08. Event-specific estimates
David Herman
event_specific_estimates.Rmd
knitr::opts_chunk$set(warning = FALSE, message = FALSE)
library(revents)
library(survival)Given that PWP, WLW and the PRBC models can be stratified by event number, these models are adequate to obtain the event-specific estimates of the regression parameters in situations in which the the research question may be: a) what is the intervention effect on the number of higher-order events? or b) what is the effect of intervention on the number of subsequent events?
From this models as well is possible to get the same effect estimate than a Coxph model for the first event, as the risk set are the same for all the models for first relapse.
Due to the number of events start to decrease as the event number increases, the estimates for the higher-order events may be less precise than for the first event. Thus, only the first three events are considered in the analysis (SEVENT <= 3).
# Load data layout corresponding to the third layout
data("data_layout_1", package = "revents")
data_layout_1 <- revents::data_layout_1Prentice Williams Peterson - (PWP) (event-specific effect)
pwp.ev.sp.relapses <- coxph(Surv(TSTART, TSTOP, STATUS) ~ strata(SEVENT)/(DISEASE_COURSE +
AGE + SEX + RACE + TIME_SINCE_DIAGNOSIS),
data = subset(data_layout_1,SEVENT <= 3))
pwp.ev.sp.relapses
#> Call:
#> coxph(formula = Surv(TSTART, TSTOP, STATUS) ~ strata(SEVENT)/(DISEASE_COURSE +
#> AGE + SEX + RACE + TIME_SINCE_DIAGNOSIS), data = subset(data_layout_1,
#> SEVENT <= 3))
#>
#> coef exp(coef) se(coef)
#> strata(SEVENT)SEVENT=1:DISEASE_COURSESPMS -0.5065415 0.6025760 0.1169950
#> strata(SEVENT)SEVENT=2:DISEASE_COURSESPMS -0.4000706 0.6702727 0.0951328
#> strata(SEVENT)SEVENT=3:DISEASE_COURSESPMS -0.6753986 0.5089535 0.0815047
#> strata(SEVENT)SEVENT=1:AGE 0.0001745 1.0001746 0.0045354
#> strata(SEVENT)SEVENT=2:AGE 0.0030625 1.0030672 0.0037363
#> strata(SEVENT)SEVENT=3:AGE 0.0040275 1.0040356 0.0032280
#> strata(SEVENT)SEVENT=1:SEXMale 0.1992437 1.2204793 0.0883283
#> strata(SEVENT)SEVENT=2:SEXMale 0.0786923 1.0818714 0.0765383
#> strata(SEVENT)SEVENT=3:SEXMale -0.1086089 0.8970812 0.0638742
#> strata(SEVENT)SEVENT=1:RACEWhite -0.1131750 0.8929943 0.1414812
#> strata(SEVENT)SEVENT=2:RACEWhite -0.1078261 0.8977837 0.1480753
#> strata(SEVENT)SEVENT=3:RACEWhite 0.1106861 1.1170442 0.1111451
#> strata(SEVENT)SEVENT=1:TIME_SINCE_DIAGNOSIS 0.0032136 1.0032188 0.0019227
#> strata(SEVENT)SEVENT=2:TIME_SINCE_DIAGNOSIS 0.0027591 1.0027629 0.0019633
#> strata(SEVENT)SEVENT=3:TIME_SINCE_DIAGNOSIS 0.0020297 1.0020317 0.0016333
#> z p
#> strata(SEVENT)SEVENT=1:DISEASE_COURSESPMS -4.330 1.49e-05
#> strata(SEVENT)SEVENT=2:DISEASE_COURSESPMS -4.205 2.61e-05
#> strata(SEVENT)SEVENT=3:DISEASE_COURSESPMS -8.287 < 2e-16
#> strata(SEVENT)SEVENT=1:AGE 0.038 0.9693
#> strata(SEVENT)SEVENT=2:AGE 0.820 0.4124
#> strata(SEVENT)SEVENT=3:AGE 1.248 0.2121
#> strata(SEVENT)SEVENT=1:SEXMale 2.256 0.0241
#> strata(SEVENT)SEVENT=2:SEXMale 1.028 0.3039
#> strata(SEVENT)SEVENT=3:SEXMale -1.700 0.0891
