Under two-stage randomization we can estimate the average treatment effect \(E(Y(i,\bar k))\) of treatment regime \((i,\bar k)\).
The estimator can be agumented in different ways: using the two randomizations and the dynamic censoring augmentatation.
Estimating \(\mu_{i,\bar k} = P(Y(i,\bar k,\epsilon=v) <= t)\), restricted mean \(E( \min(Y(i,\bar k),\tau))\) or years lost \(E( I(\epsilon=v) \cdot (\tau - \min(Y(i,\bar k),\tau)))\) using IPCW weighted estimating equations : \
The solved estimating eqution is \[\begin{align*} \sum_i \frac{I(min(T_i,t) < G_i)}{G_c(min(T_i ,t))} I(T \leq t, \epsilon=1 ) - AUG_0 - AUG_1 + AUG_C - p(i,j)) = 0 \end{align*}\] using the covariates from augmentR0 to augment with \[\begin{align*} AUG_0 = \frac{A_0(i) - \pi_0(i)}{ \pi_0(i)} X_0 \gamma_0 \end{align*}\] and using the covariates from augmentR1 to augment with \[\begin{align*} AUG_1 = \frac{A_0(i)}{\pi_0(i)} \frac{A_1(j) - \pi_1(j)}{ \pi_1(j)} X_1 \gamma_1 \end{align*}\] and censoring augmenting with \[\begin{align*} AUG_C = \int_0^t \gamma_c(s)^T (e(s) - \bar e(s)) \frac{1}{G_c(s) } dM_c(s) \end{align*}\] where \(\gamma_c(s)\) is chosen to minimize the variance given the dynamic covariates specified by augmentC.
Standard errors are estimated using the influence function of all estimators and tests of differences can therefore be computed subsequently.
Data must be given on start,stop,status survival format with
library(mets)
set.seed(100)
n <- 200
ddf <- mets:::gsim(n,covs=1,null=0,cens=1,ce=1,betac=c(0.3,1))
true <- apply(ddf$TTt<2,2,mean)
true
#> [1] 0.740 0.770 0.395 0.430
datat <- ddf$datat
## set-random response on data, only relevant after status==2
response <- rbinom(n,1,0.5)
datat$response <- as.factor(response[datat$id]*datat$Count2)
datat$A000 <- as.factor(1)
datat$A111 <- as.factor(1)
bb <- binregTSR(Event(entry,time,status)~+1+cluster(id),datat,time=2,cause=c(1),response.code=2,
treat.model0=A0.f~+1, treat.model1=A1.f~A0.f,
augmentR1=~X11+X12+TR, augmentR0=~X01+X02,
augmentC=~X01+X02+A11t+A12t+X11+X12+TR, cens.model=~strata(A0.f))
bb
#> Simple estimator :
#> coef
#> A0.f=1, response*A1.f=1 0.5913901 0.13861137
#> A0.f=1, response*A1.f=2 0.6240667 0.10605755
#> A0.f=2, response*A1.f=1 0.2446124 0.07925685
#> A0.f=2, response*A1.f=2 0.3897508 0.08252711
#>
#> First Randomization Augmentation :
#> coef
#> A0.f=1, response*A1.f=1 0.6047560 0.14921165
#> A0.f=1, response*A1.f=2 0.6441681 0.11761310
#> A0.f=2, response*A1.f=1 0.2371433 0.08089305
#> A0.f=2, response*A1.f=2 0.3806609 0.08391961
#>
#> Second Randomization Augmentation :
#> coef
#> A0.f=1, response*A1.f=1 0.5784696 0.18002763
#> A0.f=1, response*A1.f=2 0.5078635 0.14816954
#> A0.f=2, response*A1.f=1 0.2352898 0.08048304
#> A0.f=2, response*A1.f=2 0.3703686 0.08815050
