library(survival) # standard R package for survival analysis
library(stayinalive) # functions we developed for processing time series.
doParallel::registerDoParallel(cores=4)Generate 100 years of data for 225 basins. Temperature increases over the course of the century roughly according to Hector’s RCP8.5 pathway. Droughts are between 1 and 2 years long in this simulation. The \(\beta\) value of 0.5 means that each degree of global temperature change should produce about a 65% increase in drought risk relative to the baseline.
nyear <- 100
nmonth <- 12*nyear
nbasin <- 225
Tgyr <- seq(0.75, 4.5, length.out=nyear) # Approximately RCP8.5
Tgmon <- rep(Tgyr, rep(12, length(Tgyr)))
set.seed(867-5309)
basindata <- gents(nbasin, nmonth, Tgmon, beta=0.5)The code below converts the basin time series to the event data frame required by the coxph function. Then we feed that to a simple Cox model.
events <- tsmat2event(basindata, Tgyr, 1)
events$basinid <- as.factor(events$basinid)
cph <- coxph(Surv(tstart, tstop, drought)~Tg, data=events)
summary(cph)Call:
coxph(formula = Surv(tstart, tstop, drought) ~ Tg, data = events)
n= 20700, number of events= 2914
coef exp(coef) se(coef) z Pr(>|z|)
Tg 0.49164 1.63499 0.01913 25.7 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
exp(coef) exp(-coef) lower .95 upper .95
Tg 1.635 0.6116 1.575 1.697
Concordance= 0.646 (se = 0.006 )
Rsquare= 0.034 (max possible= 0.861 )
Likelihood ratio test= 718.6 on 1 df, p=<2e-16
Wald test = 660.4 on 1 df, p=<2e-16
Score (logrank) test = 690.5 on 1 df, p=<2e-16In this call we compute a clustered survival model, with basins as the clustering variable. The idea here is that events from the same basin might be more similar to each other than they are to events in other basins. This has no effect on the estimate of \(\beta\) (i.e., it will be the same as in the model above); however, there will be an additional estimate of the standard error (called the “robust standard error”) that takes this into account. We didn’t actually include any basin effects in the simulated data, so the robust standard error shouldn’t be that much different to the regular estimate.
cph_clus <- coxph(Surv(tstart, tstop, drought) ~ Tg + cluster(basinid), data=events)
summary(cph_clus)Call:
coxph(formula = Surv(tstart, tstop, drought) ~ Tg + cluster(basinid),
data = events)
n= 20700, number of events= 2914
coef exp(coef) se(coef) robust se z Pr(>|z|)
Tg 0.49164 1.63499 0.01913 0.02106 23.34 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
exp(coef) exp(-coef) lower .95 upper .95
Tg 1.635 0.6116 1.569 1.704
Concordance= 0.646 (se = 0.006 )
Rsquare= 0.034 (max possible= 0.861 )
Likelihood ratio test= 718.6 on 1 df, p=<2e-16
Wald test = 544.8 on 1 df, p=<2e-16
Score (logrank) test = 690.5 on 1 df, p=<2e-16, Robust = 181.9 p=<2e-16
(Note: the likelihood ratio and score tests assume independence of
observations within a cluster, the Wald and robust score tests do not).In the next example, we include a frailty term. In this formulation, not only are clustered items more similar to each other than they are to other observations, but they also have slightly different intrinsic hazard rates. The additional increment to the hazard rate (the “frailty” of the cluster) is chosen from a Gamma distribution with parameters that are solved for in the model fit. I think this is equivalent to a partial pooling model of the sort described in McElreath (and elsewhere, of course), but I haven’t exactly confirmed that.
At any rate, we didn’t include any basin fixed effects, so there shouldn’t be much to see here.
cph_frail <- coxph(Surv(tstart, tstop, drought) ~ Tg + frailty(basinid), data=events)
summary(cph_frail)Call:
coxph(formula = Surv(tstart, tstop, drought) ~ Tg + frailty(basinid),
data = events)
n= 20700, number of events= 2914
coef se(coef) se2 Chisq DF p
Tg 0.4916 0.01913 0.01913 660.4 1 1.2e-145
frailty(basinid) 0.0 0 8.2e-01
exp(coef) exp(-coef) lower .95 upper .95
Tg 1.635 0.6116 1.575 1.697
Iterations: 6 outer, 22 Newton-Raphson
Variance of random effect= 5e-07 I-likelihood = -20069
Degrees of freedom for terms= 1 0
Concordance= 0.647 (se = 0.647 )
Likelihood ratio test= 718.6 on 1 df, p=<2e-16We may also want to add interaction terms to allow for the possibility that different basins have different responses to climate change. If results from previous papers are any guide, this is almost certainly the case. One possibility would be to use an interaction term, like in the example below. As before, since we didn’t actually include any of these effects in our simulation, we shouldn’t see much difference to our old results.
