cens.poisson.RdFamily function for a censored Poisson response.
cens.poisson(link = "loglink", imu = NULL,
biglambda = 10, smallno = 1e-10)Link function applied to the mean;
see Links for more choices.
Optional initial value;
see CommonVGAMffArguments for more information.
Used to help robustify the code when lambda is very large
and the ppois value is so close to 0 that
the first derivative is computed to be a NA or NaN.
When this occurs mills.ratio is called.
Often a table of Poisson counts has an entry J+ meaning
\(\ge J\).
This family function is similar to poissonff
but handles such censored data. The input requires
SurvS4. Only a univariate response is allowed.
The Newton-Raphson algorithm is used.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as
vglm and
vgam.
See survival for background.
The function poissonff should be used
when there are no censored observations.
Also, NAs are not permitted with SurvS4,
nor is type = "counting".
As the response is discrete,
care is required with Surv
(the old class because of
setOldClass(c("SurvS4", "Surv"));
see
setOldClass),
especially with
"interval" censored data because of the
(start, end] format.
See the examples below.
The examples have
y < L as left censored and
y >= U (formatted as U+) as right censored observations,
therefore
L <= y < U is for uncensored and/or interval censored
observations.
Consequently the input must be tweaked to conform to the
(start, end] format.
A bit of attention has been directed to try robustify the code
when lambda is very large, however this currently works
for left and right censored data only, not interval
censored data. Sometime the fix involves an approximation,
hence it is a good idea to set trace = TRUE.
# Example 1: right censored data
set.seed(123); U <- 20
cdata <- data.frame(y = rpois(N <- 100, exp(3)))
cdata <- transform(cdata, cy = pmin(U, y),
rcensored = (y >= U))
cdata <- transform(cdata, status = ifelse(rcensored, 0, 1))
with(cdata, table(cy))
#> cy
#> 12 13 14 15 16 17 18 19 20
#> 2 1 6 4 5 9 9 12 52
with(cdata, table(rcensored))
#> rcensored
#> FALSE TRUE
#> 48 52
with(cdata, table(print(SurvS4(cy, status)))) # Check; U+ means >= U
#> time status
#> [1,] 17 1
#> [2,] 20 0
#> [3,] 12 1
#> [4,] 20 0
#> [5,] 20 0
#> [6,] 20 0
#> [7,] 14 1
#> [8,] 12 1
#> [9,] 20 0
#> [10,] 20 0