#>
#> 1st and 2nd Randomization Augmentation :
#> coef
#> A0.f=1, response*A1.f=1 0.6141209 0.19240265
#> A0.f=1, response*A1.f=2 0.5270450 0.15149921
#> A0.f=2, response*A1.f=1 0.2297845 0.08096617
#> A0.f=2, response*A1.f=2 0.3672756 0.08784395
estimate(coef=bb$riskG$riskG01[,1],vcov=crossprod(bb$riskG.iid$riskG01))
#> Estimate Std.Err 2.5% 97.5% P-value
#> A0.f=1, response*A1.f=1 0.6141 0.19240 0.23702 0.9912 1.414e-03
#> A0.f=1, response*A1.f=2 0.5270 0.15150 0.23011 0.8240 5.035e-04
#> A0.f=2, response*A1.f=1 0.2298 0.08097 0.07109 0.3885 4.539e-03
#> A0.f=2, response*A1.f=2 0.3673 0.08784 0.19510 0.5394 2.902e-05
estimate(coef=bb$riskG$riskG01[,1],vcov=crossprod(bb$riskG.iid$riskG01),f=function(p) c(p[1]/p[2],p[3]/p[4]))
#> Estimate Std.Err 2.5% 97.5% P-value
#> A0.f=1, response*A1.f=1 1.1652 0.5435 0.09991 2.231 0.03205
#> A0.f=2, response*A1.f=1 0.6256 0.2573 0.12144 1.130 0.01502
estimate(coef=bb$riskG$riskG01[,1],vcov=crossprod(bb$riskG.iid$riskG01),f=function(p) c(p[1]-p[2],p[3]-p[4]))
#> Estimate Std.Err 2.5% 97.5% P-value
#> A0.f=1, response*A1.f=1 0.08708 0.2681 -0.4384 0.61257 0.7454
#> A0.f=2, response*A1.f=1 -0.13749 0.1150 -0.3630 0.08799 0.2320## 2 levels for each response , fixed weights
datat$response.f <- as.factor(datat$response)
bb <- binregTSR(Event(entry,time,status)~+1+cluster(id),datat,time=2,cause=c(1),response.code=2,
treat.model0=A0.f~+1, treat.model1=A1.f~A0.f*response.f,
augmentR0=~X01+X02, augmentR1=~X11+X12,
augmentC=~X01+X02+A11t+A12t+X11+X12+TR, cens.model=~strata(A0.f),
estpr=c(0,0),pi0=0.5,pi1=0.5)
bb
#> Simple estimator :
#> coef
#> A0.f=1, response.f*A1.f=1,1 0.5386068 0.12844087
#> A0.f=1, response.f*A1.f=2,1 0.5450214 0.12794277
#> A0.f=1, response.f*A1.f=1,2 0.5456221 0.09349913
#> A0.f=1, response.f*A1.f=2,2 0.5520366 0.09093621
#> A0.f=2, response.f*A1.f=1,1 0.2570426 0.08524398
#> A0.f=2, response.f*A1.f=2,1 0.3522177 0.09946394
#> A0.f=2, response.f*A1.f=1,2 0.3600957 0.10342185
#> A0.f=2, response.f*A1.f=2,2 0.4552707 0.11129564
#>
#> First Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.f=1,1 0.6464138 0.14788853
#> A0.f=1, response.f*A1.f=2,1 0.6524848 0.14783874
#> A0.f=1, response.f*A1.f=1,2 0.6435582 0.09492478
#> A0.f=1, response.f*A1.f=2,2 0.6496292 0.09153841
#> A0.f=2, response.f*A1.f=1,1 0.2213105 0.09350027
#> A0.f=2, response.f*A1.f=2,1 0.3092979 0.10675847
#> A0.f=2, response.f*A1.f=1,2 0.3102643 0.11228693
#> A0.f=2, response.f*A1.f=2,2 0.3982518 0.11851483
#>
#> Second Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.f=1,1 0.4404540 0.15440522
#> A0.f=1, response.f*A1.f=2,1 0.5847041 0.16921711
#> A0.f=1, response.f*A1.f=1,2 0.5215925 0.11292250
#> A0.f=1, response.f*A1.f=2,2 0.5549930 0.10040415
#> A0.f=2, response.f*A1.f=1,1 0.2647734 0.07944743
