Package 'survidm' reference manual

Title:	Inference and Prediction in an Illness-Death Model
Description:	Newly developed methods for the estimation of several probabilities in an illness-death model. The package can be used to obtain nonparametric and semiparametric estimates for: transition probabilities, occupation probabilities, cumulative incidence function and the sojourn time distributions. Additionally, it is possible to fit proportional hazards regression models in each transition of the Illness-Death Model. Several auxiliary functions are also provided which can be used for marginal estimation of the survival functions.
Authors:	Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho
Maintainer:	Marta Sestelo <[email protected]>
License:	GPL-3
Version:	1.3.2
Built:	2024-11-07 04:12:45 UTC
Source:	https://github.com/sestelo/survidm

survidm: Inference and Prediction in an Illness-Death Model

Description

Newly developed methods for the estimation of several probabilities in an illness-death model. The package can be used to obtain nonparametric and semiparametric estimates for: transition probabilities, occupation probabilities, cumulative incidence function and the sojourn time distributions. Additionally, it is possible to fit proportional hazards regression models in each transition of the Illness-Death Model. Several auxiliary functions are also provided which can be used for marginal estimation of the survival functions.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

Maintainer: Marta Sestelo, [email protected]

References

Aalen O. O., Johansen S. (1978) An Empirical Transition Matrix for Nonhomogeneous Markov Chains Based on Censored Observations. Scandinavian Journal of Statistics, 5(3), 141–150.

Cao R., Lopez-de Ullibarri I., Janssen P., Veraverbeke N. (2005) Presmoothed kaplan-meier and nelsonaalen estimators. Journal of Nonparametric Statistics, 17, 31–56.

de Una-Alvarez J. and Meira-Machado L. (2015). Nonparametric estimation of transition probabilities in a non-Markov illness-death model: a comparative study. Biometrics, 71, 364–375.

Geskus R.B. (2011). Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. Biometrics, 67, 39–49.

Meira-Machado L. F., de Una-Alvarez J. and Cadarso-Suarez C. (2006). Nonparametric estimation of transition probabilities in a non-Markov illness-death model. Lifetime Data Anal 12(3), 325–344.

Satten G.A. and Datta S. (2002) Marginal estimation for multi-stage models: waiting time distributions and competing risks analyses. Statistics in Medicine, 21, 3–19.

Visualization of objects of class `survIDM` with ggplot2 graphics.

Description

It draws the estimated probabilities.

Usage

## S3 method for class 'survIDM'
autoplot(
  object = object,
  y = NULL,
  trans = "all",
  func = "distribution",
  conf = NULL,
  type = NULL,
  conftype = NULL,
  col = 1:6,
  confcol = 1:6,
  lty = 1,
  conflty = 2,
  xlab = "Time",
  ylab = NULL,
  ylim = NULL,
  xlim = NULL,
  interactive = FALSE,
  ...
)
## S3 method for class 'survIDM'
autoplot(
  object = object,
  y = NULL,
  trans = "all",
  func = "distribution",
  conf = NULL,
  type = NULL,
  conftype = NULL,
  col = 1:6,
  confcol = 1:6,
  lty = 1,
  conflty = 2,
  xlab = "Time",
  ylab = NULL,
  ylim = NULL,
  xlim = NULL,
  interactive = FALSE,
  ...
)

Arguments

`object`	Object of `survIDM` class.
`y`	`NULL`
`trans`	The transition probabilities plotted. It is used only when the object is of class `"AJ"`, `"LIDA"` `"LM"`, `"PLM"`, `"LMAJ"`, `"PLMAJ"`, `"PAJ"` and `"tpIPCW"`. Possible options are `"all"` (default), `"00"`, `"01"`, `"02"`, `"11"` or `"12"`.
`func`	It is used only when the object is of class "soj" or "sojIPCW". The type of curve to be drawn ("distribution" or "survival"). Default to "distribution".
`conf`	Draw the confidence intervals into the plot. By default it is `NULL`, they are drawn if the "surv" object contains them.
`type`	The type of plot that should be drawn. See details `par` for possible options. Defaults to "s" for the draw be stair steps.
`conftype`	The type of plot that should be drawn for confidence intervals. See details `par` for possible options. Defaults to "s" for the draw be stair steps.
`col`	Vector of colors. Colors are used cyclically.
`confcol`	Vector of colors for the confidence intervals. Colors are used cyclically.
`lty`	The line type. Line types can either be specified as an integer (0 = blank, 1 = solid (default), 2 = dashed, 3 = dotted, 4 = dotdash, 5 = longdash, 6 = twodash). See details in `par`.
`conflty`	The line type for confidence intervals. Line types can either be specified as an integer (0 = blank, 1 = solid (default), 2 = dashed, 3 = dotted, 4 = dotdash, 5 = longdash, 6 = twodash).
`xlab`	A title for the `x` axis: see `title`.
`ylab`	A title for the `y` axis: see `title`.
`ylim`	The `y` limits of the plot.
`xlim`	The `x` limits of the plot.
`interactive`	Logical flag indicating if an interactive plot with plotly is produced.
`...`	Other options.

Value

A ggplot object, so you can use common features from ggplot2 package to manipulate the plot.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

Examples

res <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 0,
method = "AJ", conf = FALSE, data = colonIDM)
autoplot(res)
autoplot(res, trans = "02")

  res1 <- tprob(survIDM(time1, event1, Stime, event) ~ factor(sex), s = 365,
                method = "AJ", conf = FALSE, data = colonIDM)

  autoplot(res1, trans="02", ylim=c(0,0.5))


  res2 <- CIF(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM,
              z.value = 56, conf = FALSE)

  autoplot(res2)


  res3 <- sojourn(survIDM(time1, event1, Stime, event) ~ factor(sex),
                  data = colonIDM, conf = FALSE, conf.level = 0.95)

  autoplot(res3)

res <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 0,
method = "AJ", conf = FALSE, data = colonIDM)
autoplot(res)
autoplot(res, trans = "02")

  res1 <- tprob(survIDM(time1, event1, Stime, event) ~ factor(sex), s = 365,
                method = "AJ", conf = FALSE, data = colonIDM)

  autoplot(res1, trans="02", ylim=c(0,0.5))


  res2 <- CIF(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM,
              z.value = 56, conf = FALSE)

  autoplot(res2)


  res3 <- sojourn(survIDM(time1, event1, Stime, event) ~ factor(sex),
                  data = colonIDM, conf = FALSE, conf.level = 0.95)

  autoplot(res3)

Estimation of the conditional distribution function of the response, given the covariate under random censoring.

