webuse set "https://raw.githubusercontent.com//mthevenin/analyse_duree/master/bases/"
webuse "transplantation_m", clear
webuse set
/*
list in 1/10
+----------------------------------------------------------------------------+
| id year age died stime surgery transp~t wait mois compet |
|----------------------------------------------------------------------------|
1. | 15 68 53 1 1 0 0 0 1 1 |
2. | 43 70 43 1 2 0 0 0 1 1 |
3. | 61 71 52 1 2 0 0 0 1 1 |
4. | 75 72 52 1 2 0 0 0 1 1 |
5. | 6 68 54 1 3 0 0 0 1 2 |
|----------------------------------------------------------------------------|
6. | 42 70 36 1 3 0 0 0 1 1 |
7. | 54 71 47 1 3 0 0 0 1 1 |
8. | 38 70 41 1 5 0 1 5 1 1 |
9. | 85 73 47 1 5 0 0 0 1 1 |
10. | 2 68 51 1 6 0 0 0 1 1 |
+----------------------------------------------------------------------------+
*/Stata
Ouverture de la base
Analyse non paramétrique
Méthode actuarielle
Contrairement à la formation, l’estimation sera faite sur des intervalles de 30 jours
ltable stime died, interval(30) graph
/*
Beg. Std.
Interval Total Deaths Lost Survival Error [95% Conf. Int.]
-------------------------------------------------------------------------------
0 30 103 22 1 0.7854 0.0406 0.6926 0.8531
30 60 80 14 2 0.6462 0.0475 0.5449 0.7305
60 90 64 12 0 0.5250 0.0498 0.4232 0.6171
90 120 52 5 1 0.4741 0.0499 0.3738 0.5677
120 150 46 1 1 0.4636 0.0499 0.3637 0.5575
150 180 44 2 0 0.4426 0.0498 0.3435 0.5369
180 210 42 3 1 0.4106 0.0495 0.3132 0.5053
210 240 38 1 0 0.3998 0.0494 0.3030 0.4945
240 270 37 1 1 0.3888 0.0492 0.2928 0.4836
270 300 35 2 0 0.3666 0.0488 0.2720 0.4614
300 330 33 1 0 0.3555 0.0486 0.2618 0.4502
330 360 32 3 1 0.3216 0.0478 0.2308 0.4157
360 390 28 0 1 0.3216 0.0478 0.2308 0.4157
390 420 27 0 1 0.3216 0.0478 0.2308 0.4157
420 450 26 0 2 0.3216 0.0478 0.2308 0.4157
480 510 24 0 1 0.3216 0.0478 0.2308 0.4157
510 540 23 0 1 0.3216 0.0478 0.2308 0.4157
540 570 22 0 1 0.3216 0.0478 0.2308 0.4157
570 600 21 1 1 0.3059 0.0479 0.2155 0.4010
600 630 19 0 1 0.3059 0.0479 0.2155 0.4010
660 690 18 1 1 0.2885 0.0483 0.1982 0.3849
720 750 16 1 0 0.2704 0.0485 0.1807 0.3681
840 870 15 1 1 0.2518 0.0486 0.1629 0.3506
900 930 13 0 1 0.2518 0.0486 0.1629 0.3506
930 960 12 0 1 0.2518 0.0486 0.1629 0.3506
960 990 11 1 0 0.2289 0.0493 0.1404 0.3304
990 1020 10 1 0 0.2060 0.0494 0.1192 0.3093
1020 1050 9 1 0 0.1831 0.0489 0.0992 0.2873
1140 1170 8 0 1 0.1831 0.0489 0.0992 0.2873
1320 1350 7 0 1 0.1831 0.0489 0.0992 0.2873
1380 1410 6 1 2 0.1465 0.0510 0.0645 0.2602
1560 1590 3 0 2 0.1465 0.0510 0.0645 0.2602
1770 1800 1 0 1 0.1465 0.0510 0.0645 0.2602
-------------------------------------------------------------------------------
*/
Récupération des quartiles de la durée
Installation de la commande qlt
net install qlt, from("https://mthevenin.github.io/analyse_duree/ado/qlt/") replace
* help qltltable stime died, interval(30) saving(base, replace)
use base, clear
qltDuree pour differents quantiles de la fonction de survie
Definition des bornes Stata-ltable
S(t)=0.90: t= .
S(t)=0.75: t= 7.623
S(t)=0.50: t= 74.729
S(t)=0.25: t= 849.325
S(t)=0.10: t= .Avec la définition des bornes des intervalles de Sas
qlt, sas
/*
Duree pour differents quantiles de la fonction de survie
Definition des bornes Sas-lifetest
S(t)=0.90: t= 13.977
S(t)=0.75: t= 37.623
S(t)=0.50: t= 104.729
S(t)=0.25: t= 906.993
S(t)=0.10: t= .