#> [11,] 20 0
#> [12,] 20 0
#> [13,] 17 1
#> [14,] 20 0
#> [15,] 20 0
#> [16,] 19 1
#> [17,] 16 1
#> [18,] 15 1
#> [19,] 18 1
#> [20,] 15 1
#> [21,] 17 1
#> [22,] 19 1
#> [23,] 14 1
#> [24,] 14 1
#> [25,] 18 1
#> [26,] 14 1
#> [27,] 20 0
#> [28,] 20 0
#> [29,] 20 0
#> [30,] 20 0
#> [31,] 20 0
#> [32,] 19 1
#> [33,] 18 1
#> [34,] 18 1
#> [35,] 16 1
#> [36,] 20 0
#> [37,] 19 1
#> [38,] 20 0
#> [39,] 15 1
#> [40,] 18 1
#> [41,] 17 1
#> [42,] 14 1
#> [43,] 20 0
#> [44,] 19 1
#> [45,] 19 1
#> [46,] 20 0
#> [47,] 19 1
#> [48,] 20 0
#> [49,] 13 1
#> [50,] 15 1
#> [51,] 20 0
#> [52,] 20 0
#> [53,] 17 1
#> [54,] 20 0
#> [55,] 14 1
#> [56,] 20 0
#> [57,] 20 0
#> [58,] 20 0
#> [59,] 20 0
#> [60,] 20 0
#> [61,] 17 1
#> [62,] 16 1
#> [63,] 16 1
#> [64,] 20 0
#> [65,] 20 0
#> [66,] 17 1
#> [67,] 20 0
#> [68,] 19 1
#> [69,] 20 0
#> [70,] 20 0
#> [71,] 18 1
#> [72,] 20 0
#> [73,] 19 1
#> [74,] 20 0
#> [75,] 20 0
#> [76,] 20 0
#> [77,] 18 1
#> [78,] 20 0
#> [79,] 20 0
#> [80,] 20 0
#> [81,] 20 0
#> [82,] 17 1
#> [83,] 20 0
#> [84,] 18 1
#> [85,] 20 0
#> [86,] 19 1
#> [87,] 20 0
#> [88,] 20 0
#> [89,] 20 0
#> [90,] 20 0
#> [91,] 20 0
#> [92,] 17 1
#> [93,] 19 1
#> [94,] 16 1
#> [95,] 20 0
#> [96,] 19 1
#> [97,] 20 0
#> [98,] 20 0
#> [99,] 20 0
#> [100,] 18 1
#> attr(,"type")
#> [1] "right"
#> attr(,"class")
#> [1] "SurvS4"
#>
#> 0 1 12 13 14 15 16 17 18 19 20
#> 0 0 0 0 0 0 0 0 0 0 0
fit <- vglm(SurvS4(cy, status) ~ 1, cens.poisson, data = cdata,
trace = TRUE)
#> Iteration 1: loglikelihood = -164.29209
#> Iteration 2: loglikelihood = -164.17535
#> Iteration 3: loglikelihood = -164.1743
#> Iteration 4: loglikelihood = -164.17429
#> Iteration 5: loglikelihood = -164.17429
coef(fit, matrix = TRUE)
#> loglink(mu)
#> (Intercept) 3.007622
table(print(depvar(fit))) # Another check; U+ means >= U
#> time status
#> 1 17 1
#> 2 20 0
#> 3 12 1
#> 4 20 0
#> 5 20 0
#> 6 20 0
#> 7 14 1
#> 8 12 1
#> 9 20 0
#> 10 20 0
#> 11 20 0
#> 12 20 0
#> 13 17 1
#> 14 20 0
#> 15 20 0
#> 16 19 1
#> 17 16 1
#> 18 15 1
#> 19 18 1
#> 20 15 1
#> 21 17 1
#> 22 19 1
#> 23 14 1
#> 24 14 1
#> 25 18 1
#> 26 14 1
#> 27 20 0
#> 28 20 0
#> 29 20 0
#> 30 20 0
#> 31 20 0
#> 32 19 1
#> 33 18 1
#> 34 18 1
#> 35 16 1
#> 36 20 0
#> 37 19 1
#> 38 20 0
#> 39 15 1
#> 40 18 1
#> 41 17 1
#> 42 14 1
#> 43 20 0
#> 44 19 1
#> 45 19 1
#> 46 20 0
#> 47 19 1