Description

Computes the conditional survival probability P(T > y|Z = z)

Usage

 Beran(time, status, covariate, delta, x, y, kernel = "gaussian", bw, lower.tail = FALSE)Beran(time, status, covariate, delta, x, y, kernel = "gaussian", bw, lower.tail = FALSE)

Arguments

`time`	The survival time of the process.
`status`	Censoring indicator of the total time of the process; 0 if the total time is censored and 1 otherwise.
`covariate`	Covariate values for obtaining estimates for the conditional probabilities.
`delta`	Censoring indicator of the covariate.
`x`	The first time (or covariate value) for obtaining estimates for the conditional probabilities. If missing, 0 will be used.
`y`	The total time for obtaining estimates for the conditional probabilities.
`kernel`	A character string specifying the desired kernel. See details below for possible options. Defaults to "gaussian" where the gaussian density kernel will be used.
`bw`	A single numeric value to compute a kernel density bandwidth.
`lower.tail`	logical; if FALSE (default), probabilities are P(T > y\|Z = z) otherwise, P(T <= y\|Z = z).

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine".

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho

References

R. Beran. Nonparametric regression with randomly censored survival data. Technical report, University of California, Berkeley, 1981.

Examples

obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
obj0 <- obj

#P(T>y|age=45)
library(KernSmooth)
h <- dpik(colonIDM$age)
Beran(time = obj0$Stime, status = obj0$event, covariate = colonIDM$age,
x = 45, y = 730, bw = h)

#P(T<=y|age=45)
Beran(time = obj0$Stime, status = obj0$event, covariate = colonIDM$age,
x = 45, y = 730, bw = h, lower.tail = TRUE)
obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
obj0 <- obj

#P(T>y|age=45)
library(KernSmooth)
h <- dpik(colonIDM$age)
Beran(time = obj0$Stime, status = obj0$event, covariate = colonIDM$age,
x = 45, y = 730, bw = h)

#P(T<=y|age=45)
Beran(time = obj0$Stime, status = obj0$event, covariate = colonIDM$age,
x = 45, y = 730, bw = h, lower.tail = TRUE)

Bladder Cancer Recurrences.

Description

bladderIDM is a data frame with 8 variables and 85 observations. Data on recurrences of bladder cancer, used by many people to demonstrate methodology for recurrent event modelling.

Usage

data("bladderIDM")data("bladderIDM")

Format

A data frame with 85 observations on the following 8 variables. Below a brief description is given for some of these variables.

t1: Time to first recurrence/censoring, whichever occurs first.
e1: Recurrence/censoring indicator (first recurrence=1) for the first time (t1).
t2: Time to second recurrence/censoring, whichever occurs first.
e2: Recurrence/censoring indicator (second recurrence=1) for the second time (t2)
t3: Time to recurrence/censoring, whichever occurs first.
e3: Recurrence/censoring indicator (third recurrence=1) for the third time (t3)
t4: Time to fourth recurrence/censoring, whichever occurs first.
e4: Recurrence/censoring indicator (fourth recurrence=1) for the fourth time (t4)

References

Byar, D. (1980) Veterans administration study of chemoprophylaxis for recurrent stage i bladder tumors: Comparisons of placebo, pyridoxine and topical thiotepa. Bladder Tumors and Other Topics in Urological Oncology, 18:363–370.

Examples

  data(bladderIDM)
  head(bladderIDM)
data(bladderIDM)
  head(bladderIDM)

Nonparametric estimation of the Cumulative Incident Functions in the illness-death model

Description

This function is used to obtain nonparametric estimates of the cumulative incidence probabilities in the illness-death model. They represent the probability of one individual's being or having been in state j at time t.

Usage

CIF(
  formula,
  s,
  data,
  conf = FALSE,
  n.boot = 199,
  conf.level = 0.95,
  z.value,
  bw = "dpik",
  window = "gaussian",
  method.weights = "NW",
  cluster = FALSE,
  ncores = NULL,
  presmooth = FALSE
)
CIF(
  formula,
  s,
  data,
  conf = FALSE,
  n.boot = 199,
  conf.level = 0.95,
  z.value,
  bw = "dpik",
  window = "gaussian",
  method.weights = "NW",
  cluster = FALSE,
  ncores = NULL,
  presmooth = FALSE
)

Arguments

`formula`	A `formula` object, which must have a `survIDM` object as the response on the left of the `~` operator and, if desired, a term on the right. The term may be a qualitative or quantitative variable. Without covariates, the right hand side should be `~ 1`.
`s`	The first time for obtaining estimates for the cumulative incidence functions. If missing, 0 will be used.
`data`	A data.frame including at least four columns named `time1`, `event1`, `Stime` and `event`, which correspond to disease free survival time, disease free survival indicator, time to death or censoring, and death indicator, respectively.
`conf`	Provides pointwise confidence bands. Defaults to `FALSE`.
`n.boot`	The number of bootstrap replicates to compute the variance of the estimator. Default is 199.
`conf.level`	Level of confidence. Defaults to 0.95 (corresponding to 95%).
`z.value`	The value of the covariate on the right hand side of formula at which the cumulative incidence probabilities are computed. For quantitative covariates, i.e. of class integer and numeric.
`bw`	A single numeric value to compute a kernel density bandwidth. Use `"dpik"` for the KernSmooth package based selector or `"np"` for the `'npudensbw'` function of the np package.
`window`	A character string specifying the desired kernel. See details below for possible options. Defaults to `"gaussian"` where the gaussian density kernel will be used.
`method.weights`	A character string specifying the desired weights method. Possible options are `"NW"` for the Nadaraya-Watson weights and `"LL"` for local linear weights. Defaults to `"NW"`.
`cluster`	A logical value. If `TRUE` (default), the bootstrap procedure for the confidence intervals is parallelized. Note that there are cases (e.g., a low number of bootstrap repetitions) that R will gain in performance through serial computation. R takes time to distribute tasks across the processors also it will need time for binding them all together later on. Therefore, if the time for distributing and gathering pieces together is greater than the time need for single-thread computing, it does not worth parallelize.
`ncores`	An integer value specifying the number of cores to be used in the parallelized procedure. If `NULL` (default), the number of cores to be used is equal to the number of cores of the machine - 1.
`presmooth`	A logical value. If `TRUE`, the presmoothed landmark estimator of the cumulative incidence function is computed.

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine".

Value

An object of class "survIDM" and one of the following two classes: "CIF" (Cumulative Incidence Function), and "cifIPCW" (Inverse Probability of Censoring Weighting for the Cumulative Incidence Function). Objects are implemented as a list with elements:

`est`	data.frame with estimates of the cumulative incidence probabilities.
`CI`	data.frame with the confidence intervals of the cumulative incidence probabilities.
`conf.level`	Level of confidence.
`s`	The first time for obtaining estimates for the cumulative incidence probabilities.
`t`	The time for obtaining the estimates of cumulative incidence probabilities.
`conf`	logical; if `FALSE` (default) the pointwise confidence bands are not given.
`callp`	The expression of the estimated probability.
`Nlevels`	The number of levels of the covariate. Provides important information when the covariate at the right hand side of formula is of class factor.
`levels`	The levels of the qualitative covariate (if it is of class factor) on the right hand side of formula.
`formula`	A formula object.
`call`	A call object.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

Geskus, R.B. (2011). Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. Biometrics, 67, 39–49.

