Background
Methods
Review of estimation methods
Nonparametric approaches
Semiparametric approach
Parametric approach
Global approaches over the whole follow-up period
Simulations
%par
SAS macro developed by the authors.Results
Simulations
Estimation method |
n=1,000 |
n=10,000 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Time |
A(t) | Bias | SEE | SSD | CP | Bias | SEE | SSD | CP | |
KM |
τ/4 | 0.284 | 0.001584 | 0.052440 | 0.052591 | 0.949 | −0.000011 | 0.016622 | 0.016349 | 0.944 |
τ/2 | 0.240 | 0.001496 | 0.039210 | 0.039099 | 0.948 | 0.000235 | 0.012434 | 0.012420 | 0.944 | |
3 τ/4 | 0.200 | 0.001100 | 0.035666 | 0.035948 | 0.946 | −0.000333 | 0.011353 | 0.011354 | 0.949 | |
τ
| 0.166 | 0.004047 | 0.043238 | 0.053015 | 0.912 | 0.001025 | 0.017251 | 0.019598 | 0.943 | |
WKM |
τ/4 | 0.284 | 0.001594 | 0.052516 | 0.052483 | 0.949 | 0.000003 | 0.016613 | 0.016357 | 0.946 |
τ/2 | 0.240 | 0.001541 | 0.039144 | 0.038926 | 0.950 | 0.000285 | 0.012401 | 0.012398 | 0.946 | |
3 τ/4 | 0.200 | 0.001093 | 0.035402 | 0.035479 | 0.953 | −0.000286 | 0.011283 | 0.011297 | 0.952 | |
τ
| 0.166 | 0.002922 | 0.040635 | 0.048602 | 0.902 | 0.000497 | 0.016646 | 0.018245 | 0.942 | |
COX |
τ/4 | 0.284 | 0.000977 | 0.038843 | 0.038208 | 0.958 | −0.000136 | 0.012292 | 0.012206 | 0.956 |
τ/2 | 0.240 | 0.001108 | 0.033847 | 0.033524 | 0.951 | 0.000006 | 0.010700 | 0.010616 | 0.958 | |
3 τ/4 | 0.200 | 0.001031 | 0.029264 | 0.028893 | 0.958 | −0.000081 | 0.009237 | 0.009253 | 0.954 | |
τ
| 0.166 | 0.002577 | 0.027146 | 0.027753 | 0.946 | 0.000148 | 0.008965 | 0.009087 | 0.950 | |
PCH |
τ/4 | 0.284 | 0.001356 | 0.038338 | 0.038248 | 0.952 | −0.000086 | 0.012120 | 0.012209 | 0.953 |
τ/2 | 0.240 | 0.001372 | 0.033380 | 0.033529 | 0.948 | 0.000034 | 0.010543 | 0.010608 | 0.952 | |
3 τ/4 | 0.200 | 0.001113 | 0.028804 | 0.028870 | 0.957 | −0.000081 | 0.009088 | 0.009263 | 0.952 | |
τ
| 0.166 | 0.001564 | 0.025811 | 0.025420 | 0.961 | −0.000154 | 0.008105 | 0.008153 | 0.952 | |
Simpler | – | 0.333 | 0.000826 | 0.043356 | 0.043147 | 0.952 | −0.000209 | 0.013715 | 0.013776 | 0.955 |
Estimation method |
n=1, 000 |
n=10, 000 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Time |
A(t) | Bias | SEE | SSD | CP | Bias | SEE | SSD | CP | |
KM |
τ/4 | 0.269 | 0.001799 | 0.044659 | 0.045486 | 0.940 | 0.000129 | 0.014162 | 0.014200 | 0.946 |
τ/2 | 0.231 | 0.001217 | 0.036054 | 0.036037 | 0.943 | 0.000351 | 0.011437 | 0.011547 | 0.946 | |
3 τ/4 | 0.200 | 0.001164 | 0.034218 | 0.034637 | 0.948 | −0.000204 | 0.010895 | 0.010746 | 0.956 | |