cph_inter <- coxph(Surv(tstart, tstop, drought) ~ Tg + basinid:Tg, data=events)
summary(cph_inter)Call:
coxph(formula = Surv(tstart, tstop, drought) ~ Tg + basinid:Tg,
data = events)
n= 20700, number of events= 2914
coef exp(coef) se(coef) z Pr(>|z|)
Tg 0.5891293 1.8024184 0.0805284 7.316 2.56e-13 ***
Tg:basinid2 0.0412791 1.0421430 0.1091860 0.378 0.7054
Tg:basinid3 -0.0515367 0.9497688 0.1162657 -0.443 0.6576
Tg:basinid4 -0.0284789 0.9719228 0.1094148 -0.260 0.7946
Tg:basinid5 0.0212648 1.0214925 0.1087230 0.196 0.8449
Tg:basinid6 -0.0531576 0.9482306 0.1165566 -0.456 0.6483
Tg:basinid7 -0.1188788 0.8879154 0.1179311 -1.008 0.3134
Tg:basinid8 -0.0355144 0.9651088 0.1121051 -0.317 0.7514
Tg:basinid9 -0.0588366 0.9428608 0.1145171 -0.514 0.6074
Tg:basinid10 -0.1349505 0.8737592 0.1204869 -1.120 0.2627
Tg:basinid11 -0.0821871 0.9210996 0.1181836 -0.695 0.4868
Tg:basinid12 -0.1525234 0.8585388 0.1222281 -1.248 0.2121
Tg:basinid13 -0.1998117 0.8188849 0.1266660 -1.577 0.1147
Tg:basinid14 -0.2334852 0.7917693 0.1327085 -1.759 0.0785 .
Tg:basinid15 0.0430235 1.0439624 0.1072943 0.401 0.6884
Tg:basinid16 -0.0568225 0.9447617 0.1155485 -0.492 0.6229
Tg:basinid17 -0.1393950 0.8698843 0.1218882 -1.144 0.2528
Tg:basinid18 -0.1456465 0.8644632 0.1216230 -1.198 0.2311
Tg:basinid19 -0.1462974 0.8639007 0.1247026 -1.173 0.2407
Tg:basinid20 -0.1397708 0.8695575 0.1218224 -1.147 0.2512
Tg:basinid21 -0.0771867 0.9257170 0.1162721 -0.664 0.5068
Tg:basinid22 -0.0432245 0.9576964 0.1144685 -0.378 0.7057
Tg:basinid23 -0.0489212 0.9522562 0.1133040 -0.432 0.6659
Tg:basinid24 -0.0441416 0.9568184 0.1135894 -0.389 0.6976
Tg:basinid25 -0.1274926 0.8802999 0.1182960 -1.078 0.2811
Tg:basinid26 -0.0565626 0.9450073 0.1148772 -0.492 0.6225
Tg:basinid27 -0.0287027 0.9717053 0.1130160 -0.254 0.7995
Tg:basinid28 -0.1285575 0.8793630 0.1206118 -1.066 0.2865
Tg:basinid29 -0.0760231 0.9267948 0.1185672 -0.641 0.5214
Tg:basinid30 0.0296921 1.0301373 0.1078848 0.275 0.7831
Tg:basinid31 -0.1599625 0.8521758 0.1224992 -1.306 0.1916
Tg:basinid32 -0.1073279 0.8982311 0.1197689 -0.896 0.3702
Tg:basinid33 -0.0695081 0.9328526 0.1171217 -0.593 0.5529
Tg:basinid34 -0.1075646 0.8980185 0.1181060 -0.911 0.3624
Tg:basinid35 -0.1234218 0.8838907 0.1195909 -1.032 0.3021
Tg:basinid36 -0.1916296 0.8256126 0.1261536 -1.519 0.1288
Tg:basinid37 -0.0836119 0.9197882 0.1155365 -0.724 0.4693
Tg:basinid38 -0.0851369 0.9183865 0.1175057 -0.725 0.4687
Tg:basinid39 -0.1542774 0.8570342 0.1227168 -1.257 0.2087
Tg:basinid40 0.0789735 1.0821756 0.1059449 0.745 0.4560
Tg:basinid41 -0.3430957 0.7095703 0.1447013 -2.371 0.0177 *
Tg:basinid42 -0.1476688 0.8627168 0.1228740 -1.202 0.2294
Tg:basinid43 -0.0186893 0.9814843 0.1123294 -0.166 0.8679