Kalbeisch, J. D. and Prentice R. L. (1980) The statistical analysis of failure time data. John Wiley & Sons, New York.

Examples


# Cumulative Incidence Function (CIF)
res <- CIF(survIDM(time1, event1, Stime, event) ~ 1, data = colonIDM,
conf = FALSE)
res
summary(res, time=365*1:7)
plot(res, ylim=c(0, 0.6))

res01 <- CIF(survIDM(time1, event1, Stime, event) ~ 1, data = colonIDM,
conf = FALSE, presmooth = TRUE)
res01
summary(res01, time=365*1:7)
plot(res01, ylim=c(0, 0.6))


# CIF for those in State 1 at time s=365, Y(s)=0
res1 <- CIF(survIDM(time1, event1, Stime, event) ~ 1, data = colonIDM,
s = 365, conf = FALSE)
summary(res1, time=365*1:7)
plot(res1, ylim=c(0, 0.6))


# Conditional CIF (with a factor)
res2 <- CIF(survIDM(time1, event1, Stime, event) ~ factor(sex),
data = colonIDM, s = 365, conf = FALSE)
summary(res2, time=365*1:5)
plot(res2)

res2.1 <- CIF(survIDM(time1, event1, Stime, event) ~ factor(sex),  #new
data = colonIDM, s = 365, conf = FALSE, presmooth = TRUE)
summary(res2.1, time=365*1:5)
plot(res2.1)


# Conditional CIF (with continuous covariate)
res3 <- CIF(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM,
z.value = 56, conf = FALSE)
summary(res3, time=365*1:6)
plot(res3)

# Cumulative Incidence Function (CIF)
res <- CIF(survIDM(time1, event1, Stime, event) ~ 1, data = colonIDM,
conf = FALSE)
res
summary(res, time=365*1:7)
plot(res, ylim=c(0, 0.6))

res01 <- CIF(survIDM(time1, event1, Stime, event) ~ 1, data = colonIDM,
conf = FALSE, presmooth = TRUE)
res01
summary(res01, time=365*1:7)
plot(res01, ylim=c(0, 0.6))


# CIF for those in State 1 at time s=365, Y(s)=0
res1 <- CIF(survIDM(time1, event1, Stime, event) ~ 1, data = colonIDM,
s = 365, conf = FALSE)
summary(res1, time=365*1:7)
plot(res1, ylim=c(0, 0.6))


# Conditional CIF (with a factor)
res2 <- CIF(survIDM(time1, event1, Stime, event) ~ factor(sex),
data = colonIDM, s = 365, conf = FALSE)
summary(res2, time=365*1:5)
plot(res2)

res2.1 <- CIF(survIDM(time1, event1, Stime, event) ~ factor(sex),  #new
data = colonIDM, s = 365, conf = FALSE, presmooth = TRUE)
summary(res2.1, time=365*1:5)
plot(res2.1)


# Conditional CIF (with continuous covariate)
res3 <- CIF(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM,
z.value = 56, conf = FALSE)
summary(res3, time=365*1:6)
plot(res3)

Chemotherapy for Stage B/C colon cancer.

Description

These are data from one of the first successful trials of adjuvant chemotherapy for colon cancer. Levamisole is a low-toxicity compound previously used to treat worm infestations in animals; 5-FU is a moderately toxic (as these things go) chemotherapy agent.

Usage

data("colonIDM")data("colonIDM")

Format

A data frame with 929 observations on the following 15 variables. Below a brief description is given for some of these variables.

time1: Time to recurrence/censoring/death, whichever occurs first.
event1: Recurrence/censoring indicator (recurrence=1, alive=0).
Stime: Time to censoring/death, whichever occurs first.
event: Death/censoring indicator (death=1, alive=0).
rx: Treatment - Obs(ervation), Lev(amisole), Lev(amisole)+5-FU.
sex: Sex indicator (male=1, female=0).
age: Age in years.
obstruct: Obstruction of colon by tumour.
perfor: Perforation of colon.
adhere: Adherence to nearby organs.
nodes: Number of lymph nodes with detectable cancer.
differ: Differentiation of tumour (1=well, 2=moderate, 3=poor).
extent: Extent of local spread (1=submucosa, 2=muscle, 3=serosa, 4=contiguous structures).
surg: Time from surgery to registration (0=short, 1=long).
node4: More than 4 positive lymph nodes.

Source

The study is originally described in Laurie (1989).The main report is found in Moertel (1990). This data set is closest to that of the final report in Moertel (1991). A version of the data with less follow-up time was used in the paper by Lin (1994).

References

JA Laurie, CG Moertel, TR Fleming, HS Wieand, JE Leigh, J Rubin, GW McCormack, JB Gerstner, JE Krook and J Malliard. Surgical adjuvant therapy of large-bowel carcinoma: An evaluation of levamisole and the combination of levamisole and fluorouracil: The North Central Cancer Treatment Group and the Mayo Clinic. Journal of Clinical Oncology, 7:1447-1456, 1989.

DY Lin. Cox regression analysis of multivariate failure time data: the marginal approach. Statistics in Medicine, 13:2233-2247, 1994.

CG Moertel, TR Fleming, JS MacDonald, DG Haller, JA Laurie, PJ Goodman, JS Ungerleider, WA Emerson, DC Tormey, JH Glick, MH Veeder and JA Maillard. Levamisole and fluorouracil for adjuvant therapy of resected colon carcinoma. New England Journal of Medicine, 332:352-358, 1990.

CG Moertel, TR Fleming, JS MacDonald, DG Haller, JA Laurie, CM Tangen, JS Ungerleider, WA Emerson, DC Tormey, JH Glick, MH Veeder and JA Maillard. Fluorouracil plus Levamisole as and effective adjuvant therapy after resection of stage II colon carcinoma: a final report. Annals of Internal Medicine, 122:321-326, 1991.

Examples

data(colonIDM)
head(colonIDM)
data(colonIDM)
head(colonIDM)

Fit proportional hazards regression model in each transition of the Illness-Death Model.

Description

Fits a Cox proportional hazards regression model for each transition.

Usage

coxidm(formula, data, semiMarkov = FALSE)
coxidm(formula, data, semiMarkov = FALSE)

Arguments

`formula`	A `formula` object, which must have a `survIDM` object as the response on the left of the `~` operator and, if desired, a term on the right. The term may be a qualitative or quantitative variable. Without covariates, the right hand side should be `~ 1`.
`data`	A data.frame including at least four columns named `time1`, `event1`, `Stime` and `event`, which correspond to disease free survival time, disease free survival indicator, time to death or censoring, and death indicator, respectively.
`semiMarkov`	By default, `FALSE`.

Value

A data frame or a list containing the following components:

`coef`	Estimated coeficients.
`exp(coef)`	Exponent of the estimated coefficients.
`lower 0.95`	Lower limit of the confidence interval.
`upper 0.95`	Upper limit of the confidence interval.
`pvalue`	obtained pvalue testing that the coefficient is equals to zero.