#> 48 20 0
#> 49 13 1
#> 50 15 1
#> 51 20 0
#> 52 20 0
#> 53 17 1
#> 54 20 0
#> 55 14 1
#> 56 20 0
#> 57 20 0
#> 58 20 0
#> 59 20 0
#> 60 20 0
#> 61 17 1
#> 62 16 1
#> 63 16 1
#> 64 20 0
#> 65 20 0
#> 66 17 1
#> 67 20 0
#> 68 19 1
#> 69 20 0
#> 70 20 0
#> 71 18 1
#> 72 20 0
#> 73 19 1
#> 74 20 0
#> 75 20 0
#> 76 20 0
#> 77 18 1
#> 78 20 0
#> 79 20 0
#> 80 20 0
#> 81 20 0
#> 82 17 1
#> 83 20 0
#> 84 18 1
#> 85 20 0
#> 86 19 1
#> 87 20 0
#> 88 20 0
#> 89 20 0
#> 90 20 0
#> 91 20 0
#> 92 17 1
#> 93 19 1
#> 94 16 1
#> 95 20 0
#> 96 19 1
#> 97 20 0
#> 98 20 0
#> 99 20 0
#> 100 18 1
#> attr(,"class")
#> [1] "SurvS4"
#> attr(,"type")
#> [1] "right"
#>
#> 0 1 12 13 14 15 16 17 18 19 20
#> 0 0 0 0 0 0 0 0 0 0 0
# Example 2: left censored data
L <- 15
cdata <- transform(cdata,
cY = pmax(L, y),
lcensored = y < L) # Note y < L, not cY == L or y <= L
cdata <- transform(cdata, status = ifelse(lcensored, 0, 1))
with(cdata, table(cY))
#> cY
#> 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
#> 13 5 9 9 12 8 11 9 4 4 8 3 2 1 2
with(cdata, table(lcensored))
#> lcensored
#> FALSE TRUE
#> 91 9
with(cdata, table(print(SurvS4(cY, status, type = "left")))) # Check
#> time status
#> [1,] 17 1
#> [2,] 25 1
#> [3,] 15 0
#> [4,] 20 1
#> [5,] 27 1
#> [6,] 22 1
#> [7,] 15 0
#> [8,] 15 0
#> [9,] 25 1
#> [10,] 21 1
#> [11,] 21 1
#> [12,] 20 1
#> [13,] 17 1
#> [14,] 25 1
#> [15,] 23 1
#> [16,] 19 1
#> [17,] 16 1
#> [18,] 15 1
#> [19,] 18 1
#> [20,] 15 1
#> [21,] 17 1
#> [22,] 19 1
#> [23,] 15 0
#> [24,] 15 0
#> [25,] 18 1
#> [26,] 15 0
#> [27,] 24 1
#> [28,] 24 1
#> [29,] 23 1
#> [30,] 23 1
#> [31,] 22 1
#> [32,] 19 1
#> [33,] 18 1
#> [34,] 18 1
#> [35,] 16 1
#> [36,] 23 1
#> [37,] 19 1
#> [38,] 25 1
#> [39,] 15 1
#> [40,] 18 1
#> [41,] 17 1
#> [42,] 15 0
#> [43,] 21 1
#> [44,] 19 1
#> [45,] 19 1
#> [46,] 26 1
#> [47,] 19 1
#> [48,] 26 1
#> [49,] 15 0
#> [50,] 15 1
#> [51,] 21 1
#> [52,] 21 1
#> [53,] 17 1
#> [54,] 29 1
#> [55,] 15 0
#> [56,] 21 1
#> [57,] 22 1
#> [58,] 20 1
#> [59,] 24 1
#> [60,] 29 1
#> [61,] 17 1
#> [62,] 16 1
#> [63,] 16 1
#> [64,] 22 1
#> [65,] 20 1
#> [66,] 17 1
#> [67,] 20 1
#> [68,] 19 1
#> [69,] 20 1
#> [70,] 21 1
#> [71,] 18 1
#> [72,] 22 1
#> [73,] 19 1
#> [74,] 21 1
#> [75,] 25 1
#> [76,] 22 1
#> [77,] 18 1
#> [78,] 25 1
#> [79,] 24 1
#> [80,] 22 1
#> [81,] 21 1
#> [82,] 17 1
