 28452 | 95.2 |
α
03
| 0.01 | 400.1 | 27926 | 26768 | 95.8 | 9.1 | 18791 | 17136 | 93.8 | -80.3 | 14385 | 13500 | 93.6 |
α
12
| 0.01 | 100.0 | 27898 | 26371 | 94.6 | 199.2 | 28271 | 25833 | 92.8 | 172.0 | 29132 | 26387 | 93.8 |
α
32
| 0.01 | 274.6 | 66261 | 56538 | 93.6 | 121.0 | 35562 | 33829 | 94.4 | 125.5 | 29879 | 26193 | 94.2 |
β
01
| 0.004 | -6.6 | 99 | 97 | 90.0 | -8.7 | 89 | 96 | 93.4 | -6.3 | 95 | 97 | 95.2 |
β
02
| 0.008 | -0.9 | 137 | 139 | 94.0 | -2.8 | 129 | 140 | 95.8 | -0.3 | 143 | 149 | 96.0 |
β
03
| 0.004 | -2.8 | 96 | 98 | 93.0 | -5.7 | 121 | 116 | 91.0 | -9.5 | 142 | 144 | 94.4 |
β
12
| 0.004 | 6.4 | 120 | 125 | 97.2 | 6.2 | 120 | 127 | 98.4 | 5.8 | 124 | 125 | 96.8 |
β
32
| 0.004 | 0.6 | 234 | 218 | 96.8 | 7.6 | 204 | 188 | 96.4 | 9.5 | 177 | 169 | 95.0 |
σ
2
| 0.01 | 631.4 | 7287 | 8545 | 97.6 | 705.2 | 6851 | 7982 | 96.2 | 714.8 | 7217 | 7540 | 90.4 |
Proposed method
| |||||||||||||
α
01
| 0.01 | 21.6 | 15586 | 15134 | 94.0 | -56.8 | 16268 | 15285 | 94.0 | -92.4 | 15530 | 15487 | 94.2 |
α
02
| 0.02 | -0.6 | 24316 | 22833 | 95.8 | -18.9 | 24116 | 25162 | 96.6 | 104.0 | 30008 | 28458 | 95.0 |
α
03
| 0.01 | 337.6 | 27943 | 26924 | 95.4 | -9.4 | 18629 | 17265 | 94.0 | -83.6 | 14279 | 13600 | 94.2 |
α
12
| 0.01 | 43.2 | 27653 | 26452 | 94.6 | 175.4 | 27650 | 25973 | 93.8 | 102.5 | 28481 | 26251 | 93.2 |
α
32
| 0.01 | 296.4 | 67196 | 57028 | 93.4 | 140.3 | 36513 | 34261 | 94.8 | 170.0 | 30037 | 26145 | 93.8 |
β
01
| 0.004 | -2.5 | 106 | 101 | 91.8 | -4.5 | 95 | 99 | 94.6 | -2.3 | 100 | 100 | 95.8 |
β
02
| 0.008 | 3.8 | 146 | 146 | 95.6 | 2.0 | 133 | 148 | 98.6 | 3.6 | 148 | 155 | 97.0 |
β
03
| 0.004 | 1.3 | 102 | 102 | 93.4 | -0.3 | 124 | 121 | 94.0 | -3.0 | 149 | 150 | 95.4 |
β
12
| 0.004 | 0.3 | 112 | 119 | 96.0 | 0.8 | 116 | 122 | 98.0 | 1.1 | 117 | 121 | 96.4 |
β
32
| 0.004 | 2.5 | 232 | 222 | 97.2 | 8.5 | 204 | 189 | 96.4 | 9.7 | 178 | 170 | 95.6 |
σ
2
| 0.01 | 838.4 | 8153 | 9217 | 94.2 | 852.3 | 7505 | 8446 | 93.8 | 791.2 | 7447 | 7745 | 89.2 |
Low (LTF(%)=22.3) | Moderate (LTF(%)=34.2) | High (LTF(%)=47.6) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Parameter | True value | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) |
Imputed-by-the-right-endpoint method
| |||||||||||||
α
01
| 0.01 | 3.3 | 14848 | 14915 | 95.2 | -20.8 | 16313 | 15029 | 92.0 | -63.6 | 15651 | 15144 | 95.0 |
α
02
| 0.01 | 140.0 | 22910 | 22360 | 94.0 | 23.4 | 24852 | 24383 | 95.0 | 9.0 | 26169 | 28020 | 97.2 |
α
03
| 0.01 | 79.0 | 25396 | 26622 | 96.2 | 115.9 | 18132 | 17194 | 92.8 | -4.9 | 14262 | 13148 | 93.0 |