*/Méthode Kaplan-Meier
Mode analyse des durées: stset
Les données doivent être mises en mode analyse de durée (help stset)
qui use "D:\Marc\SMS\FORMATIONS\2017\analyse biographique\A distribuer\transplantation.dta" , clear
stset stime, f(died)
/*
failure event: (assumed to fail at time=stime)
obs. time interval: (0, stime]
exit on or before: failure
------------------------------------------------------------------------------
103 total observations
0 exclusions
------------------------------------------------------------------------------
103 observations remaining, representing
103 failures in single-record/single-failure data
31,938 total analysis time at risk and under observation
at risk from t = 0
earliest observed entry t = 0
last observed exit t = 1,799
list in 1/10
+-----------------------------------------------------------------------------------+
| id year age died stime surgery transp~t wait _st _d _t _t0 |
|-----------------------------------------------------------------------------------|
1. | 1 67 30 1 50 0 0 0 1 1 50 0 |
2. | 2 68 51 1 6 0 0 0 1 1 6 0 |
3. | 3 68 54 1 16 0 1 1 1 1 16 0 |
4. | 4 68 40 1 39 0 1 36 1 1 39 0 |
5. | 5 68 20 1 18 0 0 0 1 1 18 0 |
|-----------------------------------------------------------------------------------|
6. | 6 68 54 1 3 0 0 0 1 1 3 0 |
7. | 7 68 50 1 675 0 1 51 1 1 675 0 |
8. | 8 68 45 1 40 0 0 0 1 1 40 0 |
9. | 9 68 47 1 85 0 0 0 1 1 85 0 |
10. | 10 68 42 1 58 0 1 12 1 1 58 0 |
+-----------------------------------------------------------------------------------+
*/Estimation de la fonction de survie
sts list
/*
failure _d: died
analysis time _t: stime
At Survivor Std.
Time Risk Fail Lost Function Error [95% Conf. Int.]
------------------------------------------------------------------------
1 103 1 0 0.9903 0.0097 0.9331 0.9986
2 102 3 0 0.9612 0.0190 0.8998 0.9852
3 99 3 0 0.9320 0.0248 0.8627 0.9670
5 96 2 0 0.9126 0.0278 0.8388 0.9535
6 94 2 0 0.8932 0.0304 0.8155 0.9394
8 92 1 0 0.8835 0.0316 0.8040 0.9321
9 91 1 0 0.8738 0.0327 0.7926 0.9247
11 90 0 1 0.8738 0.0327 0.7926 0.9247
12 89 1 0 0.8640 0.0338 0.7811 0.9171
16 88 3 0 0.8345 0.0367 0.7474 0.8937
17 85 1 0 0.8247 0.0375 0.7363 0.8857
18 84 1 0 0.8149 0.0383 0.7253 0.8777
21 83 2 0 0.7952 0.0399 0.7034 0.8614
28 81 1 0 0.7854 0.0406 0.6926 0.8531
30 80 1 0 0.7756 0.0412 0.6819 0.8448
31 79 0 1 0.7756 0.0412 0.6819 0.8448
32 78 1 0 0.7657 0.0419 0.6710 0.8363
35 77 1 0 0.7557 0.0425 0.6603 0.8278
36 76 1 0 0.7458 0.0431 0.6495 0.8192
37 75 1 0 0.7358 0.0436 0.6388 0.8106
39 74 1 1 0.7259 0.0442 0.6282 0.8019
40 72 2 0 0.7057 0.0452 0.6068 0.7842
43 70 1 0 0.6956 0.0457 0.5961 0.7752
45 69 1 0 0.6856 0.0461 0.5855 0.7662
50 68 1 0 0.6755 0.0465 0.5750 0.7572
51 67 1 0 0.6654 0.0469 0.5645 0.7481
53 66 1 0 0.6553 0.0472 0.5541 0.7390
58 65 1 0 0.6452 0.0476 0.5437 0.7298
61 64 1 0 0.6352 0.0479 0.5333 0.7206
66 63 1 0 0.6251 0.0482 0.5230 0.7113
68 62 2 0 0.6049 0.0487 0.5026 0.6926
69 60 1 0 0.5948 0.0489 0.4924 0.6832
72 59 2 0 0.5747 0.0493 0.4722 0.6643
77 57 1 0 0.5646 0.0494 0.4621 0.6548
78 56 1 0 0.5545 0.0496 0.4521 0.6453
80 55 1 0 0.5444 0.0497 0.4422 0.6357
81 54 1 0 0.5343 0.0498 0.4323 0.6261
85 53 1 0 0.5243 0.0499 0.4224 0.6164
90 52 1 0 0.5142 0.0499 0.4125 0.6067
96 51 1 0 0.5041 0.0499 0.4027 0.5969
100 50 1 0 0.4940 0.0499 0.3930 0.5872
102 49 1 0 0.4839 0.0499 0.3833 0.5773
109 48 0 1 0.4839 0.0499 0.3833 0.5773
110 47 1 0 0.4736 0.0499 0.3733 0.5673
131 46 0 1 0.4736 0.0499 0.3733 0.5673
149 45 1 0 0.4631 0.0499 0.3632 0.5571
153 44 1 0 0.4526 0.0499 0.3531 0.5468
165 43 1 0 0.4421 0.0498 0.3430 0.5364
180 42 0 1 0.4421 0.0498 0.3430 0.5364
186 41 1 0 0.4313 0.0497 0.3327 0.5258
188 40 1 0 0.4205 0.0497 0.3225 0.5152
207 39 1 0 0.4097 0.0495 0.3123 0.5045
219 38 1 0 0.3989 0.0494 0.3022 0.4938
263 37 1 0 0.3881 0.0492 0.2921 0.4830
265 36 0 1 0.3881 0.0492 0.2921 0.4830
285 35 2 0 0.3660 0.0488 0.2714 0.4608
308 33 1 0 0.3549 0.0486 0.2612 0.4496
334 32 1 0 0.3438 0.0483 0.2510 0.4383
340 31 1 1 0.3327 0.0480 0.2409 0.4270
342 29 1 0 0.3212 0.0477 0.2305 0.4153
370 28 0 1 0.3212 0.0477 0.2305 0.4153
397 27 0 1 0.3212 0.0477 0.2305 0.4153
427 26 0 1 0.3212 0.0477 0.2305 0.4153
445 25 0 1 0.3212 0.0477 0.2305 0.4153
482 24 0 1 0.3212 0.0477 0.2305 0.4153
515 23 0 1 0.3212 0.0477 0.2305 0.4153
545 22 0 1 0.3212 0.0477 0.2305 0.4153
583 21 1 0 0.3059 0.0478 0.2156 0.4008
596 20 0 1 0.3059 0.0478 0.2156 0.4008
620 19 0 1 0.3059 0.0478 0.2156 0.4008
