Time to Event Analysis
- Early vs Late (1st infection between 6m and 1 yr)
- Tech Failure or Death From 1st Infection
## Call: survfit(formula = Surv(Time2Fu - Time2Infection.1, Event) ~ group,
## data = dat2)
##
## n events median 0.95LCL 0.95UCL
## group=Early (<0.5yr) 2028 1139 2.20 2.04 2.33
## group=Late (>0.5yr) 911 509 1.91 1.65 2.23
## Call: survfit(formula = Surv(Time2Fu - Time2Infection.1, Event) ~ group,
## data = dat2)
##
## group=Early (<0.5yr)
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.0 2028 0 1.000 0.0000 1.000 1.000
## 0.5 1539 421 0.790 0.0091 0.773 0.808
## 1.0 1179 213 0.675 0.0107 0.654 0.696
## 2.0 726 229 0.528 0.0120 0.505 0.552
## 4.0 232 235 0.311 0.0134 0.286 0.339
## 8.0 24 41 0.218 0.0166 0.188 0.254
##
## group=Late (>0.5yr)
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.0 911 0 1.000 0.0000 1.000 1.000
## 0.5 688 191 0.788 0.0136 0.762 0.815
## 1.0 528 88 0.682 0.0158 0.651 0.713
## 2.0 295 133 0.490 0.0182 0.455 0.527
## 4.0 92 80 0.319 0.0201 0.281 0.360
## 8.0 7 17 0.233 0.0243 0.190 0.286
## Call:
## coxph(formula = Surv(Time2Fu - Time2Infection.1, Event) ~ group,
## data = dat2)
##
## n= 2939, number of events= 1648
##
## coef exp(coef) se(coef) z Pr(>|z|)
## groupLate (>0.5yr) 0.02572 1.02605 0.05333 0.482 0.63
##
## exp(coef) exp(-coef) lower .95 upper .95
## groupLate (>0.5yr) 1.026 0.9746 0.9242 1.139
##
## Concordance= 0.504 (se = 0.006 )
## Rsquare= 0 (max possible= 1 )
## Likelihood ratio test= 0.23 on 1 df, p=0.6301
## Wald test = 0.23 on 1 df, p=0.6296
## Score (logrank) test = 0.23 on 1 df, p=0.6296
- Time to Death From 1st Infection
## Call: survfit(formula = Surv(Time2Fu - Time2Infection.1, Event.Death) ~
## group, data = dat2)
##
## n events median 0.95LCL 0.95UCL
## group=Early (<0.5yr) 2028 453 7.11 6.37 NA
## group=Late (>0.5yr) 911 192 NA NA NA
## Call: survfit(formula = Surv(Time2Fu - Time2Infection.1, Event.Death) ~
## group, data = dat2)
##
## group=Early (<0.5yr)
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.0 2028 0 1.000 0.00000 1.000 1.000
## 0.5 1539 137 0.925 0.00619 0.913 0.937
## 1.0 1179 82 0.870 0.00828 0.854 0.886
## 2.0 726 110 0.774 0.01142 0.752 0.797
## 4.0 232 105 0.606 0.01775 0.572 0.641
## 8.0 24 19 0.497 0.02946 0.442 0.558
##
## group=Late (>0.5yr)
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.0 911 0 1.000 0.00000 1.000 1.000
## 0.5 688 57 0.931 0.00888 0.913 0.948
## 1.0 528 36 0.877 0.01207 0.854 0.901
## 2.0 295 59 0.755 0.01821 0.720 0.791
## 4.0 92 34 0.627 0.02609 0.578 0.680
## 8.0 7 6 0.568 0.03331 0.507 0.638
## Call:
## coxph(formula = Surv(Time2Fu - Time2Infection.1, Event.Death) ~
## group, data = dat2)
##
## n= 2939, number of events= 645
##
## coef exp(coef) se(coef) z Pr(>|z|)
## groupLate (>0.5yr) -0.02228 0.97796 0.08614 -0.259 0.796
##
## exp(coef) exp(-coef) lower .95 upper .95
## groupLate (>0.5yr) 0.978 1.023 0.826 1.158
##
## Concordance= 0.5 (se = 0.01 )
## Rsquare= 0 (max possible= 0.958 )
## Likelihood ratio test= 0.07 on 1 df, p=0.7956
## Wald test = 0.07 on 1 df, p=0.7959
## Score (logrank) test = 0.07 on 1 df, p=0.7958
- Time of 1st Infection as Continuous Variable
- Tech Failure or Death From 1st Infection
## Call:
## coxph(formula = Surv(Time2Fu - Time2Infection.1, Event) ~ Time2Infection.1,
## data = dat2)
##
## n= 2939, number of events= 1648
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Time2Infection.1 0.01347 1.01356 0.08703 0.155 0.877