τ
| 0.176 | 0.003532 | 0.041550 | 0.047835 | 0.915 | 0.000299 | 0.016351 | 0.019086 | 0.948 | |
WKM |
τ/4 | 0.269 | 0.001832 | 0.044713 | 0.045359 | 0.942 | 0.000131 | 0.014153 | 0.014197 | 0.946 |
τ/2 | 0.231 | 0.001283 | 0.035999 | 0.035858 | 0.947 | 0.000368 | 0.011408 | 0.011509 | 0.947 | |
3 τ/4 | 0.200 | 0.001132 | 0.034004 | 0.034272 | 0.950 | −0.000193 | 0.010838 | 0.010716 | 0.956 | |
τ
| 0.176 | 0.002628 | 0.039647 | 0.045615 | 0.906 | 0.000116 | 0.015851 | 0.017720 | 0.947 | |
COX |
τ/4 | 0.269 | 0.000957 | 0.036029 | 0.035611 | 0.955 | 0.000107 | 0.011401 | 0.011229 | 0.955 |
τ/2 | 0.231 | 0.001067 | 0.031741 | 0.031499 | 0.954 | 0.000129 | 0.010031 | 0.009949 | 0.953 | |
3 τ/4 | 0.200 | 0.000972 | 0.028300 | 0.028071 | 0.962 | 0.000060 | 0.008937 | 0.008899 | 0.949 | |
τ
| 0.176 | 0.002177 | 0.026818 | 0.027274 | 0.955 | 0.000168 | 0.008790 | 0.008771 | 0.956 | |
PCH |
τ/4 | 0.269 | 0.003717 | 0.035027 | 0.035896 | 0.940 | 0.002630 | 0.011076 | 0.011300 | 0.939 |
τ/2 | 0.231 | 0.002926 | 0.030819 | 0.031734 | 0.945 | 0.001853 | 0.009736 | 0.009995 | 0.936 | |
3 τ/4 | 0.200 | 0.002124 | 0.027440 | 0.028260 | 0.949 | 0.001247 | 0.008666 | 0.008949 | 0.940 | |
τ
| 0.176 | 0.001883 | 0.025457 | 0.025679 | 0.958 | 0.000621 | 0.008014 | 0.008240 | 0.946 | |
Simpler | – | 0.333 | 0.000814 | 0.041900 | 0.041749 | 0.952 | 0.000050 | 0.013257 | 0.013257 | 0.947 |
Estimation method |
n=1, 000 |
n=10, 000 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Time |
A(t) | Bias | SEE | SSD | CP | Bias | SEE | SSD | CP | |
KM |
τ/4 | 0.299 | 0.000814 | 0.064311 | 0.064377 | 0.947 | −0.000024 | 0.020388 | 0.020204 | 0.956 |
τ/2 | 0.250 | 0.002020 | 0.043388 | 0.043169 | 0.952 | 0.000210 | 0.013761 | 0.013651 | 0.944 | |
3 τ/4 | 0.200 | 0.001174 | 0.037152 | 0.037027 | 0.955 | −0.000469 | 0.011824 | 0.011798 | 0.960 | |
τ
| 0.153 | 0.007382 | 0.043968 | 0.054032 | 0.891 | 0.000554 | 0.018140 | 0.021081 | 0.939 | |
WKM |
τ/4 | 0.299 | 0.000805 | 0.064427 | 0.064296 | 0.950 | −0.000010 | 0.020380 | 0.020196 | 0.954 |
τ/2 | 0.250 | 0.002055 | 0.043322 | 0.042973 | 0.949 | 0.000272 | 0.013722 | 0.013643 | 0.947 | |
3 τ/4 | 0.200 | 0.001193 | 0.036838 | 0.036463 | 0.962 | −0.000410 | 0.011739 | 0.011741 | 0.958 | |
τ
| 0.153 | 0.005596 | 0.040652 | 0.048586 | 0.898 | 0.000055 | 0.017280 | 0.019095 | 0.935 | |
COX |
τ/4 | 0.299 | 0.001207 | 0.041863 | 0.040891 | 0.960 | −0.000209 | 0.013250 | 0.013076 | 0.962 |