670 18 0 1 0.3059 0.0478 0.2156 0.4008
675 17 1 0 0.2879 0.0483 0.1976 0.3844
733 16 1 0 0.2699 0.0485 0.1802 0.3676
841 15 0 1 0.2699 0.0485 0.1802 0.3676
852 14 1 0 0.2507 0.0487 0.1616 0.3497
915 13 0 1 0.2507 0.0487 0.1616 0.3497
941 12 0 1 0.2507 0.0487 0.1616 0.3497
979 11 1 0 0.2279 0.0493 0.1394 0.3295
995 10 1 0 0.2051 0.0494 0.1183 0.3085
1032 9 1 0 0.1823 0.0489 0.0985 0.2865
1141 8 0 1 0.1823 0.0489 0.0985 0.2865
1321 7 0 1 0.1823 0.0489 0.0985 0.2865
1386 6 1 0 0.1519 0.0493 0.0713 0.2606
1400 5 0 1 0.1519 0.0493 0.0713 0.2606
1407 4 0 1 0.1519 0.0493 0.0713 0.2606
1571 3 0 1 0.1519 0.0493 0.0713 0.2606
1586 2 0 1 0.1519 0.0493 0.0713 0.2606
1799 1 0 1 0.1519 0.0493 0.0713 0.2606
------------------------------------------------------------------------
*/sts graph
Comparaison des fonctions de survie
Tests du log rank
On va comparer les fonctions de survie pour la variable surgery.
sts graph, by(surgery)
Tests du log rank: fonction sts test. On affichera ici plusieurs variantes du test.
local test `" "l" "w" "tw" "p" "'
foreach test2 of local test {
sts test surgery, `test2'
}
/*
Log-rank test for equality of survivor functions
| Events Events
surgery | observed expected
--------+-------------------------
0 | 69 60.34
1 | 6 14.66
--------+-------------------------
Total | 75 75.00
chi2(1) = 6.59
Pr>chi2 = 0.0103
failure _d: died
analysis time _t: stime
Wilcoxon (Breslow) test for equality of survivor functions
| Events Events Sum of
surgery | observed expected ranks
--------+--------------------------------------
0 | 69 60.34 623
1 | 6 14.66 -623
--------+--------------------------------------
Total | 75 75.00 0
chi2(1) = 8.99
Pr>chi2 = 0.0027
failure _d: died
analysis time _t: stime
Tarone-Ware test for equality of survivor functions
| Events Events Sum of
surgery | observed expected ranks
--------+--------------------------------------
0 | 69 60.34 73.105398
1 | 6 14.66 -73.105398
--------+--------------------------------------
Total | 75 75.00 0
chi2(1) = 8.46
Pr>chi2 = 0.0036
failure _d: died
analysis time _t: stime
Peto-Peto test for equality of survivor functions
| Events Events Sum of
surgery | observed expected ranks
--------+--------------------------------------
0 | 69 60.34 6.0505875
1 | 6 14.66 -6.0505875
--------+--------------------------------------
Total | 75 75.00 0
chi2(1) = 8.66
Pr>chi2 = 0.0032
*/Comparaison des rmst
Installation de la commande strmst2:
ssc install strmst2arm1 = opération
arm0 = pas d’opération
strmst2 surgery
/*
Restricted Mean Survival Time (RMST) by arm
-----------------------------------------------------------
Group | Estimate Std. Err. [95% Conf. Interval]
---------+-------------------------------------------------
arm 1 | 734.758 133.478 473.145 996.370
arm 0 | 310.168 43.160 225.576 394.760
-----------------------------------------------------------
Between-group contrast (arm 1 versus arm 0)
------------------------------------------------------------------------
Contrast | Estimate [95% Conf. Interval] P>|z|
---------------------+--------------------------------------------------
RMST (arm 1 - arm 0) | 424.590 149.641 699.539 0.002
RMST (arm 1 / arm 0) | 2.369 1.513 3.710 0.000
------------------------------------------------------------------------
*/Risques proportionnels
Modèle de Cox
Estimation du modèle
Avec la correction d’Efron
stcox year age surgery, nolog noshow efron
/*
Cox regression -- Efron method for ties
No. of subjects = 103 Number of obs = 103
No. of failures = 75
Time at risk = 31938
LR chi2(3) = 17.63
Log likelihood = -289.30639 Prob > chi2 = 0.0005
------------------------------------------------------------------------------
_t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
year | 0.8872 0.0597 -1.78 0.076 0.7775 1.0124
age | 1.0300 0.0139 2.19 0.029 1.0031 1.0577
surgery | 0.3726 0.1625 -2.26 0.024 0.1584 0.8761
------------------------------------------------------------------------------
*/stcox year age surgery, nolog noshow efron nohr
/*
Cox regression -- Efron method for ties
No. of subjects = 103 Number of obs = 103
No. of failures = 75
Time at risk = 31938
LR chi2(3) = 17.63
Log likelihood = -289.30639 Prob > chi2 = 0.0005
------------------------------------------------------------------------------
_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
year | -0.1196 0.0673 -1.78 0.076 -0.2516 0.0124
age | 0.0296 0.0135 2.19 0.029 0.0031 0.0561