Other data frames or lists:

`anova`	Analysis of Deviance for the Cox Regression models.
`zph`	Test the Proportional Hazards Assumption of the Cox Regression models.
`term`	Predicted values of splines and partial residual for the terms of the model.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

Examples

  cmm1 <- coxidm(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM)
  summary(cmm1, conf.level = 0.95)

  cmm2 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age + nodes,
                 data = colonIDM)
  summary(cmm2)

  cmm3 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age + nodes,
                 data = colonIDM, semiMarkov = TRUE)
  summary(cmm3)
cmm1 <- coxidm(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM)
  summary(cmm1, conf.level = 0.95)

  cmm2 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age + nodes,
                 data = colonIDM)
  summary(cmm2)

  cmm3 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age + nodes,
                 data = colonIDM, semiMarkov = TRUE)
  summary(cmm3)

Kaplan-Meier product-limit estimate of survival

Description

This function provides survival estimates using the product-limit Kaplan-Meier estimator.

Usage

KM(time, status, t)
KM(time, status, t)

Arguments

`time`	Survival time of the process.
`status`	Censoring indicator of the survival time of the process; 0 if the survival time is censored and 1 otherwise.
`t`	The time for obtaining survival estimates.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

E. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457-481, 1958.

Examples

require(survival)
obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
KM(time = obj$Stime, status = obj$event, t = 1095)

fit <- survfit(Surv(obj$Stime, obj$event) ~ 1, data = obj)
summary(fit, time = 1095)$surv

require(survival)
obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
KM(time = obj$Stime, status = obj$event, t = 1095)

fit <- survfit(Surv(obj$Stime, obj$event) ~ 1, data = obj)
summary(fit, time = 1095)$surv

Kaplan-Meier weights

Description

This function returns a vector with the Kaplan-Meier weights.

Usage

KMW(time, status)
KMW(time, status)

Arguments

`time`	Survival time of the process.
`status`	Censoring indicator of the survival time of the process; 0 if the survival time is censored and 1 otherwise.

Value

Vector with Kaplan-Meier weights.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

E. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457-481, 1958.

Examples

obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
kmw <- KMW(time = obj$Stime, status = obj$event)

require(survival)
colon.surv <- survfit(Surv(Stime, event) ~ 1, obj)
times <- summary(colon.surv)$time
surv <- summary(colon.surv)$surv
nevent <- summary(colon.surv)$n.event
p <- match(obj$Stime, times)
kmw2 <- -diff(c(1, surv))/nevent
kmw2 <- kmw2[p]*obj$event
kmw2[is.na(kmw2)] <- 0
all.equal(kmw, kmw2)

obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
kmw <- KMW(time = obj$Stime, status = obj$event)

require(survival)
colon.surv <- survfit(Surv(Stime, event) ~ 1, obj)
times <- summary(colon.surv)$time
surv <- summary(colon.surv)$surv
nevent <- summary(colon.surv)$n.event
p <- match(obj$Stime, times)
kmw2 <- -diff(c(1, surv))/nevent
kmw2 <- kmw2[p]*obj$event
kmw2[is.na(kmw2)] <- 0
all.equal(kmw, kmw2)

Local linear weights

Description

Computes local linear weights based on Kernel smoothing.

Usage

LLW(x, kernel = "gaussian", bw, t1)
LLW(x, kernel = "gaussian", bw, t1)

Arguments

`x`	Covariate values for obtaining estimates for the conditional probabilities. If missing, unconditioned probabilities will be computed.
`kernel`	A character string specifying the desired kernel. See details below for possible options. Defaults to "gaussian" where the gaussian density kernel will be used.
`bw`	A single numeric value to compute a kernel density bandwidth.
`t1`	Covariate value to compute the weight at.

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine".

Value

A vector with local linear weights.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

Examples

LLW(x = colonIDM$age, bw = 3, t1 = 60)
LLW(x = colonIDM$age, bw = 3, t1 = 60)

This function is used to test the markov assumption in the illness-death model.

Description

The markov assumption may be tested including the sojourn time in the initial state, "times1", and other covariates in the Cox model.

Usage

markov.test(formula, s, nm.method = "LM", data)markov.test(formula, s, nm.method = "LM", data)

Arguments

`formula`	A `formula` object, which must have a `survIDM`.
`s`	The first time for obtaining a graphical test of markovianity by comparison of the estimates for transition probabilities. If missing, first quartile of the sojourn time in the initial state has been considered for the graphical test.
`nm.method`	The non-markov method used to compute the transition probabilities. Defaults to `"LM"`.
`data`	A data.frame including at least four columns named `time1`, `event1`, `Stime` and `event`, which correspond to disease free survival time, disease free survival indicator, time to death or censoring, and death indicator, respectively.

Details

The markov assumption may be tested including the sojourn time in the initial state, "times1", and other covariates in the Cox model. A graphical test for Markovianity is also available.

Value

`cox.markov.test`	An object of class `coxph` representing the fit. See `coxph.object` for details.
`TPestimates`	Dataframe with estimates of the transition probabilities for Aalen-Johansen estimator (markovian) and for non-markov estimator. Confidence intervals for the transition probability from State 1 to State 2 are also available.
`nm.method`	The non-markov method used to compute the transition probabilities.
`s`	The first time for obtaining a graphical test of markovianity by comparison of the estimates for transition probabilities.
`call`	A call object.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

L. Meira-Machado, J. de Una-Alvarez, C. Cadarso-Suarez, and P. Andersen. Multi-state models for the analysis of time to event data. Statistical Methods in Medical Research, 18:195-222, 2009.

J. de Una-Alvarez and L. Meira-Machado. Nonparametric estimation of transition probabilities in the non-markov illness-death model: A comparative study. Biometrics, 71(2):364-375, 2015.

L. Meira-Machado and M. Sestelo. Estimation in the progressive illness-death model: A nonexhaustive review. Biometrical Journal, 2018.

Examples


mk <- markov.test(survIDM(time1,event1,Stime,event)~1, s=365, nm.method = "LM", data=colonIDM)
mk$cox.markov.test
mk$TPestimates
mk$nm.method
plot(mk)

mk <- markov.test(survIDM(time1,event1,Stime,event)~1, s=365, nm.method = "LM", data=colonIDM)
mk$cox.markov.test
mk$TPestimates
mk$nm.method
plot(mk)

Count number of observed transitions.

Description

Given a dataset of class "survIDM", this function counts the number of observed transitions in the multi-state model.

Usage

nevents(dataidm, state.names=NULL)nevents(dataidm, state.names=NULL)

Arguments

`dataidm`	A dataframe including at least four columns named `time1`, `event1`, `Stime` and `event`, which correspond to disease free survival time, disease free survival indicator, time to death or censoring, and death indicator, respectively.
`state.names`	Names for the transition states. If `NULL` (default), transition states are named by `"healthy"`, `"illness"` and `"death"`.