#> A0.f=2, response.f*A1.f=2,1 0.3437537 0.09821336
#> A0.f=2, response.f*A1.f=1,2 0.3970266 0.08317368
#> A0.f=2, response.f*A1.f=2,2 0.3995221 0.11567339
#>
#> 1st and 2nd Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.f=1,1 0.5499140 0.15696306
#> A0.f=1, response.f*A1.f=2,1 0.7049532 0.19047490
#> A0.f=1, response.f*A1.f=1,2 0.6206264 0.11607918
#> A0.f=1, response.f*A1.f=2,2 0.6566749 0.09929892
#> A0.f=2, response.f*A1.f=1,1 0.2303423 0.08548320
#> A0.f=2, response.f*A1.f=2,1 0.3069402 0.10292148
#> A0.f=2, response.f*A1.f=1,2 0.3487837 0.08783732
#> A0.f=2, response.f*A1.f=2,2 0.3563507 0.11928271
## 2 levels for each response , estimated treat probabilities
bb <- binregTSR(Event(entry,time,status)~+1+cluster(id),datat,time=2,cause=c(1),response.code=2,
treat.model0=A0.f~+1, treat.model1=A1.f~A0.f*response.f,
augmentR0=~X01+X02, augmentR1=~X11+X12,
augmentC=~X01+X02+A11t+A12t+X11+X12+TR, cens.model=~strata(A0.f),estpr=c(1,1))
bb
#> Simple estimator :
#> coef
#> A0.f=1, response.f*A1.f=1,1 0.5960606 0.17488200
#> A0.f=1, response.f*A1.f=2,1 0.6241013 0.17440045
#> A0.f=1, response.f*A1.f=1,2 0.5970085 0.09374896
#> A0.f=1, response.f*A1.f=2,2 0.6250491 0.09621393
#> A0.f=2, response.f*A1.f=1,1 0.2511629 0.08214906
#> A0.f=2, response.f*A1.f=2,1 0.2897991 0.07348482
#> A0.f=2, response.f*A1.f=1,2 0.3513307 0.09298624
#> A0.f=2, response.f*A1.f=2,2 0.3899668 0.08400431
#>
#> First Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.f=1,1 0.6110247 0.18838108
#> A0.f=1, response.f*A1.f=2,1 0.6392858 0.18875912
#> A0.f=1, response.f*A1.f=1,2 0.6144511 0.10254061
#> A0.f=1, response.f*A1.f=2,2 0.6427122 0.10570324
#> A0.f=2, response.f*A1.f=1,1 0.2440860 0.08346801
#> A0.f=2, response.f*A1.f=2,1 0.2831312 0.07506141
#> A0.f=2, response.f*A1.f=1,2 0.3410878 0.09418680
#> A0.f=2, response.f*A1.f=2,2 0.3801331 0.08553880
#>
#> Second Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.f=1,1 0.4814011 0.17426935
#> A0.f=1, response.f*A1.f=2,1 0.6103501 0.18912497
#> A0.f=1, response.f*A1.f=1,2 0.6070156 0.11378882
#> A0.f=1, response.f*A1.f=2,2 0.6181593 0.09508071
#> A0.f=2, response.f*A1.f=1,1 0.2454093 0.08562583
#> A0.f=2, response.f*A1.f=2,1 0.3061112 0.06782067
#> A0.f=2, response.f*A1.f=1,2 0.3545614 0.09061532
#> A0.f=2, response.f*A1.f=2,2 0.3709128 0.08781320
#>
#> 1st and 2nd Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.f=1,1 0.5086290 0.18332584
#> A0.f=1, response.f*A1.f=2,1 0.6311793 0.20425552
#> A0.f=1, response.f*A1.f=1,2 0.6250920 0.12136105
#> A0.f=1, response.f*A1.f=2,2 0.6410325 0.10178189
#> A0.f=2, response.f*A1.f=1,1 0.2381002 0.08632006
#> A0.f=2, response.f*A1.f=2,1 0.3018155 0.06857549
#> A0.f=2, response.f*A1.f=1,2 0.3452178 0.09088007