#> [83,] 25 1
#> [84,] 18 1
#> [85,] 21 1
#> [86,] 19 1
#> [87,] 21 1
#> [88,] 20 1
#> [89,] 28 1
#> [90,] 20 1
#> [91,] 25 1
#> [92,] 17 1
#> [93,] 19 1
#> [94,] 16 1
#> [95,] 22 1
#> [96,] 19 1
#> [97,] 26 1
#> [98,] 27 1
#> [99,] 22 1
#> [100,] 18 1
#> attr(,"type")
#> [1] "left"
#> attr(,"class")
#> [1] "SurvS4"
#>
#> 0 1 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
#> 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
fit <- vglm(SurvS4(cY, status, type = "left") ~ 1, cens.poisson,
data = cdata, trace = TRUE)
#> Iteration 1: loglikelihood = -267.92333
#> Iteration 2: loglikelihood = -267.43783
#> Iteration 3: loglikelihood = -267.43756
#> Iteration 4: loglikelihood = -267.43756
coef(fit, matrix = TRUE)
#> loglink(mu)
#> (Intercept) 2.991431
# Example 3: interval censored data
cdata <- transform(cdata, Lvec = rep(L, len = N),
Uvec = rep(U, len = N))
cdata <-
transform(cdata,
icensored = Lvec <= y & y < Uvec) # Not lcensored or rcensored
with(cdata, table(icensored))
#> icensored
#> FALSE TRUE
#> 61 39
cdata <- transform(cdata, status = rep(3, N)) # 3 == interval censored
cdata <- transform(cdata,
status = ifelse(rcensored, 0, status)) # 0 means right censored
cdata <- transform(cdata,
status = ifelse(lcensored, 2, status)) # 2 means left censored
# Have to adjust Lvec and Uvec because of the (start, end] format:
cdata$Lvec[with(cdata,icensored)] <- cdata$Lvec[with(cdata,icensored)]-1
cdata$Uvec[with(cdata,icensored)] <- cdata$Uvec[with(cdata,icensored)]-1
# Unchanged:
cdata$Lvec[with(cdata, lcensored)] <- cdata$Lvec[with(cdata, lcensored)]
cdata$Lvec[with(cdata, rcensored)] <- cdata$Uvec[with(cdata, rcensored)]
with(cdata, # Check
table(ii <- print(SurvS4(Lvec, Uvec, status, type = "interval"))))
#> time status
#> [1,] 14 19 3
#> [2,] 20 1 0
#> [3,] 15 1 2
#> [4,] 20 1 0
#> [5,] 20 1 0
#> [6,] 20 1 0
#> [7,] 15 1 2
#> [8,] 15 1 2
#> [9,] 20 1 0
#> [10,] 20 1 0
#> [11,] 20 1 0
#> [12,] 20 1 0
#> [13,] 14 19 3
#> [14,] 20 1 0
#> [15,] 20 1 0
#> [16,] 14 19 3
#> [17,] 14 19 3
#> [18,] 14 19 3
#> [19,] 14 19 3
#> [20,] 14 19 3
#> [21,] 14 19 3
#> [22,] 14 19 3
#> [23,] 15 1 2
#> [24,] 15 1 2
#> [25,] 14 19 3
#> [26,] 15 1 2
#> [27,] 20 1 0
#> [28,] 20 1 0
#> [29,] 20 1 0
#> [30,] 20 1 0
#> [31,] 20 1 0
#> [32,] 14 19 3
#> [33,] 14 19 3
#> [34,] 14 19 3
#> [35,] 14 19 3