surgery | -0.9873 0.4363 -2.26 0.024 -1.8424 -0.1323
------------------------------------------------------------------------------
*/Test de l’hypothèse PH
Test Grambsch-Therneau sur les résidus de Schoenfeld
* f(t)=t - par défaut
estat phtest, detail
/*
Test of proportional-hazards assumption
Time: Time
----------------------------------------------------------------
| rho chi2 df Prob>chi2
------------+---------------------------------------------------
year | 0.10162 0.80 1 0.3720
age | 0.12937 1.61 1 0.2043
surgery | 0.29664 5.54 1 0.0186
------------+---------------------------------------------------
global test | 8.76 3 0.0327
----------------------------------------------------------------
*/
* f(t)= 1-km - solution par défaut de R
estat phtest, detail km
/*
Test of proportional-hazards assumption
Time: Kaplan-Meier
----------------------------------------------------------------
| rho chi2 df Prob>chi2
------------+---------------------------------------------------
year | 0.15920 1.96 1 0.1620
age | 0.10907 1.15 1 0.2845
surgery | 0.25096 3.96 1 0.0465
------------+---------------------------------------------------
global test | 7.99 3 0.0462
----------------------------------------------------------------
*/Intéraction avec une fonction de la durée
\(f(t)=t\)
stcox year age surgery, nolog noshow efron nohr tvc(surgery) texp(_t)
/*
Cox regression -- Efron method for ties
No. of subjects = 103 Number of obs = 103
No. of failures = 75
Time at risk = 31938
LR chi2(4) = 21.58
Log likelihood = -287.32903 Prob > chi2 = 0.0002
------------------------------------------------------------------------------
_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
main |
year | -0.1231 0.0668 -1.84 0.066 -0.2541 0.0079
age | 0.0289 0.0134 2.15 0.032 0.0025 0.0552
surgery | -1.7547 0.6744 -2.60 0.009 -3.0765 -0.4330
-------------+----------------------------------------------------------------
tvc |
surgery | 0.0022 0.0011 2.02 0.043 0.0001 0.0044
------------------------------------------------------------------------------
Note: Variables in tvc equation interacted with _t.
*/Introduction d’une variable dynamique (binaire)
Transformation de la base en format long aux temps d’évènement
Etape 1
stset stime, f(died) id(id)
/*
id: id
failure event: died != 0 & died < .
obs. time interval: (stime[_n-1], stime]
exit on or before: failure
------------------------------------------------------------------------------
103 total observations
0 exclusions
------------------------------------------------------------------------------
103 observations remaining, representing
103 subjects
75 failures in single-failure-per-subject data
31,938 total analysis time at risk and under observation
at risk from t = 0
earliest observed entry t = 0
last observed exit t = 1,799
*/Etape 2
stsplit, at(failure)
stset stime, f(died) id(id)
sort id _t
list in 1/23
/*
id: id
failure event: died != 0 & died < .
obs. time interval: (stime[_n-1], stime]
exit on or before: failure
------------------------------------------------------------------------------
105 total observations
2 ignored because id missing
------------------------------------------------------------------------------
103 observations remaining, representing
103 subjects
75 failures in single-failure-per-subject data
31,938 total analysis time at risk and under observation
at risk from t = 0
earliest observed entry t = 0
last observed exit t = 1,799
+--------------------------------------------------------------------------------------------------+
| id year age died stime surgery transp~t wait mois compet _st _d _t _t0 |
|--------------------------------------------------------------------------------------------------|
1. | 1 67 30 . 1 0 0 0 2 1 1 0 1 0 |
2. | 1 67 30 . 2 0 0 0 2 1 1 0 2 1 |
3. | 1 67 30 . 3 0 0 0 2 1 1 0 3 2 |
4. | 1 67 30 . 5 0 0 0 2 1 1 0 5 3 |
5. | 1 67 30 . 6 0 0 0 2 1 1 0 6 5 |
|--------------------------------------------------------------------------------------------------|
6. | 1 67 30 . 8 0 0 0 2 1 1 0 8 6 |
7. | 1 67 30 . 9 0 0 0 2 1 1 0 9 8 |
8. | 1 67 30 . 12 0 0 0 2 1 1 0 12 9 |
9. | 1 67 30 . 16 0 0 0 2 1 1 0 16 12 |
10. | 1 67 30 . 17 0 0 0 2 1 1 0 17 16 |
|--------------------------------------------------------------------------------------------------|
11. | 1 67 30 . 18 0 0 0 2 1 1 0 18 17 |
12. | 1 67 30 . 21 0 0 0 2 1 1 0 21 18 |
13. | 1 67 30 . 28 0 0 0 2 1 1 0 28 21 |
14. | 1 67 30 . 30 0 0 0 2 1 1 0 30 28 |