τ/2 | 0.250 | 0.001321 | 0.036377 | 0.035580 | 0.954 | −0.000062 | 0.011499 | 0.011341 | 0.958 | |
3 τ/4 | 0.200 | 0.001300 | 0.030350 | 0.029672 | 0.956 | −0.000121 | 0.009572 | 0.009502 | 0.965 | |
τ
| 0.153 | 0.002791 | 0.027165 | 0.028199 | 0.945 | −0.000309 | 0.009206 | 0.010402 | 0.945 | |
PCH |
τ/4 | 0.299 | −0.000084 | 0.041594 | 0.040674 | 0.961 | −0.001831 | 0.013151 | 0.013022 | 0.957 |
τ/2 | 0.250 | 0.000876 | 0.036176 | 0.035464 | 0.956 | −0.000759 | 0.011424 | 0.011313 | 0.958 | |
3 τ/4 | 0.200 | 0.001462 | 0.030163 | 0.029655 | 0.959 | −0.000051 | 0.009509 | 0.009485 | 0.961 | |
τ
| 0.153 | 0.002572 | 0.025716 | 0.024704 | 0.961 | 0.000622 | 0.008058 | 0.007962 | 0.945 | |
Simpler | – | 0.333 | 0.001129 | 0.044983 | 0.044481 | 0.955 | −0.000242 | 0.014226 | 0.014195 | 0.957 |
Estimation method |
n=1, 000 |
n=10, 000 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Time |
A(t) | Bias | SEE | SSD | CP | Bias | SEE | SSD | CP | |
KM |
τ/4 | 0.181 | 0.001124 | 0.045053 | 0.045787 | 0.954 | 0.000289 | 0.014277 | 0.014126 | 0.949 |
τ/2 | 0.133 | 0.001330 | 0.037581 | 0.037647 | 0.953 | −0.000029 | 0.011915 | 0.012154 | 0.935 | |
3 τ/4 | 0.109 | 0.001211 | 0.036543 | 0.036593 | 0.953 | −0.000301 | 0.011618 | 0.011608 | 0.952 | |
τ
| 0.093 | 0.002743 | 0.043713 | 0.051764 | 0.933 | −0.000888 | 0.016362 | 0.019957 | 0.950 | |
WKM |
τ/4 | 0.181 | 0.001138 | 0.045090 | 0.045739 | 0.954 | 0.000291 | 0.014274 | 0.014130 | 0.949 |
τ/2 | 0.133 | 0.001347 | 0.037587 | 0.037593 | 0.956 | −0.000024 | 0.011911 | 0.012151 | 0.938 | |
3 τ/4 | 0.109 | 0.001165 | 0.036511 | 0.036518 | 0.952 | −0.000293 | 0.011612 | 0.011607 | 0.956 | |
τ
| 0.093 | 0.001685 | 0.042617 | 0.049261 | 0.920 | −0.000708 | 0.016157 | 0.019107 | 0.946 | |
COX |
τ/4 | 0.181 | −0.018761 | 0.037521 | 0.037543 | 0.933 | −0.019843 | 0.011869 | 0.011939 | 0.621 |
τ/2 | 0.133 | 0.010548 | 0.033500 | 0.033580 | 0.941 | 0.009504 | 0.010588 | 0.010676 | 0.847 | |
3 τ/4 | 0.109 | 0.023376 | 0.030960 | 0.031017 | 0.879 | 0.022314 | 0.009775 | 0.009879 | 0.368 | |
τ
| 0.093 | 0.030360 | 0.029427 | 0.029588 | 0.830 | 0.029168 | 0.009323 | 0.009456 | 0.127 | |
PCH |
τ/4 | 0.181 | 0.026479 | 0.048525 | 0.049191 | 0.908 | −0.017516 | 0.011688 | 0.012080 | 0.672 |
τ/2 | 0.133 | 0.057418 | 0.044915 | 0.045594 | 0.738 | 0.011082 | 0.010391 | 0.010768 | 0.806 | |
3 τ/4 | 0.109 | 0.070045 | 0.042342 | 0.043042 | 0.607 | 0.023478 | 0.009571 | 0.009936 | 0.313 | |
τ
| 0.093 | 0.075924 | 0.040403 | 0.041050 | 0.525 | 0.029848 | 0.009011 | 0.009360 | 0.098 |