#> [36,] 20 1 0
#> [37,] 14 19 3
#> [38,] 20 1 0
#> [39,] 14 19 3
#> [40,] 14 19 3
#> [41,] 14 19 3
#> [42,] 15 1 2
#> [43,] 20 1 0
#> [44,] 14 19 3
#> [45,] 14 19 3
#> [46,] 20 1 0
#> [47,] 14 19 3
#> [48,] 20 1 0
#> [49,] 15 1 2
#> [50,] 14 19 3
#> [51,] 20 1 0
#> [52,] 20 1 0
#> [53,] 14 19 3
#> [54,] 20 1 0
#> [55,] 15 1 2
#> [56,] 20 1 0
#> [57,] 20 1 0
#> [58,] 20 1 0
#> [59,] 20 1 0
#> [60,] 20 1 0
#> [61,] 14 19 3
#> [62,] 14 19 3
#> [63,] 14 19 3
#> [64,] 20 1 0
#> [65,] 20 1 0
#> [66,] 14 19 3
#> [67,] 20 1 0
#> [68,] 14 19 3
#> [69,] 20 1 0
#> [70,] 20 1 0
#> [71,] 14 19 3
#> [72,] 20 1 0
#> [73,] 14 19 3
#> [74,] 20 1 0
#> [75,] 20 1 0
#> [76,] 20 1 0
#> [77,] 14 19 3
#> [78,] 20 1 0
#> [79,] 20 1 0
#> [80,] 20 1 0
#> [81,] 20 1 0
#> [82,] 14 19 3
#> [83,] 20 1 0
#> [84,] 14 19 3
#> [85,] 20 1 0
#> [86,] 14 19 3
#> [87,] 20 1 0
#> [88,] 20 1 0
#> [89,] 20 1 0
#> [90,] 20 1 0
#> [91,] 20 1 0
#> [92,] 14 19 3
#> [93,] 14 19 3
#> [94,] 14 19 3
#> [95,] 20 1 0
#> [96,] 14 19 3
#> [97,] 20 1 0
#> [98,] 20 1 0
#> [99,] 20 1 0
#> [100,] 14 19 3
#> attr(,"type")
#> [1] "interval"
#> attr(,"class")
#> [1] "SurvS4"
#>
#> 0 1 2 3 14 15 19 20
#> 0 0 0 0 0 0 0 0
fit <- vglm(SurvS4(Lvec, Uvec, status, type = "interval") ~ 1,
cens.poisson, data = cdata, trace = TRUE)
#> Iteration 1: loglikelihood = -92.864355
#> Iteration 2: loglikelihood = -92.598948
#> Iteration 3: loglikelihood = -92.598882
#> Iteration 4: loglikelihood = -92.598882
coef(fit, matrix = TRUE)
#> loglink(mu)
#> (Intercept) 2.996398
table(print(depvar(fit))) # Another check
#> time status
#> 1 14 19 3
#> 2 20 1 0
#> 3 15 1 2
#> 4 20 1 0
#> 5 20 1 0
#> 6 20 1 0
#> 7 15 1 2
#> 8 15 1 2
#> 9 20 1 0
#> 10 20 1 0
#> 11 20 1 0
#> 12 20 1 0
#> 13 14 19 3
#> 14 20 1 0
#> 15 20 1 0
#> 16 14 19 3
#> 17 14 19 3
#> 18 14 19 3
#> 19 14 19 3
#> 20 14 19 3
#> 21 14 19 3
#> 22 14 19 3
#> 23 15 1 2
#> 24 15 1 2
#> 25 14 19 3
#> 26 15 1 2
#> 27 20 1 0
#> 28 20 1 0
#> 29 20 1 0
#> 30 20 1 0
#> 31 20 1 0
#> 32 14 19 3
#> 33 14 19 3
#> 34 14 19 3
#> 35 14 19 3
#> 36 20 1 0
#> 37 14 19 3
#> 38 20 1 0
#> 39 14 19 3
#> 40 14 19 3
#> 41 14 19 3
#> 42 15 1 2
#> 43 20 1 0
#> 44 14 19 3
#> 45 14 19 3
#> 46 20 1 0
#> 47 14 19 3
#> 48 20 1 0
#> 49 15 1 2
#> 50 14 19 3
#> 51 20 1 0
#> 52 20 1 0
#> 53 14 19 3
#> 54 20 1 0
#> 55 15 1 2
#> 56 20 1 0