15. | 1 67 30 . 32 0 0 0 2 1 1 0 32 30 |
|--------------------------------------------------------------------------------------------------|
16. | 1 67 30 . 35 0 0 0 2 1 1 0 35 32 |
17. | 1 67 30 . 36 0 0 0 2 1 1 0 36 35 |
18. | 1 67 30 . 37 0 0 0 2 1 1 0 37 36 |
19. | 1 67 30 . 39 0 0 0 2 1 1 0 39 37 |
20. | 1 67 30 . 40 0 0 0 2 1 1 0 40 39 |
|--------------------------------------------------------------------------------------------------|
21. | 1 67 30 . 43 0 0 0 2 1 1 0 43 40 |
22. | 1 67 30 . 45 0 0 0 2 1 1 0 45 43 |
23. | 1 67 30 1 50 0 0 0 2 1 1 1 50 45 |
+--------------------------------------------------------------------------------------------------+
*/Etape 3
gen tvc = transplant==1 & wait<=_t
sort id _t
list id transplant wait tvc _d _t _t0 if id==10 , noobs
/*
+--------------------------------------------+
| id transp~t wait tvc _d _t _t0 |
|--------------------------------------------|
| 10 1 12 0 0 1 0 |
| 10 1 12 0 0 2 1 |
| 10 1 12 0 0 3 2 |
| 10 1 12 0 0 5 3 |
| 10 1 12 0 0 6 5 |
|--------------------------------------------|
| 10 1 12 0 0 8 6 |
| 10 1 12 0 0 9 8 |
| 10 1 12 1 0 12 9 |
| 10 1 12 1 0 16 12 |
| 10 1 12 1 0 17 16 |
|--------------------------------------------|
| 10 1 12 1 0 18 17 |
| 10 1 12 1 0 21 18 |
| 10 1 12 1 0 28 21 |
| 10 1 12 1 0 30 28 |
| 10 1 12 1 0 32 30 |
|--------------------------------------------|
| 10 1 12 1 0 35 32 |
| 10 1 12 1 0 36 35 |
| 10 1 12 1 0 37 36 |
| 10 1 12 1 0 39 37 |
| 10 1 12 1 0 40 39 |
|--------------------------------------------|
| 10 1 12 1 0 43 40 |
| 10 1 12 1 0 45 43 |
| 10 1 12 1 0 50 45 |
| 10 1 12 1 0 51 50 |
| 10 1 12 1 0 53 51 |
|--------------------------------------------|
| 10 1 12 1 1 58 53 |
+--------------------------------------------+
*/Estimation du modèle
stcox year age surgery tvc, nolog noshow efron nohr
Cox regression -- Efron method for ties
No. of subjects = 103 Number of obs = 3,573
No. of failures = 75
Time at risk = 31938
LR chi2(4) = 17.70
Log likelihood = -289.27014 Prob > chi2 = 0.0014
------------------------------------------------------------------------------
_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
year | -0.1203 0.0673 -1.79 0.074 -0.2523 0.0117
age | 0.0304 0.0139 2.19 0.029 0.0032 0.0577
surgery | -0.9829 0.4366 -2.25 0.024 -1.8385 -0.1273
tvc | -0.0822 0.3048 -0.27 0.787 -0.6797 0.5153
------------------------------------------------------------------------------Modèle à temps discret
Variable de durée = mois
Mise en forme
expand mois
bysort id: gen t=_n
gen e = died
replace e=0 if t<mois
* list in 1/31
/*
+-------------------------------------------------------------------------------------+
| id year age died stime surgery transp~t wait mois compet t e |
|-------------------------------------------------------------------------------------|
1. | 1 67 30 1 50 0 0 0 2 1 1 0 |
2. | 1 67 30 1 50 0 0 0 2 1 2 1 |
3. | 2 68 51 1 6 0 0 0 1 1 1 1 |
4. | 3 68 54 1 16 0 1 1 1 1 1 1 |
5. | 4 68 40 1 39 0 1 36 2 2 1 0 |
|-------------------------------------------------------------------------------------|
6. | 4 68 40 1 39 0 1 36 2 2 2 1 |
7. | 5 68 20 1 18 0 0 0 1 1 1 1 |
8. | 6 68 54 1 3 0 0 0 1 2 1 1 |
9. | 7 68 50 1 675 0 1 51 23 1 1 0 |
10. | 7 68 50 1 675 0 1 51 23 1 2 0 |
|-------------------------------------------------------------------------------------|
11. | 7 68 50 1 675 0 1 51 23 1 3 0 |
12. | 7 68 50 1 675 0 1 51 23 1 4 0 |
13. | 7 68 50 1 675 0 1 51 23 1 5 0 |
14. | 7 68 50 1 675 0 1 51 23 1 6 0 |
15. | 7 68 50 1 675 0 1 51 23 1 7 0 |
|-------------------------------------------------------------------------------------|
16. | 7 68 50 1 675 0 1 51 23 1 8 0 |
17. | 7 68 50 1 675 0 1 51 23 1 9 0 |
18. | 7 68 50 1 675 0 1 51 23 1 10 0 |
19. | 7 68 50 1 675 0 1 51 23 1 11 0 |
20. | 7 68 50 1 675 0 1 51 23 1 12 0 |
|-------------------------------------------------------------------------------------|
21. | 7 68 50 1 675 0 1 51 23 1 13 0 |
22. | 7 68 50 1 675 0 1 51 23 1 14 0 |
23. | 7 68 50 1 675 0 1 51 23 1 15 0 |
24. | 7 68 50 1 675 0 1 51 23 1 16 0 |
25. | 7 68 50 1 675 0 1 51 23 1 17 0 |
|-------------------------------------------------------------------------------------|
26. | 7 68 50 1 675 0 1 51 23 1 18 0 |
27. | 7 68 50 1 675 0 1 51 23 1 19 0 |
28. | 7 68 50 1 675 0 1 51 23 1 20 0 |
29. | 7 68 50 1 675 0 1 51 23 1 21 0 |
30. | 7 68 50 1 675 0 1 51 23 1 22 0 |
|-------------------------------------------------------------------------------------|
