Doubly-robust pseudo-outcome regression
Source:R/DR_pseudo_outcome_regression.R
DR_pseudo_outcome_regression.RdGenerate estimates of conditional survival probability or conditional restrcited mean survival time using doubly-robust pseudo-outcome regression with SuperLearner
Usage
DR_pseudo_outcome_regression(
time,
event,
X,
newX,
approx_times,
S_hat,
G_hat,
newtimes,
outcome,
SL.library,
V
)Arguments
- time
n x 1numeric vector of observed follow-up times. If there is censoring, these are the minimum of the event and censoring times.- event
n x 1numeric vector of status indicators of whether an event was observed.- X
n x pdata.frame of observed covariate values- newX
m x pdata.frame of new observed covariate values at which to obtainmpredictions for the estimated algorithm. Must have the same names and structure asX.- approx_times
Numeric vector of length J2 giving times at which to approximate integral appearing in the pseudo-outcomes
- S_hat
n x J2matrix of conditional event time survival function estimates- G_hat
n x J2matrix of conditional censoring time survival function estimates- newtimes
Numeric vector of times at which to generate oracle prediction function estimates. For outcome
"survival_probability", this is the times at which the survival function is to be estimated. For outcome"restricted_survival_time", this is simply the restriction time.- outcome
Outcome type, either
"survival_probability"or"restricted_survival_time"- SL.library
Super Learner library
- V
Number of cross-validation folds, to be passed to
SuperLearner
Examples
# This is a small simulation example
set.seed(123)
n <- 250
X <- data.frame(X1 = rnorm(n), X2 = rbinom(n, size = 1, prob = 0.5))
T <- rexp(n, rate = exp(-2 + X[,1] - X[,2] + .5 * X[,1] * X[,2]))
C <- rexp(n, exp(-2 -.5 * X[,1] - .25 * X[,2] + .5 * X[,1] * X[,2]))
C[C > 15] <- 15
time <- pmin(T, C)
event <- as.numeric(T <= C)
# Note that this a very small Super Learner library, for computational purposes.
SL.library <- c("SL.mean", "SL.glm")
approx_times <- c(0, sort(unique(time)))
# estimate conditional survival functions at approx_times
fit <- stackG(time = time,
event = event,
X = X,
newX = X,
newtimes = approx_times,
direction = "prospective",
bin_size = 0.1,
time_basis = "continuous",
surv_form = "PI",
learner = "SuperLearner",
time_grid_approx = approx_times,
SL_control = list(SL.library = SL.library,
V = 3))
# use DR pseudo-outcome regression to (robustly) estimate survival at t = 5
DR_preds <- DR_pseudo_outcome_regression(time = time,
event = event,
X = X,
newX = X,
newtimes = 5,
approx_times = approx_times,
S_hat = fit$S_T_preds,
G_hat = fit$S_C_preds,
outcome = "survival_probability",
SL.library = SL.library,
V = 3)
DR_preds
#> [,1]
#> [1,] 0.717678946
#> [2,] 0.629275538
#> [3,] 0.150485092
#> [4,] 0.548797775
#> [5,] 0.533065643
#> [6,] 0.108636652
#> [7,] 0.668175208
#> [8,] 1.130128400
#> [9,] 0.975372491
#> [10,] 0.686949376
#> [11,] 0.240046974
#> [12,] 0.471365958
#> [13,] 0.684272789
#> [14,] 0.538045226
#> [15,] 0.940307560
#> [16,] 0.089406689
#> [17,] 0.434420822
#> [18,] 1.317897945
#> [19,] 0.379953146
#> [20,] 0.918079525
#> [21,] 0.853469281
#> [22,] 0.626009552
#> [23,] 0.842276470
#> [24,] 0.762754921
#> [25,] 0.958828253
#> [26,] 1.242977085
#> [27,] 0.567306748
#> [28,] 0.526619255
#> [29,] 1.096157456
#> [30,] 0.232088984
#> [31,] 0.677396189
#> [32,] 0.870513268
#> [33,] 0.328091194
#> [34,] 0.556508132
#> [35,] 0.347775202
#> [36,] 0.607225483
#> [37,] 0.419414594
#> [38,] 0.808108686
#> [39,] 0.873428263
#> [40,] 0.669501189
#> [41,] 0.977474627
#> [42,] 0.623317652
#> [43,] 1.130218094
#> [44,] -0.012846040
#> [45,] 0.468230423
#> [46,] 1.092135157
#> [47,] 0.675500191
#> [48,] 0.916437227
#> [49,] 0.582782630
#> [50,] 0.589982660
#> [51,] 0.499869140
#> [52,] 0.575309617
#> [53,] 0.803012346
#> [54,] 0.425235485
#> [55,] 0.851965177
#> [56,] 0.385658930
#> [57,] 1.206057682
#> [58,] 0.635067895
#> [59,] 0.758388931
#> [60,] 0.509872979
#> [61,] 0.466059675
#> [62,] 0.925983697
#> [63,] 0.880720239
#> [64,] 0.840288101