##
## exp(coef) exp(-coef) lower .95 upper .95
## Time2Infection.1 1.014 0.9866 0.8546 1.202
##
## Concordance= 0.5 (se = 0.008 )
## Rsquare= 0 (max possible= 1 )
## Likelihood ratio test= 0.02 on 1 df, p=0.8771
## Wald test = 0.02 on 1 df, p=0.877
## Score (logrank) test = 0.02 on 1 df, p=0.877
- Time to Death From 1st Infection
## Call:
## coxph(formula = Surv(Time2Fu - Time2Infection.1, Event.Death) ~
## Time2Infection.1, data = dat2)
##
## n= 2939, number of events= 645
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Time2Infection.1 -0.07066 0.93178 0.14025 -0.504 0.614
##
## exp(coef) exp(-coef) lower .95 upper .95
## Time2Infection.1 0.9318 1.073 0.7078 1.227
##
## Concordance= 0.502 (se = 0.013 )
## Rsquare= 0 (max possible= 0.958 )
## Likelihood ratio test= 0.25 on 1 df, p=0.6137
## Wald test = 0.25 on 1 df, p=0.6144
## Score (logrank) test = 0.25 on 1 df, p=0.6144
- Multivariable Analysis
- Tech Failure or Death From 1st Infection
## coef exp(coef) se(coef) z Pr(>|z|)
## groupLate (>0.5yr) 0.0415 1.0424 0.0564 0.7354 0.4621
## age 0.0161 1.0162 0.0018 8.7338 0.0000
## genderMale -0.0428 0.9581 0.0528 -0.8112 0.4173
## race2White 0.0442 1.0452 0.0627 0.7050 0.4808
## diab2Yes 0.2837 1.3281 0.1031 2.7514 0.0059
## cause.esrdGN -0.0537 0.9477 0.1256 -0.4274 0.6691
## cause.esrdHTN -0.0630 0.9389 0.1129 -0.5582 0.5767
## cause.esrdOther -0.0896 0.9143 0.1126 -0.7959 0.4261
## pd.typeNew -0.2553 0.7747 0.0603 -4.2317 0.0000
## pd.typeOther -0.1297 0.8784 0.0763 -1.6997 0.0892
## FirstSystemTypeCAPD -0.0557 0.9458 0.0556 -1.0011 0.3168
## cultureGramNeg 0.3129 1.3674 0.0866 3.6112 0.0003
## cultureGramPos 0.1313 1.1404 0.0712 1.8452 0.0650
## Analysis of Deviance Table
## Cox model: response is Surv(Time2Fu - Time2Infection.1, Event)
## Terms added sequentially (first to last)
##
## loglik Chisq Df Pr(>|Chi|)
## NULL -10737
## group -10737 0.4934 1 0.482433
## age -10697 80.7422 1 < 2.2e-16 ***
## gender -10696 0.8959 1 0.343874
## race2 -10696 0.1249 1 0.723771
## diab2 -10674 44.8922 1 2.082e-11 ***
## cause.esrd -10673 1.2656 3 0.737322
## pd.type -10663 19.9755 2 4.596e-05 ***
## FirstSystemType -10662 1.5944 1 0.206693
## culture -10656 13.2803 2 0.001307 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
- Time to Death From 1st Infection
## coef exp(coef) se(coef) z Pr(>|z|)
## groupLate (>0.5yr) 0.0040 1.0040 0.0913 0.0436 0.9653
## age 0.0392 1.0400 0.0033 12.0310 0.0000
## genderMale 0.0203 1.0205 0.0844 0.2402 0.8102
## race2White 0.0873 1.0913 0.1057 0.8259 0.4089
## diab2Yes 0.3155 1.3709 0.1658 1.9030 0.0570
## cause.esrdGN -0.4202 0.6569 0.2147 -1.9568 0.0504
## cause.esrdHTN -0.3269 0.7212 0.1801 -1.8155 0.0694
## cause.esrdOther -0.2926 0.7463 0.1787 -1.6375 0.1015
## pd.typeNew -0.4006 0.6699 0.0953 -4.2047 0.0000
## pd.typeOther -0.1915 0.8257 0.1219 -1.5708 0.1162
## FirstSystemTypeCAPD 0.0587 1.0604 0.0915 0.6415 0.5212
## cultureGramNeg 0.0647 1.0669 0.1384 0.4678 0.6399
## cultureGramPos -0.0037 0.9963 0.1076 -0.0345 0.9725
## Analysis of Deviance Table
## Cox model: response is Surv(Time2Fu - Time2Infection.1, Event.Death)
## Terms added sequentially (first to last)
##
## loglik Chisq Df Pr(>|Chi|)
## NULL -4182.0
## group -4182.0 0.0563 1 0.8125031
## age -4097.6 168.8036 1 < 2.2e-16 ***
## gender -4097.6 0.0051 1 0.9428942
## race2 -4097.5 0.2625 1 0.6084360
## diab2 -4071.1 52.6129 1 4.062e-13 ***
## cause.esrd -4068.3 5.7114 3 0.1265251
## pd.type -4059.6 17.2940 2 0.0001757 ***
## FirstSystemType -4059.5 0.3749 1 0.5403447
## culture -4059.3 0.3661 2 0.8327439
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Subsequent Infections Analysis