31. | 7 68 50 1 675 0 1 51 23 1 23 1 |
+-------------------------------------------------------------------------------------+
*/Paramétrisation avec durée continue
Les critères d’information
gen t2=t^2
gen t3=t^3
logit e t , nolog
estat ic
logit e t t2 , nolog
estat ic
logit e t2 t3 , nolog
estat ic
Logistic regression Number of obs = 1,127
LR chi2(1) = 50.85
Prob > chi2 = 0.0000
Log likelihood = -250.26058 Pseudo R2 = 0.0922
------------------------------------------------------------------------------
e | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
t | -0.1007 0.0185 -5.45 0.000 -0.1370 -0.0645
_cons | -1.6436 0.1724 -9.53 0.000 -1.9815 -1.3057
------------------------------------------------------------------------------
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 1,127 -275.6841 -250.2606 2 504.5212 514.5758
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
*****************************************************************************
Logistic regression Number of obs = 1,127
LR chi2(2) = 65.25
Prob > chi2 = 0.0000
Log likelihood = -243.05761 Pseudo R2 = 0.1183
------------------------------------------------------------------------------
e | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
t | -0.2172 0.0357 -6.08 0.000 -0.2872 -0.1471
t2 | 0.0034 0.0008 4.50 0.000 0.0019 0.0049
_cons | -1.2326 0.1925 -6.40 0.000 -1.6098 -0.8554
------------------------------------------------------------------------------
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 1,127 -275.6841 -243.0576 3 492.1152 507.1972
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
*****************************************************************************
Logistic regression Number of obs = 1,127
LR chi2(3) = 72.86
Prob > chi2 = 0.0000
Log likelihood = -239.25267 Pseudo R2 = 0.1321
------------------------------------------------------------------------------
e | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
t | -0.4038 0.0819 -4.93 0.000 -0.5643 -0.2434
t2 | 0.0157 0.0050 3.14 0.002 0.0059 0.0254
t3 | -0.0002 0.0001 -2.31 0.021 -0.0003 -0.0000
_cons | -0.8250 0.2406 -3.43 0.001 -1.2965 -0.3536
------------------------------------------------------------------------------
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 1,127 -275.6841 -239.2527 4 486.5053 506.6146
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.Estimation du modèle
logit e t t2 t3 year age surgery, nolog
/*
Logistic regression Number of obs = 1,127
LR chi2(6) = 90.69
Prob > chi2 = 0.0000
Log likelihood = -230.33671 Pseudo R2 = 0.1645
------------------------------------------------------------------------------
e | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
t | -0.3721 0.0824 -4.52 0.000 -0.5335 -0.2106
t2 | 0.0142 0.0050 2.83 0.005 0.0044 0.0241
t3 | -0.0002 0.0001 -2.11 0.035 -0.0003 -0.0000
year | -0.1327 0.0738 -1.80 0.072 -0.2773 0.0119
age | 0.0333 0.0147 2.27 0.023 0.0046 0.0621
surgery | -1.0109 0.4486 -2.25 0.024 -1.8902 -0.1317
_cons | 7.0827 5.3077 1.33 0.182 -3.3203 17.4856
------------------------------------------------------------------------------
*/Paramétrisation avec durée discrète
Pour l’exemple seulement, on prendra des intervalles découpés sur les quartiles de la durée
xtile ct4=t, n(4)
bysort id ct4: keep if _n==_N
tab ct4 e
logit e i.ct4 year age surgery, nolog
/*
4 |
quantiles | e
of t | 0 1 | Total
-----------+----------------------+----------
1 | 50 53 | 103
2 | 35 11 | 46
3 | 27 5 | 32
4 | 10 6 | 16
-----------+----------------------+----------
Total | 122 75 | 197
Logistic regression Number of obs = 197
LR chi2(6) = 39.30
Prob > chi2 = 0.0000
Log likelihood = -111.23965 Pseudo R2 = 0.1501
------------------------------------------------------------------------------
e | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ct4 |
2 | -1.0334 0.4189 -2.47 0.014 -1.8543 -0.2124
3 | -1.6152 0.5449 -2.96 0.003 -2.6831 -0.5473
4 | -0.4789 0.5993 -0.80 0.424 -1.6535 0.6957
|
year | -0.2032 0.0932 -2.18 0.029 -0.3859 -0.0206
age | 0.0469 0.0185 2.53 0.011 0.0106 0.0831
surgery | -1.1102 0.5026 -2.21 0.027 -2.0952 -0.1252
_cons | 12.4467 6.6537 1.87 0.061 -0.5943 25.4877
------------------------------------------------------------------------------
*/Modèles paramétriques
Commande streg
Modèle AFT
Weibull
Par défaut, le modèle de Weibull est exécuté sous paramétrisation PH. Pour une paramétrisation type AFT, ajouter l’option time.