α
12
| 0.0125 | -100.2 | 27253 | 26397 | 94.4 | 10.5 | 30146 | 26715 | 93.0 | 74.9 | 25881 | 25844 | 95.4 |
α
32
| 0.01 | 479.4 | 59836 | 50929 | 92.0 | -108.0 | 37118 | 33609 | 95.2 | 125.6 | 26069 | 25027 | 94.6 |
β
01
| 0.004 | -11.6 | 89 | 86 | 89.4 | -10.8 | 92 | 87 | 88.6 | -11.3 | 86 | 87 | 89.2 |
β
02
| 0.004 | -1.2 | 83 | 92 | 96.4 | -3.9 | 89 | 94 | 95.2 | -0.5 | 102 | 101 | 92.8 |
β
03
| 0.004 | -8.6 | 83 | 85 | 91.4 | -10.3 | 109 | 103 | 90.8 | -11.6 | 149 | 133 | 89.4 |
β
12
| 0.005 | 3.7 | 133 | 130 | 96.0 | 2.3 | 125 | 126 | 96.2 | 3.0 | 131 | 129 | 96.0 |
β
32
| 0.004 | 0.4 | 197 | 199 | 95.8 | 6.6 | 172 | 171 | 95.2 | 3.4 | 139 | 151 | 96.2 |
σ
2
| 0.01 | 878.9 | 8926 | 8822 | 92.6 | 734.8 | 6989 | 7754 | 91.4 | 775.5 | 7514 | 7231 | 87.6 |
Proposed method
| |||||||||||||
α
01
| 0.01 | 29.1 | 15161 | 15024 | 95.2 | 11.9 | 16449 | 15111 | 91.8 | -99.5 | 15704 | 15169 | 94.8 |
α
02
| 0.01 | 126.2 | 22920 | 22435 | 93.8 | -49.7 | 25179 | 24488 | 95.2 | -34.2 | 26495 | 28218 | 97.4 |
α
03
| 0.01 | 9.4 | 26768 | 26779 | 95.8 | 98.7 | 17948 | 17287 | 93.8 | 1.1 | 14013 | 13191 | 93.8 |
α
12
| 0.0125 | 21.2 | 26832 | 26404 | 95.2 | 44.7 | 29934 | 26567 | 92.8 | 52.4 | 25781 | 25861 | 95.6 |
α
32
| 0.01 | 280.8 | 60729 | 51753 | 91.4 | -181.5 | 36859 | 33796 | 95.4 | 173.3 | 26819 | 25056 | 93.2 |
β
01
| 0.004 | -7.5 | 95 | 90 | 92.2 | -6.8 | 95 | 90 | 90.8 | -8.1 | 89 | 90 | 93.0 |
β
02
| 0.004 | 4.1 | 88 | 96 | 97.2 | 1.8 | 94 | 99 | 96.2 | 4.6 | 106 | 105 | 93.4 |
β
03
| 0.004 | -3.9 | 88 | 89 | 93.6 | -4.1 | 116 | 108 | 92.8 | -6.3 | 154 | 138 | 90.6 |
β
12
| 0.005 | -0.9 | 124 | 124 | 96.4 | -2.0 | 117 | 122 | 97.0 | -1.2 | 123 | 124 | 95.4 |
β
32
| 0.004 | 2.3 | 195 | 200 | 95.8 | 6.9 | 171 | 172 | 95.6 | 3.8 | 137 | 152 | 97.2 |
σ
2
| 0.01 | 999.2 | 9282 | 9124 | 93.0 | 936.4 | 8781 | 8219 | 88.6 | 873.0 | 8002 | 7404 | 85.6 |
N(0,0.01) | U(−0.173,0.173) | DE(0.007) | G(100.5,0.01) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(LTF(%)=34.2) | (LTF(%)=34.4) | (LTF(%)=34.5) | (LTF(%)=34.5) | ||||||||||
Parameter | True value | r.Bias (%) | SEM (×105) | CP (%) | r.Bias (%) | SEM (×105) | CP (%) | r.Bias (%) | SEM (×105) | CP (%) | r.Bias (%) | SEM (×105) | CP (%) |
α
01
| 0.01 | 18.8 | 15299 | 94.0 | 40.9 | 15169 | 94.2 | 36.7 | 15215 | 94.8 | -28.7 | 15089 | 96.2 |
α
02
| 0.01 | 1.3 | 24633 | 93.2 | -83.8 | 24639 | 97.0 | 89.0 | 24401 | 94.4 | 45.0 | 24623 | 96.6 |
α
03