Tg:basinid44 -0.0599265 0.9418338 0.1150958 -0.521 0.6026
Tg:basinid45 -0.1032809 0.9018736 0.1164644 -0.887 0.3752
Tg:basinid46 -0.1423479 0.8673194 0.1233452 -1.154 0.2485
Tg:basinid47 -0.0126212 0.9874582 0.1119334 -0.113 0.9102
Tg:basinid48 -0.1196548 0.8872266 0.1205765 -0.992 0.3210
Tg:basinid49 -0.1299216 0.8781643 0.1219314 -1.066 0.2866
Tg:basinid50 -0.1166196 0.8899236 0.1200855 -0.971 0.3315
Tg:basinid51 0.0088137 1.0088527 0.1113287 0.079 0.9369
Tg:basinid52 -0.0187208 0.9814533 0.1115804 -0.168 0.8668
Tg:basinid53 -0.0212385 0.9789855 0.1111705 -0.191 0.8485
Tg:basinid54 -0.0780429 0.9249247 0.1158052 -0.674 0.5004
Tg:basinid55 -0.1787691 0.8362990 0.1269127 -1.409 0.1590
Tg:basinid56 0.0011225 1.0011231 0.1113977 0.010 0.9920
Tg:basinid57 -0.1034763 0.9016974 0.1182170 -0.875 0.3814
Tg:basinid58 -0.0193943 0.9807925 0.1115190 -0.174 0.8619
Tg:basinid59 -0.1156863 0.8907546 0.1202658 -0.962 0.3361
Tg:basinid60 -0.0796423 0.9234466 0.1158454 -0.687 0.4918
Tg:basinid61 -0.0926264 0.9115340 0.1190513 -0.778 0.4365
Tg:basinid62 -0.0953620 0.9090438 0.1162206 -0.821 0.4119
Tg:basinid63 -0.0984671 0.9062255 0.1173110 -0.839 0.4013
Tg:basinid64 0.0126554 1.0127358 0.1116329 0.113 0.9097
Tg:basinid65 -0.0436596 0.9572798 0.1140296 -0.383 0.7018
Tg:basinid66 -0.1192036 0.8876271 0.1218663 -0.978 0.3280
Tg:basinid67 -0.2589129 0.7718903 0.1352226 -1.915 0.0555 .
Tg:basinid68 -0.0236279 0.9766491 0.1112865 -0.212 0.8319
Tg:basinid69 -0.1061214 0.8993155 0.1185752 -0.895 0.3708
Tg:basinid70 -0.1300791 0.8780260 0.1189326 -1.094 0.2741
Tg:basinid71 -0.0924412 0.9117029 0.1171332 -0.789 0.4300
Tg:basinid72 -0.0058318 0.9941852 0.1113288 -0.052 0.9582
Tg:basinid73 -0.0968730 0.9076712 0.1213177 -0.799 0.4246
Tg:basinid74 -0.0231063 0.9771586 0.1122706 -0.206 0.8369
Tg:basinid75 -0.2051846 0.8144969 0.1272590 -1.612 0.1069
Tg:basinid76 0.0294828 1.0299217 0.1082503 0.272 0.7853
Tg:basinid77 -0.0096484 0.9903980 0.1122104 -0.086 0.9315
Tg:basinid78 -0.2019178 0.8171621 0.1256274 -1.607 0.1080
Tg:basinid79 0.0427132 1.0436385 0.1093652 0.391 0.6961
Tg:basinid80 -0.0754216 0.9273524 0.1157586 -0.652 0.5147
Tg:basinid81 -0.0979195 0.9067219 0.1164470 -0.841 0.4004
Tg:basinid82 0.0237234 1.0240070 0.1108327 0.214 0.8305
Tg:basinid83 -0.0920835 0.9120290 0.1162381 -0.792 0.4282
Tg:basinid84 -0.2123109 0.8087132 0.1308250 -1.623 0.1046
Tg:basinid85 -0.1977835 0.8205475 0.1291311 -1.532 0.1256
Tg:basinid86 -0.0808703 0.9223133 0.1155576 -0.700 0.4840
Tg:basinid87 -0.0410695 0.9597624 0.1118612 -0.367 0.7135
Tg:basinid88 -0.0703093 0.9321055 0.1121561 -0.627 0.5307
Tg:basinid89 -0.0749198 0.9278179 0.1160229 -0.646 0.5185
Tg:basinid90 -0.2402081 0.7864642 0.1299433 -1.849 0.0645 .