webuse set "https://raw.githubusercontent.com//mthevenin/analyse_duree/master/bases/"
webuse "transplantation_m", clear
webuse set
stset stime, f(died)
streg year age surgery , dist(weibull) time nolog noshow
estat ic
/*
Weibull AFT regression
No. of subjects = 103 Number of obs = 103
No. of failures = 75
Time at risk = 31938
LR chi2(3) = 18.87
Log likelihood = -188.6278 Prob > chi2 = 0.0003
------------------------------------------------------------------------------
_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
year | 0.1620 0.1218 1.33 0.184 -0.0768 0.4008
age | -0.0615 0.0247 -2.49 0.013 -0.1100 -0.0130
surgery | 1.9703 0.7794 2.53 0.011 0.4427 3.4980
_cons | -3.0220 8.7284 -0.35 0.729 -20.1294 14.0854
-------------+----------------------------------------------------------------
/ln_p | -0.5868 0.0927 -6.33 0.000 -0.7685 -0.4051
-------------+----------------------------------------------------------------
p | 0.5561 0.0516 0.4637 0.6669
1/p | 1.7983 0.1667 1.4995 2.1566
------------------------------------------------------------------------------
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 103 -198.0632 -188.6278 5 387.2556 400.4292
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
*/Loglogistique
streg year age surgery , dist(loglog) nolog noshow
estat ic
/*
Loglogistic AFT regression
No. of subjects = 103 Number of obs = 103
No. of failures = 75
Time at risk = 31938
LR chi2(3) = 21.69
Log likelihood = -183.03937 Prob > chi2 = 0.0001
------------------------------------------------------------------------------
_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
year | 0.2408 0.1172 2.05 0.040 0.0110 0.4705
age | -0.0427 0.0213 -2.00 0.045 -0.0845 -0.0010
surgery | 2.2747 0.6913 3.29 0.001 0.9198 3.6296
_cons | -10.4034 8.3410 -1.25 0.212 -26.7515 5.9446
-------------+----------------------------------------------------------------
/lngamma | 0.1805 0.0970 1.86 0.063 -0.0095 0.3706
-------------+----------------------------------------------------------------
gamma | 1.1979 0.1161 0.9906 1.4486
------------------------------------------------------------------------------
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 103 -193.8865 -183.0394 5 376.0787 389.2524
-----------------------------------------------------------------------------
*/Risques concurrents
Non paramétrique: estimation des IC
Installer les commandes stcompet et stcomlist
ssc install stcompet
ssc install stcomlistLe risque d’intérêt est compet=1, le risque concurrent est compet=2
stset stime, failure(compet==1)
stcomlist, compet1(2)
/*
failure: compet == 1
competing failures: compet == 2
Time CIF SE [95% Conf. Int.]
--------------------------------------------------
1 0.0097 0.0097 0.0009 0.0477
2 0.0388 0.0190 0.0127 0.0892
3 0.0583 0.0231 0.0239 0.1149
5 0.0777 0.0264 0.0363 0.1395
6 0.0874 0.0278 0.0429 0.1515
8 0.0971 0.0292 0.0497 0.1634
9 0.1068 0.0304 0.0566 0.1751
12 0.1166 0.0316 0.0638 0.1868
16 0.1362 0.0338 0.0785 0.2099
18 0.1461 0.0349 0.0860 0.2212
21 0.1657 0.0367 0.1014 0.2437
32 0.1756 0.0376 0.1093 0.2550
37 0.1856 0.0384 0.1173 0.2662
40 0.1957 0.0393 0.1254 0.2775
43 0.2058 0.0400 0.1337 0.2888
45 0.2158 0.0408 0.1420 0.2999
50 0.2259 0.0415 0.1503 0.3110
51 0.2360 0.0422 0.1588 0.3221
53 0.2461 0.0428 0.1673 0.3330
58 0.2562 0.0434 0.1759 0.3439
61 0.2662 0.0440 0.1845 0.3548
66 0.2763 0.0445 0.1932 0.3656
69 0.2864 0.0450 0.2020 0.3763
72 0.3066 0.0459 0.2197 0.3976
77 0.3167 0.0464 0.2286 0.4082
78 0.3267 0.0467 0.2376 0.4187
81 0.3368 0.0471 0.2466 0.4292
85 0.3469 0.0475 0.2556 0.4396
90 0.3570 0.0478 0.2648 0.4500
96 0.3671 0.0481 0.2739 0.4604
102 0.3771 0.0484 0.2831 0.4707
110 0.3874 0.0487 0.2925 0.4812
149 0.3980 0.0489 0.3021 0.4920
165 0.4085 0.0492 0.3118 0.5027
186 0.4193 0.0495 0.3217 0.5137
188 0.4301 0.0497 0.3316 0.5246
207 0.4408 0.0499 0.3417 0.5354
219 0.4516 0.0501 0.3517 0.5462
263 0.4624 0.0502 0.3618 0.5570
285 0.4846 0.0505 0.3826 0.5791
308 0.4957 0.0506 0.3931 0.5900
340 0.5068 0.0507 0.4037 0.6009
583 0.5221 0.0514 0.4171 0.6168
675 0.5401 0.0524 0.4322 0.6361
733 0.5580 0.0532 0.4477 0.6548
995 0.5808 0.0548 0.4659 0.6795
1032 0.6036 0.0559 0.4851 0.7031
1386 0.6340 0.0583 0.5083 0.7357
failure: compet == 2
competing failures: compet == 1
Time CIF SE [95% Conf. Int.]