#> strata(SEVENT)SEVENT=1:RACEWhite -0.800 0.4238
#> strata(SEVENT)SEVENT=2:RACEWhite -0.728 0.4665
#> strata(SEVENT)SEVENT=3:RACEWhite 0.996 0.3193
#> strata(SEVENT)SEVENT=1:TIME_SINCE_DIAGNOSIS 1.671 0.0946
#> strata(SEVENT)SEVENT=2:TIME_SINCE_DIAGNOSIS 1.405 0.1599
#> strata(SEVENT)SEVENT=3:TIME_SINCE_DIAGNOSIS 1.243 0.2140
#>
#> Likelihood ratio test=153.9 on 15 df, p=< 2.2e-16
#> n= 3823, number of events= 2580WLW (event-specific effect)
wlw.ev.sp.relapses <- coxph(Surv(TSTOP, STATUS) ~ strata(SEVENT)/(DISEASE_COURSE + AGE + SEX +
RACE + TIME_SINCE_DIAGNOSIS) + cluster(ID),
data = subset(data_layout_1,SEVENT <= 3))
wlw.ev.sp.relapses
#> Call:
#> coxph(formula = Surv(TSTOP, STATUS) ~ strata(SEVENT) + strata(SEVENT):DISEASE_COURSE +
#> strata(SEVENT):AGE + strata(SEVENT):SEX + strata(SEVENT):RACE +
#> strata(SEVENT):TIME_SINCE_DIAGNOSIS, data = subset(data_layout_1,
#> SEVENT <= 3), cluster = ID)
#>
#> coef exp(coef) se(coef)
#> strata(SEVENT)SEVENT=1:DISEASE_COURSESPMS -0.5065415 0.6025760 0.1169950
#> strata(SEVENT)SEVENT=2:DISEASE_COURSESPMS -0.4404396 0.6437533 0.0947142
#> strata(SEVENT)SEVENT=3:DISEASE_COURSESPMS -0.7281646 0.4827943 0.0816680
#> strata(SEVENT)SEVENT=1:AGE 0.0001745 1.0001746 0.0045354
#> strata(SEVENT)SEVENT=2:AGE 0.0029697 1.0029741 0.0037188
#> strata(SEVENT)SEVENT=3:AGE 0.0029396 1.0029439 0.0032037
#> strata(SEVENT)SEVENT=1:SEXMale 0.1992437 1.2204793 0.0883283
#> strata(SEVENT)SEVENT=2:SEXMale 0.0878825 1.0918598 0.0765051
#> strata(SEVENT)SEVENT=3:SEXMale -0.0283382 0.9720596 0.0637972
#> strata(SEVENT)SEVENT=1:RACEWhite -0.1131750 0.8929943 0.1414812
#> strata(SEVENT)SEVENT=2:RACEWhite -0.1356986 0.8731057 0.1478525
#> strata(SEVENT)SEVENT=3:RACEWhite -0.0103108 0.9897421 0.1111327
#> strata(SEVENT)SEVENT=1:TIME_SINCE_DIAGNOSIS 0.0032136 1.0032188 0.0019227
#> strata(SEVENT)SEVENT=2:TIME_SINCE_DIAGNOSIS 0.0032351 1.0032404 0.0019462
#> strata(SEVENT)SEVENT=3:TIME_SINCE_DIAGNOSIS 0.0027669 1.0027708 0.0016681
#> robust se z p
#> strata(SEVENT)SEVENT=1:DISEASE_COURSESPMS 0.1087082 -4.660 3.17e-06
#> strata(SEVENT)SEVENT=2:DISEASE_COURSESPMS 0.0966364 -4.558 5.17e-06
#> strata(SEVENT)SEVENT=3:DISEASE_COURSESPMS 0.0715327 -10.179 < 2e-16
#> strata(SEVENT)SEVENT=1:AGE 0.0041946 0.042 0.9668
#> strata(SEVENT)SEVENT=2:AGE 0.0038243 0.777 0.4374
#> strata(SEVENT)SEVENT=3:AGE 0.0029963 0.981 0.3266
#> strata(SEVENT)SEVENT=1:SEXMale 0.0837183 2.380 0.0173
#> strata(SEVENT)SEVENT=2:SEXMale 0.0771347 1.139 0.2546
#> strata(SEVENT)SEVENT=3:SEXMale 0.0582100 -0.487 0.6264
#> strata(SEVENT)SEVENT=1:RACEWhite 0.1270028 -0.891 0.3729
#> strata(SEVENT)SEVENT=2:RACEWhite 0.1162681 -1.167 0.2432
#> strata(SEVENT)SEVENT=3:RACEWhite 0.1162035 -0.089 0.9293
#> strata(SEVENT)SEVENT=1:TIME_SINCE_DIAGNOSIS 0.0015630 2.056 0.0398
#> strata(SEVENT)SEVENT=2:TIME_SINCE_DIAGNOSIS 0.0016149 2.003 0.0451
#> strata(SEVENT)SEVENT=3:TIME_SINCE_DIAGNOSIS 0.0015270 1.812 0.0700
#>
#> Likelihood ratio test=179.2 on 15 df, p=< 2.2e-16
#> n= 3823, number of events= 2580PCRB (event-specific effect)