Tg:basinid91 0.0086491 1.0086866 0.1107572 0.078 0.9378
Tg:basinid92 -0.1347233 0.8739577 0.1192149 -1.130 0.2584
Tg:basinid93 0.0003453 1.0003454 0.1114360 0.003 0.9975
Tg:basinid94 -0.1578860 0.8539471 0.1228512 -1.285 0.1987
Tg:basinid95 -0.0847029 0.9187852 0.1155924 -0.733 0.4637
Tg:basinid96 -0.1150635 0.8913096 0.1180564 -0.975 0.3297
Tg:basinid97 -0.0575884 0.9440384 0.1126214 -0.511 0.6091
Tg:basinid98 -0.1523679 0.8586723 0.1254744 -1.214 0.2246
Tg:basinid99 0.0437680 1.0447400 0.1066791 0.410 0.6816
Tg:basinid100 -0.0382101 0.9625107 0.1145776 -0.333 0.7388
Tg:basinid101 -0.1805105 0.8348439 0.1289969 -1.399 0.1617
Tg:basinid102 -0.1848025 0.8312684 0.1252590 -1.475 0.1401
Tg:basinid103 -0.0478238 0.9533017 0.1146362 -0.417 0.6765
Tg:basinid104 -0.0749612 0.9277795 0.1158503 -0.647 0.5176
Tg:basinid105 -0.0666864 0.9354885 0.1126553 -0.592 0.5539
Tg:basinid106 0.0412795 1.0421434 0.1092299 0.378 0.7055
Tg:basinid107 0.0296758 1.0301205 0.1110657 0.267 0.7893
Tg:basinid108 0.1392782 1.1494438 0.1070419 1.301 0.1932
Tg:basinid109 -0.0344404 0.9661459 0.1139198 -0.302 0.7624
Tg:basinid110 -0.1566103 0.8550372 0.1220314 -1.283 0.1994
Tg:basinid111 -0.1041543 0.9010863 0.1216512 -0.856 0.3919
Tg:basinid112 0.0261788 1.0265244 0.1075504 0.243 0.8077
Tg:basinid113 -0.0110256 0.9890349 0.1105762 -0.100 0.9206
Tg:basinid114 -0.1506209 0.8601737 0.1241691 -1.213 0.2251
Tg:basinid115 -0.0857131 0.9178575 0.1191580 -0.719 0.4719
Tg:basinid116 0.0082277 1.0082617 0.1104025 0.075 0.9406
Tg:basinid117 -0.1240886 0.8833016 0.1206012 -1.029 0.3035
Tg:basinid118 -0.2458159 0.7820662 0.1354933 -1.814 0.0696 .
Tg:basinid119 0.0319121 1.0324267 0.1094475 0.292 0.7706
Tg:basinid120 -0.0384262 0.9623028 0.1133874 -0.339 0.7347
Tg:basinid121 -0.0491861 0.9520040 0.1128895 -0.436 0.6631
Tg:basinid122 -0.0942682 0.9100386 0.1175596 -0.802 0.4226
Tg:basinid123 -0.1867762 0.8296294 0.1252851 -1.491 0.1360
Tg:basinid124 -0.0327615 0.9677693 0.1125380 -0.291 0.7710
Tg:basinid125 -0.1819529 0.8336406 0.1265744 -1.438 0.1506
Tg:basinid126 -0.1866563 0.8297288 0.1280296 -1.458 0.1449
Tg:basinid127 0.1305133 1.1394130 0.1047675 1.246 0.2129
Tg:basinid128 -0.0665055 0.9356577 0.1148026 -0.579 0.5624
Tg:basinid129 -0.0522760 0.9490669 0.1149070 -0.455 0.6492
Tg:basinid130 -0.1431776 0.8666001 0.1232026 -1.162 0.2452
Tg:basinid131 -0.1261959 0.8814421 0.1194547 -1.056 0.2908
Tg:basinid132 -0.1183570 0.8883788 0.1190259 -0.994 0.3200
Tg:basinid133 0.0168234 1.0169657 0.1074108 0.157 0.8755
Tg:basinid134 -0.2515586 0.7775879 0.1355146 -1.856 0.0634 .
Tg:basinid135 0.1095242 1.1157471 0.1060628 1.033 0.3018
Tg:basinid136 -0.2618810 0.7696026 0.1357675 -1.929 0.0537 .