#> A0.f=2, response.f*A1.f=2,2 0.3666639 0.08738161
## 2 and 3 levels for each response , fixed weights
datat$A1.23.f <- as.numeric(datat$A1.f)
dtable(datat,~A1.23.f+response)
#>
#> response 0 1
#> A1.23.f
#> 1 116 23
#> 2 120 23
datat <- dtransform(datat,A1.23.f=2+rbinom(nrow(datat),1,0.5),
Count2==1 & A1.23.f==2 & response==0)
dtable(datat,~A1.23.f+response)
#>
#> response 0 1
#> A1.23.f
#> 1 116 23
#> 2 111 23
#> 3 9 0
datat$A1.23.f <- as.factor(datat$A1.23.f)
dtable(datat,~A1.23.f+response|Count2==1)
#>
#> response 0 1
#> A1.23.f
#> 1 17 23
#> 2 10 23
#> 3 9 0
###
bb <- binregTSR(Event(entry,time,status)~+1+cluster(id),datat,time=2,cause=c(1),response.code=2,
treat.model0=A0.f~+1, treat.model1=A1.23.f~A0.f*response.f,
augmentR0=~X01+X02, augmentR1=~X11+X12,
augmentC=~X01+X02+A11t+A12t+X11+X12+TR, cens.model=~strata(A0.f),
estpr=c(1,0),pi1=c(0.3,0.5))
bb
#> Simple estimator :
#> coef
#> A0.f=1, response.f*A1.23.f=1,1 0.6138741 0.14546619
#> A0.f=1, response.f*A1.23.f=2,1 0.6257528 0.14027635
#> A0.f=1, response.f*A1.23.f=3,1 0.5753190 0.13540555
#> A0.f=1, response.f*A1.23.f=1,2 0.6216688 0.10602763
#> A0.f=1, response.f*A1.23.f=2,2 0.6335476 0.09548483
#> A0.f=1, response.f*A1.23.f=3,2 0.5831138 0.08882984
#> A0.f=2, response.f*A1.23.f=1,1 0.2719027 0.09932666
#> A0.f=2, response.f*A1.23.f=2,1 0.2562909 0.08395583
#> A0.f=2, response.f*A1.23.f=3,1 0.3361501 0.11249207
#> A0.f=2, response.f*A1.23.f=1,2 0.3655873 0.11106102
#> A0.f=2, response.f*A1.23.f=2,2 0.3499755 0.09860883
#> A0.f=2, response.f*A1.23.f=3,2 0.4298347 0.11791066
#>
#> First Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.23.f=1,1 0.6254238 0.15870500
#> A0.f=1, response.f*A1.23.f=2,1 0.6402288 0.15454601
#> A0.f=1, response.f*A1.23.f=3,1 0.5922315 0.14938976
#> A0.f=1, response.f*A1.23.f=1,2 0.6367920 0.11621860
#> A0.f=1, response.f*A1.23.f=2,2 0.6515970 0.10470729
#> A0.f=1, response.f*A1.23.f=3,2 0.6035997 0.09759337
#> A0.f=2, response.f*A1.23.f=1,1 0.2643835 0.10132734
#> A0.f=2, response.f*A1.23.f=2,1 0.2534870 0.08372325
#> A0.f=2, response.f*A1.23.f=3,1 0.3252664 0.11484580
#> A0.f=2, response.f*A1.23.f=1,2 0.3552907 0.11311288
#> A0.f=2, response.f*A1.23.f=2,2 0.3443942 0.09915534
#> A0.f=2, response.f*A1.23.f=3,2 0.4161736 0.11990969
#>
#> Second Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.23.f=1,1 0.5052801 0.17545930
#> A0.f=1, response.f*A1.23.f=2,1 0.6490684 0.15881690
#> A0.f=1, response.f*A1.23.f=3,1 0.6854636 0.21833075
#> A0.f=1, response.f*A1.23.f=1,2 0.5585969 0.14220646
#> A0.f=1, response.f*A1.23.f=2,2 0.6777914 0.10735131
#> A0.f=1, response.f*A1.23.f=3,2 0.5813296 0.09751519
#> A0.f=2, response.f*A1.23.f=1,1 0.2422917 0.10988029
#> A0.f=2, response.f*A1.23.f=2,1 0.2797783 0.06601642
#> A0.f=2, response.f*A1.23.f=3,1 0.3401244 0.10216861
