  
Truth

Waiting times

wGLM^{k}

wGLM adhoc^{l}


Patients^{m}

Donor

\( w \)

Survival S

log(−log(S))^{d}

\( {f}_{01}(w) \)

\( \overline{q}(w) \)
^{e}

\( {\overline{\gamma}}_1 \)
^{f}

\( {\widehat{f}}_{01}(w) \)
^{g}

Bias^{h}

SE_{est}^{i}

Coverage^{j}

Bias^{h}

SE_{est}^{i}

Coverage^{j}


\( n=1000 \)

No

–

0.333^{a}

0.10

–

–

–

–

−0.003

0.125

95.5%

−0.003

0.125

95.5%


Yes

–

0.620^{b}

−0.74

–

–

–

–

−0.002

0.078

92.2%

−0.002

0.098

94.0%

 
0.5

0.733^{c}

−1.17

0.33

0.46

0.72

0.33

−0.003

0.164

94.7%

−0.002

0.172

94.0%

 
1

0.681^{c}

−0.96

0.33

0.39

0.86

0.33

−0.010

0.134

94.6%

−0.011

0.161

95.1%

 
3

0.451^{c}

−0.23

0.33

0.15

2.26

0.33

0.000

0.106

86.4%

0.004

0.191

93.7%

\( n=400 \)
^{n}

No

–

0.333^{a}

0.10

–

–

–

–

−0.004

0.210

95.6%

−0.003

0.210

95.6%


Yes

–

0.620^{b}

−0.74

–

–

–

–

−0.007

0.124

92.8%

−0.007

0.156

92.0%

 
0.5

0.733^{c}

−1.17

0.33

0.46

0.72

0.33

−0.024

0.263

95.4%

−0.019

0.277

95.4%

 
1

0.681^{c}

−0.96

0.33

0.39

0.86

0.33

−0.019

0.224

93.8%

−0.026

0.269

94.9%

 
3

0.451^{c}

−0.23

0.33

0.15

2.26

0.33

−0.001

0.170

85.6%

−0.017

0.309

93.4%

 Weighted generalised linear model (wGLM) with loglog link; 0–6 years uniform censoring was used
 ^{a}True survival \( {S}_0(5) \) in patients without a donor available
 ^{b}True survival \( {S}_1(5) \) in patients with a donor available
 ^{c}True survival \( {S}_1\left(5\leftw\right.\right) \) in patients with a donor available at waiting time w
 ^{d}loglog transformation of true survival probabilities \( \mathrm{S} \)
 ^{e}Mean observed proportion of patients with a 0 → 1 transition at \( w \) = 0.5, 1 and 3
 ^{f}Mean estimated weight for \( w \) = 0.5, 1 and 3
 ^{g}Mean estimated probabilities for \( {f}_{01}(w) \) at \( w \) = 0.5, 1 and 3
 ^{h}Mean difference between estimated and true \( \log \left(\log \left(\mathrm{S}\right)\right) \) values
 ^{i}Mean of standard errors of \( \log \left(\log \left(\mathrm{S}\right)\right) \) estimates
 ^{j}Coverage of the 95% confidence intervals for \( \log \left(\log \left(\mathrm{S}\right)\right) \)
 ^{k}The weighted generalised linear model (wGLM) uses \( {\widehat{V}}_{i,1}\left({t}^{\ast}\right) \) according to eq. (6)
 ^{l}The weighted generalised linear model (wGLM) uses the adhoc correction suggested to estimate \( {\widehat{V}}_{i,1}\left({t}^{\ast}\right) \) (with one repetition per observation per simulation run)
 ^{m}\( n \) represents the size of the entire sample where 25% of the patients have no donor; 25% of the patients have a donor available at \( w \) =0.5, 25% at \( w \) =1, and 25% at \( w \) =3, respectively
 ^{n}Two of 1000 simulation runs were excluded due to nonconvergence during parameter estimation