Tg:basinid137 -0.0974303 0.9071656 0.1142965 -0.852 0.3940
Tg:basinid138 -0.0555856 0.9459311 0.1136460 -0.489 0.6248
Tg:basinid139 -0.1294233 0.8786020 0.1200368 -1.078 0.2809
Tg:basinid140 -0.1378010 0.8712721 0.1222312 -1.127 0.2596
Tg:basinid141 -0.0318777 0.9686251 0.1137731 -0.280 0.7793
Tg:basinid142 -0.3869031 0.6791569 0.1526494 -2.535 0.0113 *
Tg:basinid143 -0.0489210 0.9522564 0.1134588 -0.431 0.6663
Tg:basinid144 0.0546452 1.0561659 0.1100557 0.497 0.6195
Tg:basinid145 -0.1124001 0.8936866 0.1205284 -0.933 0.3510
Tg:basinid146 0.0501247 1.0514022 0.1118140 0.448 0.6539
Tg:basinid147 -0.0726815 0.9298969 0.1145128 -0.635 0.5256
Tg:basinid148 -0.0554833 0.9460279 0.1144593 -0.485 0.6279
Tg:basinid149 0.0398403 1.0406445 0.1089198 0.366 0.7145
Tg:basinid150 0.0215128 1.0217459 0.1115227 0.193 0.8470
Tg:basinid151 -0.1273784 0.8804005 0.1208650 -1.054 0.2919
Tg:basinid152 -0.0956530 0.9087793 0.1175401 -0.814 0.4158
Tg:basinid153 -0.1005974 0.9042970 0.1174559 -0.856 0.3917
Tg:basinid154 -0.2030214 0.8162608 0.1272593 -1.595 0.1106
Tg:basinid155 -0.1622567 0.8502229 0.1232354 -1.317 0.1880
Tg:basinid156 -0.1178002 0.8888736 0.1207233 -0.976 0.3292
Tg:basinid157 -0.0858035 0.9177746 0.1186407 -0.723 0.4695
Tg:basinid158 -0.0611121 0.9407178 0.1128054 -0.542 0.5880
Tg:basinid159 -0.1880602 0.8285648 0.1262502 -1.490 0.1363
Tg:basinid160 -0.0571116 0.9444887 0.1147266 -0.498 0.6186
Tg:basinid161 -0.1858810 0.8303724 0.1289551 -1.441 0.1495
Tg:basinid162 -0.0486801 0.9524857 0.1138869 -0.427 0.6691
Tg:basinid163 -0.0394757 0.9612933 0.1130441 -0.349 0.7269
Tg:basinid164 -0.2054022 0.8143197 0.1286225 -1.597 0.1103
Tg:basinid165 -0.0136895 0.9864038 0.1140073 -0.120 0.9044
Tg:basinid166 0.0665098 1.0687714 0.1068226 0.623 0.5335
[ reached getOption("max.print") -- omitted 59 rows ]
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
exp(coef) exp(-coef) lower .95 upper .95
Tg 1.8024 0.5548 1.5393 2.1106
Tg:basinid2 1.0421 0.9596 0.8414 1.2908
Tg:basinid3 0.9498 1.0529 0.7562 1.1928
Tg:basinid4 0.9719 1.0289 0.7843 1.2044
Tg:basinid5 1.0215 0.9790 0.8254 1.2641
Tg:basinid6 0.9482 1.0546 0.7546 1.1916
Tg:basinid7 0.8879 1.1262 0.7047 1.1188
Tg:basinid8 0.9651 1.0362 0.7747 1.2023
Tg:basinid9 0.9429 1.0606 0.7533 1.1801
Tg:basinid10 0.8738 1.1445 0.6900 1.1065
Tg:basinid11 0.9211 1.0857 0.7306 1.1612
Tg:basinid12 0.8585 1.1648 0.6756 1.0909
Tg:basinid13 0.8189 1.2212 0.6389 1.0496
Tg:basinid14 0.7918 1.2630 0.6104 1.0270
Tg:basinid15 1.0440 0.9579 0.8460 1.2883
Tg:basinid16 0.9448 1.0585 0.7533 1.1849
Tg:basinid17 0.8699 1.1496 0.6850 1.1046
Tg:basinid18 0.8645 1.1568 0.6811 1.0972
Tg:basinid19 0.8639 1.1575 0.6766 1.1031
Tg:basinid20 0.8696 1.1500 0.6849 1.1041
Tg:basinid21 0.9257 1.0802 0.7371 1.1627
Tg:basinid22 0.9577 1.0442 0.7652 1.1986
Tg:basinid23 0.9523 1.0501 0.7626 1.1890
Tg:basinid24 0.9568 1.0451 0.7658 1.1954