#> A0.f=2, response.f*A1.23.f=1,2 0.3485496 0.10783283
#> A0.f=2, response.f*A1.23.f=2,2 0.3412911 0.09398459
#> A0.f=2, response.f*A1.23.f=3,2 0.4201655 0.10601190
#>
#> 1st and 2nd Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.23.f=1,1 0.5364106 0.17539959
#> A0.f=1, response.f*A1.23.f=2,1 0.6790927 0.17741623
#> A0.f=1, response.f*A1.23.f=3,1 0.7120475 0.23374336
#> A0.f=1, response.f*A1.23.f=1,2 0.5848366 0.14466454
#> A0.f=1, response.f*A1.23.f=2,2 0.7002151 0.11773612
#> A0.f=1, response.f*A1.23.f=3,2 0.6093505 0.10260212
#> A0.f=2, response.f*A1.23.f=1,1 0.2325801 0.11079752
#> A0.f=2, response.f*A1.23.f=2,1 0.2794200 0.06590063
#> A0.f=2, response.f*A1.23.f=3,1 0.3304444 0.10321469
#> A0.f=2, response.f*A1.23.f=1,2 0.3371281 0.10787101
#> A0.f=2, response.f*A1.23.f=2,2 0.3408481 0.09407294
#> A0.f=2, response.f*A1.23.f=3,2 0.4097042 0.10540790
## 2 and 3 levels for each response , estimated
bb <- binregTSR(Event(entry,time,status)~+1+cluster(id),datat,time=2,cause=c(1),response.code=2,
treat.model0=A0.f~+1, treat.model1=A1.23.f~A0.f*response.f,
augmentR0=~X01+X02, augmentR1=~X11+X12,
augmentC=~X01+X02+A11t+A12t+X11+X12+TR, cens.model=~strata(A0.f),estpr=c(1,1))
bb
#> Simple estimator :
#> coef
#> A0.f=1, response.f*A1.23.f=1,1 0.5960607 0.17488240
#> A0.f=1, response.f*A1.23.f=2,1 0.6694918 0.18436102
#> A0.f=1, response.f*A1.23.f=3,1 0.5787109 0.17389417
#> A0.f=1, response.f*A1.23.f=1,2 0.5970086 0.09374912
#> A0.f=1, response.f*A1.23.f=2,2 0.6704397 0.12466711
#> A0.f=1, response.f*A1.23.f=3,2 0.5796588 0.09175040
#> A0.f=2, response.f*A1.23.f=1,1 0.2511630 0.08214910
#> A0.f=2, response.f*A1.23.f=2,1 0.2466693 0.07985946
#> A0.f=2, response.f*A1.23.f=3,1 0.3390904 0.13291742
#> A0.f=2, response.f*A1.23.f=1,2 0.3513309 0.09298631
#> A0.f=2, response.f*A1.23.f=2,2 0.3468372 0.09363568
#> A0.f=2, response.f*A1.23.f=3,2 0.4392583 0.13816514
#>
#> First Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.23.f=1,1 0.6110248 0.18838149
#> A0.f=1, response.f*A1.23.f=2,1 0.6824835 0.19886165
#> A0.f=1, response.f*A1.23.f=3,1 0.5960883 0.18774606
#> A0.f=1, response.f*A1.23.f=1,2 0.6144512 0.10254079
#> A0.f=1, response.f*A1.23.f=2,2 0.6859099 0.13389812
#> A0.f=1, response.f*A1.23.f=3,2 0.5995147 0.10050974
#> A0.f=2, response.f*A1.23.f=1,1 0.2440861 0.08346805
#> A0.f=2, response.f*A1.23.f=2,1 0.2436866 0.08028322
#> A0.f=2, response.f*A1.23.f=3,1 0.3282110 0.13608467
#> A0.f=2, response.f*A1.23.f=1,2 0.3410881 0.09418688
#> A0.f=2, response.f*A1.23.f=2,2 0.3406886 0.09477872
#> A0.f=2, response.f*A1.23.f=3,2 0.4252130 0.14126153
#>
#> Second Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.23.f=1,1 0.4814004 0.17426965
#> A0.f=1, response.f*A1.23.f=2,1 0.6135499 0.17753447