Details

The colums of the dataset needs to have the format of class "survIDM", which holds the transition matrix of the multi-state model. The arguments time1 and Stime must be numeric and nonnegative; event1 and event must be 0 or 1 if numeric and TRUE or FALSE if logical. Stime must be greater or equal to argument arguments time1. Stime and time1 must be equal when argument event1 equals 0 or FALSE. Argument event must be equal to 0 or FALSE when argument event1 equals 0 or FALSE. When arguments Stime and time1 are equal and argument event1 equals 1 or TRUE, argument event must be equal to 1 or TRUE.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

L. Meira-Machado, J. de Una-Alvarez, C. Cadarso-Suarez, and P. Andersen. Multi-state models for the analysis of time to event data. Statistical Methods in Medical Research, 18:195-222, 2009.

J. de Una-Alvarez and L. Meira-Machado. Nonparametric estimation of transition probabilities in the non-markov illness-death model: A comparative study. Biometrics, 71(2):364-375, 2015.

L. Meira-Machado and M. Sestelo. Estimation in the progressive illness-death model: A nonexhaustive review. Biometrical Journal, 2018.

Examples


nevents(colonIDM)

nevents(colonIDM, c('State0','State1', 'State2'))

nevents(colonIDM)

nevents(colonIDM, c('State0','State1', 'State2'))

Nadaraya-Watson weights.

Description

Computes the Nadaraya-Watson weights.

Usage

NWW(covariate, x, kernel = "gaussian", bw)
NWW(covariate, x, kernel = "gaussian", bw)

Arguments

`covariate`	Covariate values for obtaining weights.
`x`	Covariate value to compute the weight at.
`kernel`	A character string specifying the desired kernel. See details below for possible options. Defaults to "gaussian" where the gaussian density kernel will be used.
`bw`	A single numeric value to compute a kernel density bandwidth.

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine".

Value

A vector with Nadaraya-Watson weights.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

Examples

NWW(covariate = colonIDM$age, x=40, kernel = "gaussian", bw = 3)
NWW(covariate = colonIDM$age, x=40, kernel = "gaussian", bw = 3)

Presmoothed Kaplan-Meier product-limit estimate of survival

Description

This function provides survival estimates using the presmoothed product-limit Kaplan-Meier estimator.

Usage

PKM(time, status, t)
PKM(time, status, t)

Arguments

`time`	Survival time of the process.
`status`	Censoring indicator of the survival time of the process; 0 if the survival time is censored and 1 otherwise.
`t`	The time for obtaining survival estimates.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

R. Cao, I. Lopez-de Ullibarri, P. Janssen, and N. Veraverbeke. Presmoothed kaplan-meier and nelsonaalen estimators. Journal of Nonparametric Statistics, 17:31-56, 2005.

G. Dikta. On semiparametric random censorship models. Journal of Statistical Planning and Inference, 66:253-279, 1998.

E. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457-481, 1958.

Examples

obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
PKM(time = obj$Stime, status = obj$event, t = 1095)
obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
PKM(time = obj$Stime, status = obj$event, t = 1095)

Presmoothed Kaplan-Meier weights

Description

This function returns a vector with the presmoothed Kaplan-Meier weights.

Usage

PKMW(time, status)
PKMW(time, status)

Arguments

`time`	Survival time of the process.
`status`	Censoring indicator of the survival time of the process; 0 if the survival time is censored and 1 otherwise.

Value

Vector with presmoothed Kaplan-Meier weights.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

R. Cao, I. Lopez-de Ullibarri, P. Janssen, and N. Veraverbeke. Presmoothed kaplan-meier and nelsonaalen estimators. Journal of Nonparametric Statistics, 17:31-56, 2005.

G. Dikta. On semiparametric random censorship models. Journal of Statistical Planning and Inference, 66:253-279, 1998.

E. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457-481, 1958.

Examples

obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
PKMW(time = obj$Stime, status = obj$event)
obj <- with(colonIDM, survIDM(time1, event1, Stime, event))
PKMW(time = obj$Stime, status = obj$event)

Plot for an object of class "survIDM".

Description

It draws the estimated probabilities.

Usage

## S3 method for class 'survIDM'
plot(x = object, y = NULL, trans = "all",
func = "distribution", conf = NULL,
type = NULL, conftype = NULL, col = 1:6, confcol = 1:6, lty = 1, conflty = 2,
xlab = "Time (years)", ylab = NULL, ylim = NULL, xlim = NULL, ...)
## S3 method for class 'survIDM'
plot(x = object, y = NULL, trans = "all",
func = "distribution", conf = NULL,
type = NULL, conftype = NULL, col = 1:6, confcol = 1:6, lty = 1, conflty = 2,
xlab = "Time (years)", ylab = NULL, ylim = NULL, xlim = NULL, ...)

Arguments

`x`	An object of class "survIDM".
`y`	`NULL`
`trans`	The transition probabilities plotted. It is used only when the object is of class `"AJ"`, `"LIDA"` `"LM"`, `"PLM"`, `"LMAJ"`, `"PLMAJ"`, `"PAJ"` and `"tpIPCW"`. Possible options are `"all"` (default), `"00"`, `"01"`, `"02"`, `"11"` or `"12"`.
`func`	It is used only when the object is of class "soj" or "sojIPCW". The type of curve to be drawn ("distribution" or "survival"). Default to "distribution".
`conf`	Draw the confidence intervals into the plot. By default it is `NULL`, they are drawn if the "surv" object contains them.
`type`	The type of plot that should be drawn. See details `par` for possible options. Defaults to "s" for the draw be stair steps.
`conftype`	The type of plot that should be drawn for confidence intervals. See details `par` for possible options. Defaults to "s" for the draw be stair steps.
`col`	Vector of colors. Colors are used cyclically.
`confcol`	Vector of colors for the confidence intervals. Colors are used cyclically.
`lty`	The line type. Line types can either be specified as an integer (0 = blank, 1 = solid (default), 2 = dashed, 3 = dotted, 4 = dotdash, 5 = longdash, 6 = twodash). See details in `par`.
`conflty`	The line type for confidence intervals. Line types can either be specified as an integer (0 = blank, 1 = solid (default), 2 = dashed, 3 = dotted, 4 = dotdash, 5 = longdash, 6 = twodash).
`xlab`	A title for the `x` axis: see `title`.
`ylab`	A title for the `y` axis: see `title`.
`ylim`	The `y` limits of the plot.
`xlim`	The `x` limits of the plot.
`...`	Other options.