Tg:basinid25 0.8803 1.1360 0.6981 1.1100
Tg:basinid26 0.9450 1.0582 0.7545 1.1836
Tg:basinid27 0.9717 1.0291 0.7786 1.2126
Tg:basinid28 0.8794 1.1372 0.6942 1.1139
Tg:basinid29 0.9268 1.0790 0.7346 1.1693
Tg:basinid30 1.0301 0.9707 0.8338 1.2727
Tg:basinid31 0.8522 1.1735 0.6703 1.0834
Tg:basinid32 0.8982 1.1133 0.7103 1.1359
Tg:basinid33 0.9329 1.0720 0.7415 1.1736
Tg:basinid34 0.8980 1.1136 0.7124 1.1319
Tg:basinid35 0.8839 1.1314 0.6992 1.1174
Tg:basinid36 0.8256 1.2112 0.6448 1.0572
Tg:basinid37 0.9198 1.0872 0.7334 1.1535
Tg:basinid38 0.9184 1.0889 0.7295 1.1562
Tg:basinid39 0.8570 1.1668 0.6738 1.0901
Tg:basinid40 1.0822 0.9241 0.8793 1.3319
Tg:basinid41 0.7096 1.4093 0.5343 0.9422
Tg:basinid42 0.8627 1.1591 0.6781 1.0976
Tg:basinid43 0.9815 1.0189 0.7875 1.2232
Tg:basinid44 0.9418 1.0618 0.7516 1.1802
Tg:basinid45 0.9019 1.1088 0.7178 1.1331
Tg:basinid46 0.8673 1.1530 0.6811 1.1045
Tg:basinid47 0.9875 1.0127 0.7929 1.2297
Tg:basinid48 0.8872 1.1271 0.7005 1.1237
Tg:basinid49 0.8782 1.1387 0.6915 1.1152
Tg:basinid50 0.8899 1.1237 0.7033 1.1261
Tg:basinid51 1.0089 0.9912 0.8111 1.2548
Tg:basinid52 0.9815 1.0189 0.7887 1.2214
Tg:basinid53 0.9790 1.0215 0.7873 1.2173
Tg:basinid54 0.9249 1.0812 0.7371 1.1606
Tg:basinid55 0.8363 1.1957 0.6521 1.0725
Tg:basinid56 1.0011 0.9989 0.8048 1.2454
Tg:basinid57 0.9017 1.1090 0.7152 1.1368
Tg:basinid58 0.9808 1.0196 0.7882 1.2204
Tg:basinid59 0.8908 1.1226 0.7037 1.1275
Tg:basinid60 0.9234 1.0829 0.7359 1.1588
Tg:basinid61 0.9115 1.0971 0.7218 1.1511
Tg:basinid62 0.9090 1.1001 0.7239 1.1416
Tg:basinid63 0.9062 1.1035 0.7201 1.1405
Tg:basinid64 1.0127 0.9874 0.8137 1.2604
Tg:basinid65 0.9573 1.0446 0.7656 1.1970
Tg:basinid66 0.8876 1.1266 0.6990 1.1271
Tg:basinid67 0.7719 1.2955 0.5922 1.0061
Tg:basinid68 0.9766 1.0239 0.7853 1.2147
Tg:basinid69 0.8993 1.1120 0.7128 1.1346
Tg:basinid70 0.8780 1.1389 0.6955 1.1085
Tg:basinid71 0.9117 1.0968 0.7247 1.1470
Tg:basinid72 0.9942 1.0058 0.7993 1.2366
Tg:basinid73 0.9077 1.1017 0.7156 1.1513
Tg:basinid74 0.9772 1.0234 0.7842 1.2177
Tg:basinid75 0.8145 1.2278 0.6347 1.0452
Tg:basinid76 1.0299 0.9709 0.8330 1.2733
Tg:basinid77 0.9904 1.0097 0.7949 1.2340
Tg:basinid78 0.8172 1.2237 0.6388 1.0453
Tg:basinid79 1.0436 0.9582 0.8423 1.2931
Tg:basinid80 0.9274 1.0783 0.7391 1.1635
Tg:basinid81 0.9067 1.1029 0.7217 1.1392
Tg:basinid82 1.0240 0.9766 0.8241 1.2725
Tg:basinid83 0.9120 1.0965 0.7262 1.1454
Tg:basinid84 0.8087 1.2365 0.6258 1.0451
Tg:basinid85 0.8205 1.2187 0.6371 1.0569
Tg:basinid86 0.9223 1.0842 0.7354 1.1568
Tg:basinid87 0.9598 1.0419 0.7708 1.1950
Tg:basinid88 0.9321 1.0728 0.7482 1.1613
Tg:basinid89 0.9278 1.0778 0.7391 1.1647
Tg:basinid90 0.7865 1.2715 0.6096 1.0146
Tg:basinid91 1.0087 0.9914 0.8119 1.2532
Tg:basinid92 0.8740 1.1442 0.6919 1.1040
Tg:basinid93 1.0003 0.9997 0.8041 1.2445