prcb.relapses <- coxph(Surv(TSTART, TSTOP, STATUS) ~ strata(SEVENT)/(DISEASE_COURSE + AGE + SEX + RACE + TIME_SINCE_DIAGNOSIS) + cluster(ID), data = subset(data_layout_1,SEVENT <= 3))
prcb.relapses
#> Call:
#> coxph(formula = Surv(TSTART, TSTOP, STATUS) ~ strata(SEVENT) +
#> strata(SEVENT):DISEASE_COURSE + strata(SEVENT):AGE + strata(SEVENT):SEX +
#> strata(SEVENT):RACE + strata(SEVENT):TIME_SINCE_DIAGNOSIS,
#> data = subset(data_layout_1, SEVENT <= 3), cluster = ID)
#>
#> coef exp(coef) se(coef)
#> strata(SEVENT)SEVENT=1:DISEASE_COURSESPMS -0.5065415 0.6025760 0.1169950
#> strata(SEVENT)SEVENT=2:DISEASE_COURSESPMS -0.4000706 0.6702727 0.0951328
#> strata(SEVENT)SEVENT=3:DISEASE_COURSESPMS -0.6753986 0.5089535 0.0815047
#> strata(SEVENT)SEVENT=1:AGE 0.0001745 1.0001746 0.0045354
#> strata(SEVENT)SEVENT=2:AGE 0.0030625 1.0030672 0.0037363
#> strata(SEVENT)SEVENT=3:AGE 0.0040275 1.0040356 0.0032280
#> strata(SEVENT)SEVENT=1:SEXMale 0.1992437 1.2204793 0.0883283
#> strata(SEVENT)SEVENT=2:SEXMale 0.0786923 1.0818714 0.0765383
#> strata(SEVENT)SEVENT=3:SEXMale -0.1086089 0.8970812 0.0638742
#> strata(SEVENT)SEVENT=1:RACEWhite -0.1131750 0.8929943 0.1414812
#> strata(SEVENT)SEVENT=2:RACEWhite -0.1078261 0.8977837 0.1480753
#> strata(SEVENT)SEVENT=3:RACEWhite 0.1106861 1.1170442 0.1111451
#> strata(SEVENT)SEVENT=1:TIME_SINCE_DIAGNOSIS 0.0032136 1.0032188 0.0019227
#> strata(SEVENT)SEVENT=2:TIME_SINCE_DIAGNOSIS 0.0027591 1.0027629 0.0019633
#> strata(SEVENT)SEVENT=3:TIME_SINCE_DIAGNOSIS 0.0020297 1.0020317 0.0016333
#> robust se z p
#> strata(SEVENT)SEVENT=1:DISEASE_COURSESPMS 0.1087082 -4.660 3.17e-06
#> strata(SEVENT)SEVENT=2:DISEASE_COURSESPMS 0.0969919 -4.125 3.71e-05
#> strata(SEVENT)SEVENT=3:DISEASE_COURSESPMS 0.0713733 -9.463 < 2e-16
#> strata(SEVENT)SEVENT=1:AGE 0.0041946 0.042 0.9668
#> strata(SEVENT)SEVENT=2:AGE 0.0038467 0.796 0.4260
#> strata(SEVENT)SEVENT=3:AGE 0.0028922 1.393 0.1638
#> strata(SEVENT)SEVENT=1:SEXMale 0.0837183 2.380 0.0173
#> strata(SEVENT)SEVENT=2:SEXMale 0.0766892 1.026 0.3048
#> strata(SEVENT)SEVENT=3:SEXMale 0.0570834 -1.903 0.0571
#> strata(SEVENT)SEVENT=1:RACEWhite 0.1270028 -0.891 0.3729
#> strata(SEVENT)SEVENT=2:RACEWhite 0.1173143 -0.919 0.3580
#> strata(SEVENT)SEVENT=3:RACEWhite 0.1070650 1.034 0.3012
#> strata(SEVENT)SEVENT=1:TIME_SINCE_DIAGNOSIS 0.0015630 2.056 0.0398
#> strata(SEVENT)SEVENT=2:TIME_SINCE_DIAGNOSIS 0.0015624 1.766 0.0774
#> strata(SEVENT)SEVENT=3:TIME_SINCE_DIAGNOSIS 0.0013680 1.484 0.1379
#>
#> Likelihood ratio test=153.9 on 15 df, p=< 2.2e-16
#> n= 3823, number of events= 2580The PWP and PCRB models provide same point estimates with few differences in the 95% confidence intervals due to the lack of time dependent covariates in the conditional model. The risk of the second and third relapse was 33% and 50% significantly lower in SPMS participants than in RRMS group in those models.
For the WLW, the risk of 2nd and 3rd relapse were also significantly lower (36% and 52% respectively) in the SPMS group.