| 0.01 | -143.8 | 17210 | 94.4 | 58.9 | 17266 | 93.8 | -110.5 | 16925 | 93.8 | 119.9 | 17198 | 93.6 |
α
12
| 0.01 | 181.1 | 25925 | 96.4 | -27.9 | 26141 | 94.8 | 27.1 | 26318 | 93.2 | 159.3 | 25682 | 95.2 |
α
32
| 0.01 | -16.5 | 33404 | 95.4 | -80.1 | 33158 | 94.0 | -22.5 | 33619 | 94.0 | -82.4 | 33595 | 91.8 |
β
01
| 0.004 | -4.3 | 91 | 94.8 | -5.8 | 90 | 94.0 | -3.3 | 91 | 94.0 | -6.7 | 90 | 92.2 |
β
02
| 0.004 | 2.7 | 99 | 96.4 | 4.9 | 100 | 94.8 | 5.4 | 101 | 97.0 | 4.4 | 99 | 95.4 |
β
03
| 0.004 | -2.2 | 109 | 93.2 | -2.9 | 109 | 91.0 | -2.8 | 110 | 94.4 | -2.9 | 108 | 91.8 |
β
12
| 0.004 | 0.1 | 111 | 96.6 | 2.3 | 111 | 95.0 | 0.6 | 110 | 94.8 | -0.3 | 111 | 95.6 |
β
32
| 0.004 | 8.0 | 174 | 97.0 | 0.8 | 169 | 96.0 | 2.9 | 171 | 96.8 | 5.2 | 170 | 96.4 |
σ
2
| 0.01 | 955.8 | 8431 | 89.2 | 974.2 | 8325 | 89.4 | 926.1 | 8284 | 89.6 | 928.7 | 8462 | 89.2 |
Illustrative data analysis
Gender | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Women | Men | |||||||||
Certificate | Certificate | |||||||||
All | With | Without | With | Without | ||||||
mean | mean | mean | mean |
n
| mean | |||||
Age |
n
| (±SD) |
n
| (±SD) |
n
| (±SD) |
n
| (±SD) |
n
| (±SD) |
at entry | 1000 | 75.0 | 456 | 76.0 | 122 | 74.4 | 306 | 74.7 | 116 | 72.8 |
(±6.84) | (±7.03) | (±7.02) | (±6.67) | (±5.61) | ||||||
at DM diagnosis | 186 | 83.3 | 109 | 84.2 | 17 | 83.3 | 45 | 81.5 | 15 | 81.9 |
(±5.46) | (±5.60) | (±5.39) | (±4.92) | (±4.99) | ||||||
at death after DM | 127 | 87.6 | 72 | 88.8 | 10 | 88.9 | 36 | 85.4 | 9 | 84.8 |
(±5.93) | (±6.21) | (±5.19) | (±5.23) | (±4.12) | ||||||
at death without DM | 438 | 84 | 170 | 85.9 | 47 | 84.5 | 161 | 82.8 | 60 | 81.1 |
(±7.03) | (±7.17) | (±6.91) | (±6.44) | (±6.78) | ||||||
at death after LTF | 159 | 87.2 | 80 | 87.7 | 20 | 86.3 | 43 | 87.3 | 16 | 85.9 |
(±6.42) | (±6.04) | (±6.85) | (±6.75) | (±7.12) |
Covariate | Transition models | ||||
---|---|---|---|---|---|
0→1 | 0→2 | 1→2 | 0→3 | 3→2 | |
Gender | 0.063 | <0.001 | 0.093 | 0.354 | 0.062 |
Certificate | 0.963 | <0.001 | 0.147 | 0.754 | 0.148 |
Covariate | Param | Est | SE |
P
|
---|---|---|---|---|
Gender |
β
01
| -0.0156 | 0.0132 | 0.245 |
β
02
| 0.0295 | 0.0136 | 0.004 | |
β
12
| 0.0101 | 0.205 | 0.961 | |
β
03
| -8.49 ×10−3 | 0.0108 | 0.439 | |
β
32
| 6.19 ×10−3 | 1.57 ×10−3 | <0.001 | |
Certificate |
α
01
| -2.10 ×10−3 | 0.190 | 0.991 |
α
02
| -3.00 ×10−5 | 0.128 | 0.999 | |
α
12
| 3.90 ×10−5 | 0.621 | 0.999 | |
α
03
| -9.80 ×10−4 | 0.151 | 0.995 | |
α
32
| 3.85 ×10−4 | 1.133 | 0.999 | |
σ
2
| 0.999 | 2.55 ×10−3 | <0.001 |