Tg:basinid94 0.8539 1.1710 0.6712 1.0864
Tg:basinid95 0.9188 1.0884 0.7325 1.1524
Tg:basinid96 0.8913 1.1219 0.7072 1.1234
Tg:basinid97 0.9440 1.0593 0.7571 1.1772
Tg:basinid98 0.8587 1.1646 0.6715 1.0981
Tg:basinid99 1.0447 0.9572 0.8476 1.2877
Tg:basinid100 0.9625 1.0389 0.7689 1.2049
Tg:basinid101 0.8348 1.1978 0.6483 1.0750
Tg:basinid102 0.8313 1.2030 0.6503 1.0626
Tg:basinid103 0.9533 1.0490 0.7615 1.1935
Tg:basinid104 0.9278 1.0778 0.7393 1.1643
Tg:basinid105 0.9355 1.0690 0.7501 1.1666
Tg:basinid106 1.0421 0.9596 0.8413 1.2909
Tg:basinid107 1.0301 0.9708 0.8286 1.2806
Tg:basinid108 1.1494 0.8700 0.9319 1.4178
Tg:basinid109 0.9661 1.0350 0.7728 1.2078
Tg:basinid110 0.8550 1.1695 0.6731 1.0861
Tg:basinid111 0.9011 1.1098 0.7099 1.1437
Tg:basinid112 1.0265 0.9742 0.8314 1.2674
Tg:basinid113 0.9890 1.0111 0.7963 1.2284
Tg:basinid114 0.8602 1.1626 0.6744 1.0972
Tg:basinid115 0.9179 1.0895 0.7267 1.1593
Tg:basinid116 1.0083 0.9918 0.8121 1.2518
Tg:basinid117 0.8833 1.1321 0.6974 1.1188
Tg:basinid118 0.7821 1.2787 0.5997 1.0199
Tg:basinid119 1.0324 0.9686 0.8331 1.2794
Tg:basinid120 0.9623 1.0392 0.7705 1.2018
Tg:basinid121 0.9520 1.0504 0.7630 1.1878
Tg:basinid122 0.9100 1.0989 0.7228 1.1458
Tg:basinid123 0.8296 1.2054 0.6490 1.0605
Tg:basinid124 0.9678 1.0333 0.7762 1.2066
Tg:basinid125 0.8336 1.1996 0.6505 1.0684
Tg:basinid126 0.8297 1.2052 0.6456 1.0664
Tg:basinid127 1.1394 0.8776 0.9279 1.3991
Tg:basinid128 0.9357 1.0688 0.7471 1.1718
Tg:basinid129 0.9491 1.0537 0.7577 1.1888
Tg:basinid130 0.8666 1.1539 0.6807 1.1033
Tg:basinid131 0.8814 1.1345 0.6975 1.1140
Tg:basinid132 0.8884 1.1256 0.7035 1.1218
Tg:basinid133 1.0170 0.9833 0.8239 1.2553
Tg:basinid134 0.7776 1.2860 0.5962 1.0141
Tg:basinid135 1.1157 0.8963 0.9063 1.3736
Tg:basinid136 0.7696 1.2994 0.5898 1.0042
Tg:basinid137 0.9072 1.1023 0.7251 1.1349
Tg:basinid138 0.9459 1.0572 0.7570 1.1819
Tg:basinid139 0.8786 1.1382 0.6944 1.1116
Tg:basinid140 0.8713 1.1477 0.6857 1.1071
Tg:basinid141 0.9686 1.0324 0.7750 1.2106
Tg:basinid142 0.6792 1.4724 0.5035 0.9160
Tg:basinid143 0.9523 1.0501 0.7624 1.1894
Tg:basinid144 1.0562 0.9468 0.8512 1.3104
Tg:basinid145 0.8937 1.1190 0.7057 1.1318
Tg:basinid146 1.0514 0.9511 0.8445 1.3090
Tg:basinid147 0.9299 1.0754 0.7430 1.1639
Tg:basinid148 0.9460 1.0571 0.7559 1.1839
Tg:basinid149 1.0406 0.9609 0.8406 1.2883
Tg:basinid150 1.0217 0.9787 0.8211 1.2714
Tg:basinid151 0.8804 1.1358 0.6947 1.1157
Tg:basinid152 0.9088 1.1004 0.7218 1.1442
Tg:basinid153 0.9043 1.1058 0.7183 1.1384
Tg:basinid154 0.8163 1.2251 0.6361 1.0475
Tg:basinid155 0.8502 1.1762 0.6678 1.0825
Tg:basinid156 0.8889 1.1250 0.7016 1.1262
Tg:basinid157 0.9178 1.0896 0.7274 1.1580
Tg:basinid158 0.9407 1.0630 0.7541 1.1735
Tg:basinid159 0.8286 1.2069 0.6469 1.0612
Tg:basinid160 0.9445 1.0588 0.7543 1.1826
Tg:basinid161 0.8304 1.2043 0.6449 1.0692
Tg:basinid162 0.9525 1.0499 0.7619 1.1907