#> A0.f=1, response.f*A1.23.f=3,1 0.6888656 0.25450984
#> A0.f=1, response.f*A1.23.f=1,2 0.6070155 0.11378895
#> A0.f=1, response.f*A1.23.f=2,2 0.6754339 0.10506823
#> A0.f=1, response.f*A1.23.f=3,2 0.5781644 0.09243287
#> A0.f=2, response.f*A1.23.f=1,1 0.2454092 0.08562594
#> A0.f=2, response.f*A1.23.f=2,1 0.2755312 0.06176367
#> A0.f=2, response.f*A1.23.f=3,1 0.3436018 0.10039784
#> A0.f=2, response.f*A1.23.f=1,2 0.3545614 0.09061545
#> A0.f=2, response.f*A1.23.f=2,2 0.3396800 0.09092113
#> A0.f=2, response.f*A1.23.f=3,2 0.4176542 0.11160494
#>
#> 1st and 2nd Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.23.f=1,1 0.5086283 0.18332613
#> A0.f=1, response.f*A1.23.f=2,1 0.6349396 0.19140558
#> A0.f=1, response.f*A1.23.f=3,1 0.7148045 0.26881972
#> A0.f=1, response.f*A1.23.f=1,2 0.6250918 0.12136117
#> A0.f=1, response.f*A1.23.f=2,2 0.6956879 0.11422414
#> A0.f=1, response.f*A1.23.f=3,2 0.6145399 0.09722634
#> A0.f=2, response.f*A1.23.f=1,1 0.2381001 0.08632018
#> A0.f=2, response.f*A1.23.f=2,1 0.2746787 0.06225545
#> A0.f=2, response.f*A1.23.f=3,1 0.3340444 0.10201691
#> A0.f=2, response.f*A1.23.f=1,2 0.3452178 0.09088021
#> A0.f=2, response.f*A1.23.f=2,2 0.3384473 0.09094019
#> A0.f=2, response.f*A1.23.f=3,2 0.4068396 0.11084657
## 2 and 1 level for each response
datat$A1.21.f <- as.numeric(datat$A1.f)
dtable(datat,~A1.21.f+response|Count2==1)
#>
#> response 0 1
#> A1.21.f
#> 1 17 23
#> 2 19 23
datat <- dtransform(datat,A1.21.f=1,Count2==1 & response==1)
dtable(datat,~A1.21.f+response|Count2==1)
#>
#> response 0 1
#> A1.21.f
#> 1 17 46
#> 2 19 0
datat$A1.21.f <- as.factor(datat$A1.21.f)
dtable(datat,~A1.21.f+response|Count2==1)
#>
#> response 0 1
#> A1.21.f
#> 1 17 46
#> 2 19 0
bb <- binregTSR(Event(entry,time,status)~+1+cluster(id),datat,time=2,cause=c(1),response.code=2,
treat.model0=A0.f~+1, treat.model1=A1.21.f~A0.f*response.f,
augmentR0=~X01+X02, augmentR1=~X11+X12,
augmentC=~X01+X02+A11t+A12t+X11+X12+TR, cens.model=~strata(A0.f),estpr=c(1,1))
bb
#> Simple estimator :
#> coef
#> A0.f=1, response.f*A1.21.f=1,1 0.5965662 0.09733539
#> A0.f=1, response.f*A1.21.f=2,1 0.6246068 0.09822505
#> A0.f=2, response.f*A1.21.f=1,1 0.2996312 0.07727063
#> A0.f=2, response.f*A1.21.f=2,1 0.3382673 0.06699693
#>
#> First Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.21.f=1,1 0.6128521 0.10629676
#> A0.f=1, response.f*A1.21.f=2,1 0.6411132 0.10832312
#> A0.f=2, response.f*A1.21.f=1,1 0.2910224 0.07750644
#> A0.f=2, response.f*A1.21.f=2,1 0.3300676 0.06746375
#>
#> Second Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.21.f=1,1 0.6051429 0.09770130
#> A0.f=1, response.f*A1.21.f=2,1 0.6483866 0.09264360
#> A0.f=2, response.f*A1.21.f=1,1 0.3025669 0.07788942
#> A0.f=2, response.f*A1.21.f=2,1 0.3325213 0.07135192
#>