--------------------------------------------------
3 0.0097 0.0097 0.0009 0.0477
6 0.0194 0.0136 0.0038 0.0619
16 0.0292 0.0166 0.0079 0.0761
17 0.0391 0.0191 0.0128 0.0897
28 0.0489 0.0213 0.0182 0.1029
30 0.0587 0.0232 0.0240 0.1157
35 0.0686 0.0250 0.0302 0.1286
36 0.0786 0.0267 0.0367 0.1411
39 0.0885 0.0282 0.0435 0.1534
40 0.0986 0.0296 0.0504 0.1658
68 0.1188 0.0322 0.0650 0.1901
80 0.1288 0.0334 0.0724 0.2020
100 0.1389 0.0345 0.0800 0.2138
153 0.1495 0.0356 0.0880 0.2261
334 0.1605 0.0368 0.0964 0.2392
342 0.1720 0.0381 0.1052 0.2526
852 0.1913 0.0417 0.1175 0.2787
979 0.2141 0.0460 0.1320 0.3094
*/Modèle cause-specific (Cox)
Attention: non relié aux IC
stcox year age surgery, nohr
/*
Iteration 0: log likelihood = -222.40766
Iteration 1: log likelihood = -214.66912
Iteration 2: log likelihood = -214.47069
Iteration 3: log likelihood = -214.46905
Iteration 4: log likelihood = -214.46905
Refining estimates:
Iteration 0: log likelihood = -214.46905
Cox regression -- Breslow method for ties
No. of subjects = 103 Number of obs = 103
No. of failures = 56
Time at risk = 31938
LR chi2(3) = 15.88
Log likelihood = -214.46905 Prob > chi2 = 0.0012
------------------------------------------------------------------------------
_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
year | -0.1033 0.0774 -1.33 0.182 -0.2550 0.0485
age | 0.0385 0.0163 2.36 0.018 0.0065 0.0704
surgery | -1.1099 0.5290 -2.10 0.036 -2.1468 -0.0730
------------------------------------------------------------------------------
*/Modèle de Fine-Gray
La commande stcrreg est installée avec les commandes de base. Relié directement aux IC, la définition du risque diffère du risque instantané usuel (risque de sous répartition).
stcrreg year age surgery, compete(compet=2) nohr
/*
failure _d: compet == 1
analysis time _t: stime
Iteration 0: log pseudolikelihood = -227.92407
Iteration 1: log pseudolikelihood = -227.69764
Iteration 2: log pseudolikelihood = -227.69531
Iteration 3: log pseudolikelihood = -227.69531
Competing-risks regression No. of obs = 103
No. of subjects = 103
Failure event : compet == 1 No. failed = 56
Competing event: compet == 2 No. competing = 19
No. censored = 28
Wald chi2(3) = 11.42
Log pseudolikelihood = -227.69531 Prob > chi2 = 0.0097
------------------------------------------------------------------------------
| Robust
_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
year | -0.0724 0.0716 -1.01 0.312 -0.2128 0.0679
age | 0.0370 0.0177 2.09 0.037 0.0022 0.0718
surgery | -0.8688 0.4510 -1.93 0.054 -1.7528 0.0153
------------------------------------------------------------------------------
*/Modèle logistique multinomial
Attention: non relié aux IC Pour la variable de durée on utilise la variable mois
expand mois
bysort id: gen t=_n
gen t2=t*t
gen e = compet
replace e=0 if t<mois
mlogit e t t2 year age surgery
/*
Iteration 0: log likelihood = -318.13171
Iteration 1: log likelihood = -285.78811
Iteration 2: log likelihood = -275.20206
Iteration 3: log likelihood = -275.00574
Iteration 4: log likelihood = -275.00542
Iteration 5: log likelihood = -275.00542
Multinomial logistic regression Number of obs = 1,127
LR chi2(10) = 86.25
Prob > chi2 = 0.0000
Log likelihood = -275.00542 Pseudo R2 = 0.1356
------------------------------------------------------------------------------
e | RRR Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
0 | (base outcome)
-------------+----------------------------------------------------------------
1 |
t | 0.8159 0.0338 -4.91 0.000 0.7522 0.8850
t2 | 1.0032 0.0009 3.53 0.000 1.0014 1.0049
year | 0.8795 0.0718 -1.57 0.116 0.7494 1.0321
age | 1.0449 0.0183 2.51 0.012 1.0097 1.0813
surgery | 0.3175 0.1711 -2.13 0.033 0.1104 0.9129
* Constante non reportée
-------------+----------------------------------------------------------------
2 |
t | 0.8168 0.0565 -2.93 0.003 0.7134 0.9353
t2 | 1.0030 0.0015 1.94 0.052 1.0000 1.0060
year | 0.8158 0.1127 -1.47 0.141 0.6223 1.0695
age | 1.0111 0.0248 0.45 0.654 0.9635 1.0610
surgery | 0.5412 0.4221 -0.79 0.431 0.1173 2.4959
* Constante non reportée
------------------------------------------------------------------------------
*/