Tg:basinid163 0.9613 1.0403 0.7703 1.1997
Tg:basinid164 0.8143 1.2280 0.6329 1.0478
Tg:basinid165 0.9864 1.0138 0.7889 1.2334
Tg:basinid166 1.0688 0.9357 0.8669 1.3177
Tg:basinid167 0.8612 1.1611 0.6768 1.0960
Tg:basinid168 0.8968 1.1151 0.7085 1.1350
Tg:basinid169 0.9909 1.0091 0.7956 1.2343
Tg:basinid170 0.8753 1.1425 0.6880 1.1134
Tg:basinid171 0.8612 1.1612 0.6783 1.0933
Tg:basinid172 0.8855 1.1293 0.7025 1.1162
Tg:basinid173 0.9821 1.0182 0.7868 1.2258
Tg:basinid174 0.8114 1.2324 0.6295 1.0459
Tg:basinid175 1.0069 0.9931 0.8103 1.2513
Tg:basinid176 0.9378 1.0664 0.7513 1.1705
Tg:basinid177 0.9850 1.0153 0.7920 1.2250
Tg:basinid178 0.7549 1.3247 0.5771 0.9874
Tg:basinid179 0.9399 1.0640 0.7485 1.1802
Tg:basinid180 1.0324 0.9686 0.8396 1.2695
Tg:basinid181 0.8786 1.1381 0.6954 1.1102
Tg:basinid182 1.0441 0.9577 0.8432 1.2929
Tg:basinid183 1.0896 0.9178 0.8835 1.3437
Tg:basinid184 0.6958 1.4372 0.5173 0.9358
Tg:basinid185 0.8650 1.1561 0.6766 1.1058
Tg:basinid186 1.0259 0.9747 0.8281 1.2711
Tg:basinid187 0.7327 1.3648 0.5585 0.9612
Tg:basinid188 0.9591 1.0426 0.7658 1.2013
Tg:basinid189 0.9309 1.0742 0.7419 1.1680
Tg:basinid190 0.8330 1.2005 0.6522 1.0639
Tg:basinid191 0.9642 1.0372 0.7702 1.2069
Tg:basinid192 1.0558 0.9471 0.8555 1.3031
Tg:basinid193 0.9326 1.0723 0.7467 1.1648
Tg:basinid194 0.9675 1.0336 0.7732 1.2106
Tg:basinid195 0.9244 1.0818 0.7322 1.1670
Tg:basinid196 0.9333 1.0715 0.7474 1.1653
Tg:basinid197 0.9899 1.0102 0.7988 1.2266
Tg:basinid198 0.8773 1.1398 0.6917 1.1129
Tg:basinid199 0.9373 1.0669 0.7491 1.1728
Tg:basinid200 0.9181 1.0892 0.7310 1.1531
Tg:basinid201 0.9527 1.0497 0.7595 1.1950
Tg:basinid202 0.7991 1.2514 0.6196 1.0307
Tg:basinid203 1.0207 0.9797 0.8265 1.2605
Tg:basinid204 0.9415 1.0621 0.7507 1.1809
Tg:basinid205 0.9400 1.0639 0.7519 1.1750
Tg:basinid206 1.0081 0.9920 0.8151 1.2467
Tg:basinid207 1.0865 0.9204 0.8800 1.3414
Tg:basinid208 0.8980 1.1136 0.7114 1.1336
Tg:basinid209 0.9575 1.0444 0.7663 1.1963
Tg:basinid210 1.0006 0.9994 0.8092 1.2373
Tg:basinid211 0.8475 1.1800 0.6656 1.0792
Tg:basinid212 0.8760 1.1416 0.6928 1.1076
Tg:basinid213 0.9458 1.0573 0.7560 1.1834
Tg:basinid214 0.8823 1.1333 0.6984 1.1148
Tg:basinid215 0.8150 1.2270 0.6291 1.0557
Tg:basinid216 1.0049 0.9951 0.8092 1.2479
Tg:basinid217 1.0802 0.9258 0.8731 1.3363
Tg:basinid218 0.9148 1.0931 0.7290 1.1480
Tg:basinid219 0.9345 1.0701 0.7469 1.1690
Tg:basinid220 0.8288 1.2065 0.6447 1.0656
Tg:basinid221 0.8810 1.1351 0.6965 1.1143
Tg:basinid222 0.9104 1.0984 0.7242 1.1446
Tg:basinid223 0.8993 1.1119 0.7114 1.1369
Tg:basinid224 0.9081 1.1012 0.7209 1.1439
Tg:basinid225 0.8916 1.1215 0.7059 1.1263
Concordance= 0.663 (se = 0.006 )
Rsquare= 0.044 (max possible= 0.861 )
Likelihood ratio test= 923.3 on 225 df, p=<2e-16
Wald test = 880.9 on 225 df, p=<2e-16
Score (logrank) test = 936.6 on 225 df, p=<2e-16