#> 57 20 1 0
#> 58 20 1 0
#> 59 20 1 0
#> 60 20 1 0
#> 61 14 19 3
#> 62 14 19 3
#> 63 14 19 3
#> 64 20 1 0
#> 65 20 1 0
#> 66 14 19 3
#> 67 20 1 0
#> 68 14 19 3
#> 69 20 1 0
#> 70 20 1 0
#> 71 14 19 3
#> 72 20 1 0
#> 73 14 19 3
#> 74 20 1 0
#> 75 20 1 0
#> 76 20 1 0
#> 77 14 19 3
#> 78 20 1 0
#> 79 20 1 0
#> 80 20 1 0
#> 81 20 1 0
#> 82 14 19 3
#> 83 20 1 0
#> 84 14 19 3
#> 85 20 1 0
#> 86 14 19 3
#> 87 20 1 0
#> 88 20 1 0
#> 89 20 1 0
#> 90 20 1 0
#> 91 20 1 0
#> 92 14 19 3
#> 93 14 19 3
#> 94 14 19 3
#> 95 20 1 0
#> 96 14 19 3
#> 97 20 1 0
#> 98 20 1 0
#> 99 20 1 0
#> 100 14 19 3
#> attr(,"class")
#> [1] "SurvS4"
#> attr(,"type")
#> [1] "interval"
#>
#> 0 1 2 3 14 15 19 20
#> 0 0 0 0 0 0 0 0
# Example 4: Add in some uncensored observations
index <- (1:N)[with(cdata, icensored)]
index <- head(index, 4)
cdata$status[index] <- 1 # actual or uncensored value
cdata$Lvec[index] <- cdata$y[index]
with(cdata, table(ii <- print(SurvS4(Lvec, Uvec, status,
type = "interval")))) # Check
#> time status
#> [1,] 17 1 1
#> [2,] 20 1 0
#> [3,] 15 1 2
#> [4,] 20 1 0
#> [5,] 20 1 0
#> [6,] 20 1 0
#> [7,] 15 1 2
#> [8,] 15 1 2
#> [9,] 20 1 0
#> [10,] 20 1 0
#> [11,] 20 1 0
#> [12,] 20 1 0
#> [13,] 17 1 1
#> [14,] 20 1 0
#> [15,] 20 1 0
#> [16,] 19 1 1
#> [17,] 16 1 1
#> [18,] 14 19 3
#> [19,] 14 19 3
#> [20,] 14 19 3
#> [21,] 14 19 3
#> [22,] 14 19 3
#> [23,] 15 1 2
#> [24,] 15 1 2
#> [25,] 14 19 3
#> [26,] 15 1 2
#> [27,] 20 1 0
#> [28,] 20 1 0
#> [29,] 20 1 0
#> [30,] 20 1 0
#> [31,] 20 1 0
#> [32,] 14 19 3
#> [33,] 14 19 3
#> [34,] 14 19 3
#> [35,] 14 19 3
#> [36,] 20 1 0
#> [37,] 14 19 3
#> [38,] 20 1 0
#> [39,] 14 19 3
#> [40,] 14 19 3
#> [41,] 14 19 3
#> [42,] 15 1 2
#> [43,] 20 1 0
#> [44,] 14 19 3
#> [45,] 14 19 3
#> [46,] 20 1 0
#> [47,] 14 19 3
#> [48,] 20 1 0
#> [49,] 15 1 2
#> [50,] 14 19 3
#> [51,] 20 1 0
#> [52,] 20 1 0
#> [53,] 14 19 3
#> [54,] 20 1 0
#> [55,] 15 1 2
#> [56,] 20 1 0
#> [57,] 20 1 0
#> [58,] 20 1 0
#> [59,] 20 1 0
#> [60,] 20 1 0
#> [61,] 14 19 3
#> [62,] 14 19 3
#> [63,] 14 19 3
#> [64,] 20 1 0
#> [65,] 20 1 0
#> [66,] 14 19 3
#> [67,] 20 1 0
#> [68,] 14 19 3
#> [69,] 20 1 0
#> [70,] 20 1 0
#> [71,] 14 19 3
#> [72,] 20 1 0
#> [73,] 14 19 3
#> [74,] 20 1 0
#> [75,] 20 1 0
#> [76,] 20 1 0
#> [77,] 14 19 3
#> [78,] 20 1 0
#> [79,] 20 1 0
#> [80,] 20 1 0
#> [81,] 20 1 0