#> [65,] 1.078400206
#> [66,] 0.710299564
#> [67,] 0.447707021
#> [68,] 0.777351746
#> [69,] 0.544695791
#> [70,] 0.242838564
#> [71,] 0.922961347
#> [72,] 1.409580986
#> [73,] 0.522354989
#> [74,] 0.757484821
#> [75,] 0.975681829
#> [76,] 0.517046782
#> [77,] 0.643887880
#> [78,] 0.894390948
#> [79,] 0.743012798
#> [80,] 0.604843053
#> [81,] 0.789995415
#> [82,] 0.688418927
#> [83,] 0.890744338
#> [84,] 0.395203516
#> [85,] 0.850550816
#> [86,] 0.478868610
#> [87,] 0.274103161
#> [88,] 0.675063035
#> [89,] 0.878772891
#> [90,] 0.484062933
#> [91,] 0.525629565
#> [92,] 0.420892193
#> [93,] 0.727642281
#> [94,] 0.735726518
#> [95,] 0.203494209
#> [96,] 0.952196038
#> [97,] 0.206104426
#> [98,] 0.157470068
#> [99,] 0.854622747
#> [100,] 0.842387932
#> [101,] 0.757807550
#> [102,] 0.722783954
#> [103,] 0.633695569
#> [104,] 0.660687992
#> [105,] 0.822367290
#> [106,] 0.803589733
#> [107,] 0.777746713
#> [108,] 1.237958330
#> [109,] 0.669435755
#> [110,] 0.321702199
#> [111,] 0.945528242
#> [112,] 0.404949149
#> [113,] 1.000691085
#> [114,] 0.806409194
#> [115,] 0.652520251
#> [116,] 0.710935301
#> [117,] 0.763254236
#> [118,] 0.963021413
#> [119,] 1.018959253
#> [120,] 0.841774455
#> [121,] 0.760050390
#> [122,] 1.045127201
#> [123,] 0.922834556
#> [124,] 0.636211538
#> [125,] 0.074164478
#> [126,] 0.742161783
#> [127,] 0.504668576
#> [128,] 0.770672173
#> [129,] 0.825107481
#> [130,] 0.586754572
#> [131,] 0.404908055
#> [132,] 0.670694346
#> [133,] 0.556633275
#> [134,] 0.904618318
#> [135,] 1.117215219
#> [136,] 0.264869811
#> [137,] 1.182474547
#> [138,] 0.593493235
#> [139,] 0.280571779
#> [140,] 0.954123253
#> [141,] 0.603707505
#> [142,] 0.861714632
#> [143,] 1.212318314
#> [144,] 0.973065855
#> [145,] 0.996315979
#> [146,] 0.933633878
#> [147,] 1.182773111
#> [148,] 0.383550092
#> [149,] 0.005580680
#> [150,] 1.136008409
#> [151,] 0.580702013
#> [152,] 0.585706109
#> [153,] 0.478756034
#> [154,] 1.061427455
#> [155,] 0.823509351
#> [156,] 0.866585237
#> [157,] 0.640855558
#> [158,] 0.667351381
#> [159,] 0.530053900
#> [160,] 0.667924708
#> [161,] 0.509782808
#> [162,] 1.072347571
#> [163,] 0.904946297
#> [164,] -0.075917386
#> [165,] 0.679239961
#> [166,] 0.487849347
#> [167,] 0.621162033
#> [168,] 0.697151731
#> [169,] 0.653201456
#> [170,] 0.468916798
#> [171,] 0.625315165
#> [172,] 0.774062680
#> [173,] 0.576787164
#> [174,] -0.002005237
#> [175,] 0.766085756
#> [176,] 1.084878619
#> [177,] 0.781424221
#> [178,] 0.484569823
#> [179,] 0.450834827
#> [180,] 0.690349397
#> [181,] 1.076134547
#> [182,] 0.453450089
#> [183,] 0.885121164
#> [184,] 1.023190360
#> [185,] 0.854777771
#> [186,] 0.844311778
#> [187,] 0.494471021
#> [188,] 0.544989448
#> [189,] 0.365848700
#> [190,] 0.701303313
#> [191,] 0.510273448
#> [192,] 0.878439490
#> [193,] 0.766223158
#> [194,] 0.807310736
#> [195,] 0.918501639
#> [196,] 0.256989425
#> [197,] 0.406891064
#> [198,] 0.902568550
#> [199,] 0.731246059
#> [200,] 0.884959693
#> [201,] 0.203032543
#> [202,] 0.216405373
#> [203,] 0.638634512
#> [204,] 0.646153764
#> [205,] 0.678566121
#> [206,] 0.919004377
#> [207,] 1.002605600
#> [208,] 0.726816858
#> [209,] 0.125808238
#> [210,] 0.582129637
#> [211,] 0.759622519
#> [212,] 0.726315903
#> [213,] 0.461669350
#> [214,] 0.929661272
#> [215,] 0.833311009
#> [216,] 0.119173405
#> [217,] 0.685745297
#> [218,] 0.761195806
#> [219,] 1.122423339
#> [220,] 0.911519842
#> [221,] 0.721291604
#> [222,] 0.626135952
#> [223,] 0.494490332
#> [224,] 0.602154075
#> [225,] 0.888870075
#> [226,] 0.775546275
#> [227,] 0.980121521
#> [228,] 0.983499684
#> [229,] 0.554763871
#> [230,] 0.839489761
#> [231,] 0.044340016
#> [232,] 0.815711979
#> [233,] 0.734117447
#> [234,] 0.989203126
#> [235,] 0.721402734
#> [236,] 0.920164960
#> [237,] 0.840497669
#> [238,] 0.679398677
#> [239,] 0.480869975
#> [240,] 0.776845282
#> [241,] 1.002610721
#> [242,] 0.702081284
#> [243,] 0.167252565
#> [244,] 1.095934421
#> [245,] 0.615591830
#> [246,] 0.282376189
#> [247,] 0.818563839
#> [248,] 0.931626841
#> [249,] 0.969461925
#> [250,] 0.661606134