- Number of Infections After First Infection
## Call:
## coxph(formula = Surv(tstart, tstop, infect) ~ group, data = dat3,
## method = "breslow")
##
## n= 7517, number of events= 4578
##
## coef exp(coef) se(coef) z Pr(>|z|)
## groupLate (>0.5yr) -0.03437 0.96621 0.03239 -1.061 0.289
##
## exp(coef) exp(-coef) lower .95 upper .95
## groupLate (>0.5yr) 0.9662 1.035 0.9068 1.03
##
## Concordance= 0.505 (se = 0.004 )
## Rsquare= 0 (max possible= 1 )
## Likelihood ratio test= 1.13 on 1 df, p=0.2875
## Wald test = 1.13 on 1 df, p=0.2886
## Score (logrank) test = 1.13 on 1 df, p=0.2885
## Call:
## coxph(formula = Surv(tstart, tstop, infect) ~ group + cluster(ID),
## data = dat3, method = "breslow")
##
## n= 7517, number of events= 4578
##
## coef exp(coef) se(coef) robust se z Pr(>|z|)
## groupLate (>0.5yr) -0.03437 0.96621 0.03239 0.05537 -0.621 0.535
##
## exp(coef) exp(-coef) lower .95 upper .95
## groupLate (>0.5yr) 0.9662 1.035 0.8668 1.077
##
## Concordance= 0.505 (se = 0.004 )
## Rsquare= 0 (max possible= 1 )
## Likelihood ratio test= 1.13 on 1 df, p=0.2875
## Wald test = 0.39 on 1 df, p=0.5347
## Score (logrank) test = 1.13 on 1 df, p=0.2885, Robust = 0.39 p=0.5325
##
## (Note: the likelihood ratio and score tests assume independence of
## observations within a cluster, the Wald and robust score tests do not).
- Time to second infection from first infection
## Call: survfit(formula = Surv(tstop - tstart, infect) ~ group, data = subset(dat3,
## enum == 2))
##
## n events median 0.95LCL 0.95UCL
## group=Early (<0.5yr) 1122 671 0.520 0.460 0.613
## group=Late (>0.5yr) 502 285 0.624 0.487 0.764
## Call:
## coxph(formula = Surv(tstop - tstart, infect) ~ group, data = subset(dat3,
## enum == 2))
##
## n= 1624, number of events= 956
##
## coef exp(coef) se(coef) z Pr(>|z|)
## groupLate (>0.5yr) -0.04335 0.95758 0.07074 -0.613 0.54
##
## exp(coef) exp(-coef) lower .95 upper .95
## groupLate (>0.5yr) 0.9576 1.044 0.8336 1.1
##
## Concordance= 0.502 (se = 0.008 )
## Rsquare= 0 (max possible= 1 )
## Likelihood ratio test= 0.38 on 1 df, p=0.5389
## Wald test = 0.38 on 1 df, p=0.54
## Score (logrank) test = 0.38 on 1 df, p=0.54
- Circle length for a third or subsequent infections