#> [82,] 14 19 3
#> [83,] 20 1 0
#> [84,] 14 19 3
#> [85,] 20 1 0
#> [86,] 14 19 3
#> [87,] 20 1 0
#> [88,] 20 1 0
#> [89,] 20 1 0
#> [90,] 20 1 0
#> [91,] 20 1 0
#> [92,] 14 19 3
#> [93,] 14 19 3
#> [94,] 14 19 3
#> [95,] 20 1 0
#> [96,] 14 19 3
#> [97,] 20 1 0
#> [98,] 20 1 0
#> [99,] 20 1 0
#> [100,] 14 19 3
#> attr(,"type")
#> [1] "interval"
#> attr(,"class")
#> [1] "SurvS4"
#>
#> 0 1 2 3 14 15 16 17 19 20
#> 0 0 0 0 0 0 1 2 1 0
fit <- vglm(SurvS4(Lvec, Uvec, status, type = "interval") ~ 1,
cens.poisson, data = cdata, trace = TRUE, crit = "c")
#> Iteration 1: coefficients = 3.0153027
#> Iteration 2: coefficients = 2.9962444
#> Iteration 3: coefficients = 2.9963726
#> Iteration 4: coefficients = 2.9963736
#> Iteration 5: coefficients = 2.9963736
coef(fit, matrix = TRUE)
#> loglink(mu)
#> (Intercept) 2.996374
table(print(depvar(fit))) # Another check
#> time status
#> 1 17 1 1
#> 2 20 1 0
#> 3 15 1 2
#> 4 20 1 0
#> 5 20 1 0
#> 6 20 1 0
#> 7 15 1 2
#> 8 15 1 2
#> 9 20 1 0
#> 10 20 1 0
#> 11 20 1 0
#> 12 20 1 0
#> 13 17 1 1
#> 14 20 1 0
#> 15 20 1 0
#> 16 19 1 1
#> 17 16 1 1
#> 18 14 19 3
#> 19 14 19 3
#> 20 14 19 3
#> 21 14 19 3
#> 22 14 19 3
#> 23 15 1 2
#> 24 15 1 2
#> 25 14 19 3
#> 26 15 1 2
#> 27 20 1 0
#> 28 20 1 0
#> 29 20 1 0
#> 30 20 1 0
#> 31 20 1 0
#> 32 14 19 3
#> 33 14 19 3
#> 34 14 19 3
#> 35 14 19 3
#> 36 20 1 0
#> 37 14 19 3
#> 38 20 1 0
#> 39 14 19 3
#> 40 14 19 3
#> 41 14 19 3
#> 42 15 1 2
#> 43 20 1 0
#> 44 14 19 3
#> 45 14 19 3
#> 46 20 1 0
#> 47 14 19 3
#> 48 20 1 0
#> 49 15 1 2
#> 50 14 19 3
#> 51 20 1 0
#> 52 20 1 0
#> 53 14 19 3
#> 54 20 1 0
#> 55 15 1 2
#> 56 20 1 0
#> 57 20 1 0
#> 58 20 1 0
#> 59 20 1 0
#> 60 20 1 0
#> 61 14 19 3
#> 62 14 19 3
#> 63 14 19 3
#> 64 20 1 0
#> 65 20 1 0
#> 66 14 19 3
#> 67 20 1 0
#> 68 14 19 3
#> 69 20 1 0
#> 70 20 1 0
#> 71 14 19 3
#> 72 20 1 0
#> 73 14 19 3
#> 74 20 1 0
#> 75 20 1 0
#> 76 20 1 0
#> 77 14 19 3
#> 78 20 1 0
#> 79 20 1 0
#> 80 20 1 0
#> 81 20 1 0
#> 82 14 19 3
#> 83 20 1 0
#> 84 14 19 3
#> 85 20 1 0
#> 86 14 19 3
#> 87 20 1 0
#> 88 20 1 0
#> 89 20 1 0
#> 90 20 1 0
#> 91 20 1 0
#> 92 14 19 3
#> 93 14 19 3
#> 94 14 19 3
#> 95 20 1 0
#> 96 14 19 3
#> 97 20 1 0
#> 98 20 1 0
#> 99 20 1 0
#> 100 14 19 3
#> attr(,"class")
#> [1] "SurvS4"
#> attr(,"type")
#> [1] "interval"
#>
#> 0 1 2 3 14 15 16 17 19 20
#> 0 0 0 0 0 0 1 2 1 0