#> 1st and 2nd Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.21.f=1,1 0.6326858 0.10838935
#> A0.f=1, response.f*A1.21.f=2,1 0.6766156 0.10446225
#> A0.f=2, response.f*A1.21.f=1,1 0.2944012 0.07730608
#> A0.f=2, response.f*A1.21.f=2,1 0.3287928 0.07092539
## known weights
bb <- binregTSR(Event(entry,time,status)~+1+cluster(id),datat,time=2,cause=c(1),response.code=2,
treat.model0=A0.f~+1, treat.model1=A1.21.f~A0.f*response.f,
augmentR0=~X01+X02, augmentR1=~X11+X12,
augmentC=~X01+X02+A11t+A12t+X11+X12+TR, cens.model=~strata(A0.f),estpr=c(1,0),pi1=c(0.5,1))
bb
#> Simple estimator :
#> coef
#> A0.f=1, response.f*A1.21.f=1,1 0.6023494 0.09968651
#> A0.f=1, response.f*A1.21.f=2,1 0.6094767 0.09708463
#> A0.f=2, response.f*A1.21.f=1,1 0.2805174 0.06945416
#> A0.f=2, response.f*A1.21.f=2,1 0.3670402 0.07983587
#>
#> First Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.21.f=1,1 0.6178310 0.10889407
#> A0.f=1, response.f*A1.21.f=2,1 0.6267140 0.10667341
#> A0.f=2, response.f*A1.21.f=1,1 0.2722077 0.07020526
#> A0.f=2, response.f*A1.21.f=2,1 0.3586436 0.07971457
#>
#> Second Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.21.f=1,1 0.6052636 0.10251830
#> A0.f=1, response.f*A1.21.f=2,1 0.6359914 0.09334072
#> A0.f=2, response.f*A1.21.f=1,1 0.3008284 0.06070542
#> A0.f=2, response.f*A1.21.f=2,1 0.3281989 0.09349507
#>
#> 1st and 2nd Randomization Augmentation :
#> coef
#> A0.f=1, response.f*A1.21.f=1,1 0.6337891 0.11081838
#> A0.f=1, response.f*A1.21.f=2,1 0.6661916 0.10467515
#> A0.f=2, response.f*A1.21.f=1,1 0.2984575 0.05975394
#> A0.f=2, response.f*A1.21.f=2,1 0.3290272 0.09244601sessionInfo()
#> R version 4.3.2 (2023-10-31)
#> Platform: aarch64-apple-darwin22.6.0 (64-bit)
#> Running under: macOS Sonoma 14.3.1
#>
#> Matrix products: default
#> BLAS: /Users/kkzh/.asdf/installs/R/4.3.2/lib/R/lib/libRblas.dylib
#> LAPACK: /Users/kkzh/.asdf/installs/R/4.3.2/lib/R/lib/libRlapack.dylib; LAPACK version 3.11.0
#>
#> locale:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#>
#> time zone: Europe/Copenhagen
#> tzcode source: internal
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] mets_1.3.4 timereg_2.0.5 survival_3.5-7
#>
#> loaded via a namespace (and not attached):
#> [1] cli_3.6.2 knitr_1.45 rlang_1.1.3
#> [4] xfun_0.41 jsonlite_1.8.8 listenv_0.9.1
#> [7] future.apply_1.11.1 lava_1.7.4 htmltools_0.5.6.1
#> [10] sass_0.4.7 rmarkdown_2.25 grid_4.3.2
#> [13] evaluate_0.23 jquerylib_0.1.4 fastmap_1.1.1
#> [16] mvtnorm_1.2-4 yaml_2.3.7 numDeriv_2016.8-1.1
#> [19] compiler_4.3.2 codetools_0.2-19 ucminf_1.2.0
#> [22] Rcpp_1.0.12 future_1.33.1 lattice_0.22-5
#> [25] digest_0.6.34 R6_2.5.1 parallelly_1.37.0
#> [28] parallel_4.3.2 splines_4.3.2 bslib_0.5.1
#> [31] Matrix_1.6-5 tools_4.3.2 globals_0.16.2
#> [34] cachem_1.0.8