## Call: survfit(formula = Surv(tstop - tstart, infect) ~ group, data = subset(dat3,
## enum > 3))
##
## n events median 0.95LCL 0.95UCL
## group=Early (<0.5yr) 1431 987 0.274 0.268 0.287
## group=Late (>0.5yr) 567 379 0.312 0.257 0.402
## Call:
## coxph(formula = Surv(tstop - tstart, infect) ~ group, data = subset(dat3,
## enum > 3))
##
## n= 1998, number of events= 1366
##
## coef exp(coef) se(coef) z Pr(>|z|)
## groupLate (>0.5yr) -0.007755 0.992275 0.060489 -0.128 0.898
##
## exp(coef) exp(-coef) lower .95 upper .95
## groupLate (>0.5yr) 0.9923 1.008 0.8813 1.117
##
## Concordance= 0.5 (se = 0.007 )
## Rsquare= 0 (max possible= 1 )
## Likelihood ratio test= 0.02 on 1 df, p=0.8979
## Wald test = 0.02 on 1 df, p=0.898
## Score (logrank) test = 0.02 on 1 df, p=0.898
GramNeg versus GramPos
- Time to Tech Failure or Death From 1st Infection
## Call: survfit(formula = Surv(Time2Fu, Event) ~ culture, data = dat2)
##
## 255 observations deleted due to missingness
## n events median 0.95LCL 0.95UCL
## culture=CNEG 503 254 2.78 2.48 3.41
## culture=GramNeg 504 292 2.17 1.93 2.65
## culture=GramPos 1677 940 2.46 2.29 2.68
## Call:
## coxph(formula = Surv(Time2Fu, Event) ~ culture, data = dat2)
##
## n= 2684, number of events= 1486
## (255 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## cultureGramNeg 0.26537 1.30391 0.08584 3.092 0.00199 **
## cultureGramPos 0.10846 1.11456 0.07073 1.534 0.12515
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## cultureGramNeg 1.304 0.7669 1.1020 1.543
## cultureGramPos 1.115 0.8972 0.9703 1.280
##
## Concordance= 0.526 (se = 0.007 )
## Rsquare= 0.004 (max possible= 1 )
## Likelihood ratio test= 9.8 on 2 df, p=0.007453
## Wald test = 9.94 on 2 df, p=0.00693
## Score (logrank) test = 9.98 on 2 df, p=0.006821
- Time to Death From 1st Infection
## Call: survfit(formula = Surv(Time2Fu, Event.Death) ~ culture, data = dat2)
##
## 255 observations deleted due to missingness
## n events median 0.95LCL 0.95UCL
## culture=CNEG 503 115 7.17 5.60 NA
## culture=GramNeg 504 99 NA NA NA
## culture=GramPos 1677 372 NA 6.47 NA
## Call:
## coxph(formula = Surv(Time2Fu, Event.Death) ~ culture, data = dat2)
##
## n= 2684, number of events= 586
## (255 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## cultureGramNeg -0.01152 0.98855 0.13716 -0.084 0.933
## cultureGramPos -0.02205 0.97819 0.10671 -0.207 0.836
##
## exp(coef) exp(-coef) lower .95 upper .95
## cultureGramNeg 0.9885 1.012 0.7555 1.293
## cultureGramPos 0.9782 1.022 0.7936 1.206
##
## Concordance= 0.5 (se = 0.011 )
## Rsquare= 0 (max possible= 0.956 )
## Likelihood ratio test= 0.04 on 2 df, p=0.9778
## Wald test = 0.05 on 2 df, p=0.9777
## Score (logrank) test = 0.05 on 2 df, p=0.9777