Value

No value is returned.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

Examples

res <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 0,
method = "AJ", conf = FALSE, data = colonIDM)

plot(res)
plot(res, trans = "02")


res1 <- tprob(survIDM(time1, event1, Stime, event) ~ factor(sex), s = 365,
method = "AJ", conf = FALSE, data = colonIDM)

plot(res1, trans="02", ylim=c(0,0.5))


res2 <- CIF(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM,
z.value = 56, conf = FALSE)

plot(res2)


res3 <- sojourn(survIDM(time1, event1, Stime, event) ~ factor(sex),
data = colonIDM, conf = FALSE, conf.level = 0.95)

plot(res3)

res <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 0,
method = "AJ", conf = FALSE, data = colonIDM)

plot(res)
plot(res, trans = "02")


res1 <- tprob(survIDM(time1, event1, Stime, event) ~ factor(sex), s = 365,
method = "AJ", conf = FALSE, data = colonIDM)

plot(res1, trans="02", ylim=c(0,0.5))


res2 <- CIF(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM,
z.value = 56, conf = FALSE)

plot(res2)


res3 <- sojourn(survIDM(time1, event1, Stime, event) ~ factor(sex),
data = colonIDM, conf = FALSE, conf.level = 0.95)

plot(res3)

Nonparametric estimation of the Sojourn time distributions in the recurrence state in the illness-death model

Description

This function is used to obtain nonparametric estimates of of the sojourn probabilities in the recurrence state in the illness-death model.

Usage

sojourn(
  formula,
  data,
  conf = FALSE,
  n.boot = 199,
  conf.level = 0.95,
  z.value,
  bw = "dpik",
  window = "gaussian",
  method.weights = "NW",
  method = "LM",
  presmooth = FALSE,
  cluster = FALSE,
  ncores = NULL
)
sojourn(
  formula,
  data,
  conf = FALSE,
  n.boot = 199,
  conf.level = 0.95,
  z.value,
  bw = "dpik",
  window = "gaussian",
  method.weights = "NW",
  method = "LM",
  presmooth = FALSE,
  cluster = FALSE,
  ncores = NULL
)

Arguments

`formula`	A `formula` object, which must have a `survIDM` object as the response on the left of the `~` operator and, if desired, a term on the right. The term may be a qualitative or quantitative variable. Without covariates, the right hand side should be `~ 1`.
`data`	A data.frame including at least four columns named `time1`, `event1`, `Stime` and `event`, which correspond to disease free survival time, disease free survival indicator, time to death or censoring, and death indicator, respectively.
`conf`	Provides pointwise confidence bands. Defaults to `FALSE`.
`n.boot`	The number of bootstrap replicates to compute the variance of the non-Markovian estimator. Default is 199.
`conf.level`	Level of confidence. Defaults to 0.95 (corresponding to 95%).
`z.value`	The value of the covariate on the right hand side of formula at which the sojourn probabilities are computed. For quantitative covariates, i.e. of class integer and numeric.
`bw`	A single numeric value to compute a kernel density bandwidth. Use `"dpik"` for the KernSmooth package based selector or `"np"` for the `'npudensbw'` function of the np package.
`window`	A character string specifying the desired kernel. See details below for possible options. Defaults to `"gaussian"` where the gaussian density kernel will be used.
`method.weights`	A character string specifying the desired weights method. Possible options are `"NW"` for the Nadaraya-Watson weights and `"LL"` for local linear weights. Defaults to `"NW"`.
`method`	The method used to compute the sojourn estimates. Possible options are `"LM"` and `"Satten-Datta"`. Defaults to `"LM"`.
`presmooth`	- A logical value. If `TRUE`, the presmoothed landmark estimator of the sojourn function is computed. Only valid for `method = "LM"`.
`cluster`	A logical value. If `TRUE` (default), the bootstrap procedure for the confidence intervals is parallelized. Note that there are cases (e.g., a low number of bootstrap repetitions) that R will gain in performance through serial computation. R takes time to distribute tasks across the processors also it will need time for binding them all together later on. Therefore, if the time for distributing and gathering pieces together is greater than the time need for single-thread computing, it does not worth parallelize.
`ncores`	An integer value specifying the number of cores to be used in the parallelized procedure. If `NULL` (default), the number of cores to be used is equal to the number of cores of the machine - 1. #'

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine".

Value

An object of class "survIDM" and one of the following two classes: "soj" (Sojourn Time Distribution), and "sojIPCW" (Inverse Probability of Censoring Weighting for the Sojourn Time Distribution). Objects are implemented as a list with elements:

`est`	data.frame with estimates of the sojourn probabilities.
`CI`	data.frame with the confidence intervals of the sojourn probabilities.
`conf.level`	Level of confidence.
`t`	The time for obtaining the estimates of sojourn probabilities.
`conf`	logical; if `FALSE` (default) the pointwise confidence bands are not given.
`callp`	The expression of the estimated probability.
`Nlevels`	The number of levels of the covariate. Provides important information when the covariate at the right hand side of formula is of class factor.
`levels`	The levels of the qualitative covariate (if it is of class factor) on the right hand side of formula.
`formula`	A formula object.
`call`	A call object.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

Satten, G.A. and Datta, S. (2002) Marginal estimation for multi-stage models: waiting time distributions and competing risks analyses. Statistics in Medicine, 21, 3–19.

Examples


res <- sojourn(survIDM(time1, event1, Stime, event) ~ 1,
data = colonIDM, conf = FALSE, conf.level = 0.95)
res
summary(res, time=365*1:6)
plot(res)

res1 <- sojourn(survIDM(time1, event1, Stime, event) ~ 1,
data = colonIDM, conf = FALSE, conf.level = 0.95, method = "LM",
presmooth = TRUE)
res1
summary(res1, time=365*1:6)
plot(res1)


# not run:
#res2 <- sojourn(survIDM(time1, event1, Stime, event) ~ 1,
#data = colonIDM, conf = FALSE, conf.level = 0.95, method = "Satten-Datta")
#res2


# with a factor
res3 <- sojourn(survIDM(time1, event1, Stime, event) ~ factor(sex),
data = colonIDM, conf = FALSE, conf.level = 0.95)
res3
summary(res3, time=365*1:6)
plot(res3)

# with a qualitative covariate
res4 <- sojourn(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM,
z.value = 56, conf = FALSE, conf.level = 0.95)
res4
summary(res4, time=365*1:6)
plot(res4)

res <- sojourn(survIDM(time1, event1, Stime, event) ~ 1,
data = colonIDM, conf = FALSE, conf.level = 0.95)
res
summary(res, time=365*1:6)
plot(res)

res1 <- sojourn(survIDM(time1, event1, Stime, event) ~ 1,
data = colonIDM, conf = FALSE, conf.level = 0.95, method = "LM",
presmooth = TRUE)
res1
summary(res1, time=365*1:6)
plot(res1)


# not run:
#res2 <- sojourn(survIDM(time1, event1, Stime, event) ~ 1,
#data = colonIDM, conf = FALSE, conf.level = 0.95, method = "Satten-Datta")
#res2


# with a factor
res3 <- sojourn(survIDM(time1, event1, Stime, event) ~ factor(sex),
data = colonIDM, conf = FALSE, conf.level = 0.95)
res3
summary(res3, time=365*1:6)
plot(res3)

# with a qualitative covariate
res4 <- sojourn(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM,
z.value = 56, conf = FALSE, conf.level = 0.95)
res4
summary(res4, time=365*1:6)
plot(res4)

Summarizing fits of `cmm` class

Description

Produces a summary of a fitted coxidm model (proportional hazards regression model in each transition of the Illness-Death Model.

Usage

  ## S3 method for class 'cmm'
summary(object, type=NULL, conf.level = 0.95, ...)
## S3 method for class 'cmm'
summary(object, type=NULL, conf.level = 0.95, ...)

Arguments

`object`	A fitted `cmm` object as produced by `coxidm()`.
`type`	Type of summary of the Cox model. Default value is `"NULL"` that produces a summary of a fitted coxidm model. Possible choices are `"anova"` and `"ph"`. The `"anova"` option provides the Analysis of Deviance of the regression model. The `"ph"` option computes the tests of the proportional hazards assumption of the Cox Regression models.
`conf.level`	Level for computation of the confidence intervals. If set to `FALSE` no confidence intervals are printed.
`...`	Other options.

Value

A data frame or a list containing the following components:

`coef`	Estimated coeficients.
`exp(coef)`	Exponent of the estimated coefficients.
`lower 0.95`	Lower limit of the confidence interval.
`upper 0.95`	Upper limit of the confidence interval.
`pvalue`	obtained pvalue testing that the coefficient is equals to zero.

Other data frames with the Analysis of Deviance or the tests of the Proportional Hazards Assumption of the Cox Regression models.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

Examples


  cmm1 <- coxidm(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM)
  summary(cmm1, conf.level = 0.95)

  cmm2 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age + nodes,
                 data = colonIDM)
  summary(cmm2)

  summary(cmm2,type = 'anova')

  cmm3 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age + nodes,
                 data = colonIDM, semiMarkov = TRUE)
  summary(cmm3)

  cmm4 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age +
                pspline(nodes) + surg + adhere, data = colonIDM)

  summary(cmm4, type = 'ph')
  
cmm1 <- coxidm(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM)
  summary(cmm1, conf.level = 0.95)

  cmm2 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age + nodes,
                 data = colonIDM)
  summary(cmm2)

  summary(cmm2,type = 'anova')

  cmm3 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age + nodes,
                 data = colonIDM, semiMarkov = TRUE)
  summary(cmm3)

  cmm4 <- coxidm(survIDM(time1, event1, Stime, event) ~ rx + sex + age +
                pspline(nodes) + surg + adhere, data = colonIDM)

  summary(cmm4, type = 'ph')

Summarizing fits of `survIDM` class

Description

Returns a a data.frame or list containing the estimates of the probabilities, its confidence limits and other information.

Usage

  ## S3 method for class 'survIDM'
summary(object, times = NULL, ...)
## S3 method for class 'survIDM'
summary(object, times = NULL, ...)

Arguments

`object`	A fitted `survIDM` object as produced by `tprob()`, `CIF()` or `sojourn()`.
`times`	Vector of times; the returned data frame will contain 1 row for each time. Missing values are not allowed.
`...`	For future methods.

Value

A data frame or a list containing the following components:

`y`	The total time for obtaining the estimates of the probabilities.
`est`	Estimates of the probability.
`lower 95% CI`	The lower probabilities of the interval.
`upper 95% CI`	The upper probabilities of the interval.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

Examples

fit <- tprob(survIDM(time1,event1,Stime, event) ~ 1, s = 365,
method = "AJ", conf = TRUE, conf.level = 0.95,
conf.type = "linear", n.boot = 50, data = colonIDM)

summary(fit)
summary(fit, times = c(400, 1000, 2900))

    fit <- tprob(survIDM(time1,event1,Stime, event) ~ 1, s = 365,
method = "AJ", conf = TRUE, conf.level = 0.95,
conf.type = "linear", n.boot = 50, data = colonIDM)

summary(fit)
summary(fit, times = c(400, 1000, 2900))

Create a survIDM object

Description

Creates a "survIDM" object, usually used as a response variable in a model formula.

Usage

survIDM(time1, event1, Stime, event, ...)
survIDM(time1, event1, Stime, event, ...)

Arguments

`time1`	First time or censoring time.
`event1`	Indicator of the first time; 0 if the first time is censored and 1 otherwise.
`Stime`	The total time of the process.
`event`	Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.
`...`	Other options.

Details

Arguments in this function must be introduced in the following order: time1, event1, Stime and event, where time1 and Stime are the sojourn time in the initial state and the total time, respectively. event1 and event denote their corresponding indicator statuses. This function checks the following conditions: (i) the arguments time1 and Stime must be numeric and nonnegative; event1 and event must be 0 or 1 if numeric and TRUE or FALSE if logical. Stime must be greater or equal to argument arguments time1. Stime and time1 must be equal when argument event1 equals 0 or FALSE. Argument event must be equal to 0 or FALSE when argument event1 equals 0 or FALSE. When arguments Stime and time1 are equal and argument event1 equals 1 or TRUE, argument event must be equal to 1 or TRUE.

Value

An object of class "survIDM". "survIDM" objects are implemented as a single dataframe.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

Examples

with(colonIDM, survIDM(time1, event1, Stime, event))
with(colonIDM, survIDM(time1, event1, Stime, event))

Nonparametric estimation of transition probabilities in the illness-death model

Description

This function is used to obtain nonparametric estimates of the transition probabilities in the illness-death model.

Usage

tprob(
  formula,
  s,
  method = "AJ",
  conf = FALSE,
  conf.level = 0.95,
  conf.type = "log",
  n.boot = 199,
  data,
  z.value,
  bw = "dpik",
  window = "gaussian",
  method.weights = "NW",
  cluster = FALSE,
  ncores = NULL,
  na.rm = TRUE
)
tprob(
  formula,
  s,
  method = "AJ",
  conf = FALSE,
  conf.level = 0.95,
  conf.type = "log",
  n.boot = 199,
  data,
  z.value,
  bw = "dpik",
  window = "gaussian",
  method.weights = "NW",
  cluster = FALSE,
  ncores = NULL,
  na.rm = TRUE
)

Arguments

`formula`	A `formula` object, which must have a `survIDM` object as the response on the left of the `~` operator and, if desired, a term on the right. The term may be a qualitative or quantitative variable. Without covariates, the right hand side should be `~ 1`.
`s`	The first time for obtaining estimates for the transition probabilities. If missing, 0 will be used.
`method`	The method used to compute the transition probabilities. Possible options are `"AJ"`, `"LIDA"` `"LM"`, `"PLM"`, `"LMAJ"`, `"PLMAJ"`, `"PAJ"`, `"IPCW"` and `"breslow"`. Defaults to `"AJ"`. The `"IPCW"` method is recommended to obtain conditional transition probabilities (i.e., with a quantitative term on the right hand side of formula). The `"breslow"` method is based on a Cox's regression model (Cox, 1972) fitted marginally to each allowed transition, with the corresponding baseline hazard function estimated by the Breslow's method (Breslow, 1972).
`conf`	Provides pointwise confidence bands. Defaults to `FALSE`.
`conf.level`	Level of confidence. Defaults to 0.95 (corresponding to 95%).
`conf.type`	Method to compute the confidence intervals. Depends on the choice of the estimation method of the transition probabilities. For Aalen-Johansen type estimators (`"AJ"`, `"LMAJ"`, `"PAJ"` and `"PLMAJ"`) possible choices are `"linear"`, `"log"` and `"log-log"`. Default method is `"log"`. The `"linear"` option provides the standard intervals curve +-k *se(curve), where k is determined from `"conf.int"`. The `"log"` option calculates the intervals based on the cumulative hazard or -log(survival). The `"log-log"` option uses the log hazard function or log(-log(survival)). For the remaining estimation methods (`"LIDA"`, `"LM"`, `"PLM"`, `"IPCW"` and `"breslow"`) the percentile bootstrap which resamples each datum with probability 1/n is used.
`n.boot`	The number of bootstrap replicates to compute the variance of the non-Markovian estimator. Default is 199.
`data`	A data.frame including at least four columns named `time1`, `event1`, `Stime` and `event`, which correspond to disease free survival time, disease free survival indicator, time to death or censoring, and death indicator, respectively.
`z.value`	The value of the covariate on the right hand side of formula at which the transition probabilities are computed. For quantitative covariates, i.e. of class integer and numeric.
`bw`	A single numeric value to compute a kernel density bandwidth. Use `"dpik"` for the KernSmooth package based selector or `"np"` for the `'npudensbw'` function of the np package.
`window`	A character string specifying the desired kernel. See details below for possible options. Defaults to `"gaussian"` where the gaussian density kernel will be used.
`method.weights`	A character string specifying the desired weights method. Possible options are `"NW"` for the Nadaraya-Watson weights and `"LL"` for local linear weights. Defaults to `"NW"`.
`cluster`	A logical value. If `TRUE` (default), the bootstrap procedure for the confidence intervals is parallelized. Note that there are cases (e.g., a low number of bootstrap repetitions) that R will gain in performance through serial computation. R takes time to distribute tasks across the processors also it will need time for binding them all together later on. Therefore, if the time for distributing and gathering pieces together is greater than the time need for single-thread computing, it does not worth parallelize.
`ncores`	An integer value specifying the number of cores to be used in the parallelized procedure. If `NULL` (default), the number of cores to be used is equal to the number of cores of the machine - 1.
`na.rm`	A logical value indicating whether NA values should be stripped in the computation.

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine". The LIDA estimator was labelled according to the acronym of the Lifetime Data Analysis journal in which the estimator was described for the first time (Meira-Machado, U?a-?lvarez and Cadarso-Su?rez, 2006).

Possible methods are:

AJ Aalen-Johansen estimator
PAJ Presmoothed Aalen-Johansen estimator
LIDA LIDA estimator
LM Landmark approach estimator
PLM Presmoothed Landmark approach estimator
LMAJ Landmark approach Aalen-Johansen estimator
PLDAJ Presmoothed Landmark approach Aalen-Johansen estimator
tpIPCW Inverse Probability of Censoring Weighting for Transition Probabilities
tpBreslow Breslow method

Value

An object of class "survIDM" and one of the following five classes: "AJ", "LIDA", "LM", "PLM", "LMAJ", "PLMAJ", "PAJ", "tpIPCW" and "tpBreslow". Objects are implemented as a list with elements:

`est`	data.frame with estimates of the transition probabilities.
`CI`	data.frame with the confidence intervals of the transition probabilities.
`conf.level`	Level of confidence.
`s`	The first time for obtaining estimates for the transition probabilities.
`t`	The time for obtaining the estimates of transition probabilities.
`conf`	logical; if `FALSE` (default) the pointwise confidence bands are not given.
`conf.type`	Type of the confidence interval.
`callp`	The expression of the estimated probability.
`Nlevels`	The number of levels of the covariate. Provides important information when the covariate at the right hand side of formula is of class factor.
`levels`	The levels of the qualitative covariate (if it is of class factor) on the right hand side of formula.
`formula`	A formula object.
`call`	A call object.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

Aalen O. O., Johansen S. (1978) An Empirical Transition Matrix for Nonhomogeneous Markov Chains Based on Censored Observations. Scandinavian Journal of Statistics 5(3), 141–150.

Meira-Machado L. F., de Una-Alvarez J. and Cadarso-Suarez C. (2006). Nonparametric estimation of transition probabilities in a non-Markov illness-death model. Lifetime Data Anal 12(3), 325–344.

de Una-Alvarez J. and Meira-Machado L. (2015). Nonparametric estimation of transition probabilities in a non-Markov illness-death model: a comparative study. Biometrics 71, 364–375.

Cox, DR (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B 34, 187-200.

Breslow, N. (1972). Discussion of paper by dr cox. Journal of Royal Statistical Society, Series B 34, 216-217.

Examples

## Not run: 
# Aalen-Johansen
res <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 0,
method = "AJ", conf = FALSE, data = colonIDM)
summary(res, time=365*1:6)
plot(res)
# Transition Probabilities Pij(t)=Pij(365,t)
# LIDA
res1 <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 365,
             method = "LIDA", conf = FALSE, data = colonIDM)

summary(res1, time=365*1:6)
plot(res1)
plot(res1, trans="01", ylim=c(0,0.15))
# Landmark (LM)
res2 <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 365,
              method = "LM", conf = FALSE, data = colonIDM)
summary(res2, time=365*1:6)
plot(res2)
# Presmoothed LM
res3 <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 365,
              method = "PLM", conf = TRUE, data = colonIDM)
summary(res3, time=365*1:6)
autoplot(res3, interactive = TRUE)
# Conditional transition probabilities
# With factor
res4 <- tprob(survIDM(time1, event1, Stime, event) ~ factor(sex), s = 365,
              method = "AJ", conf = TRUE, data = colonIDM)
summary(res4, time=365*1:6)
plot(res4, trans="02", ylim=c(0,0.5))
res5 <- tprob(survIDM(time1, event1, Stime, event) ~ rx, s =365,
              method = "breslow", z.value='Lev', conf = TRUE, data =colonIDM)
summary(res5, time=365*1:6)
plot(res5,trans="02", ylim=c(0,0.5))
# with continuous covariate (IPCW and Breslow Method)
res6 <- tprob(survIDM(time1, event1, Stime, event) ~ age, s = 365,
              method = "IPCW", z.value = 48, conf = FALSE, data = colonIDM,
              bw = "dpik", window = "gaussian", method.weights = "NW")
summary(res6, time=365*1:6)
plot(res6)
res7 <- tprob(survIDM(time1, event1, Stime, event) ~ age, s =365,
              method = "breslow", z.value=60, conf = FALSE, data =colonIDM)
summary(res7, time=365*1:6)
autoplot(res7, interactive=TRUE)
res8 <- tprob(survIDM(time1, event1, Stime, event) ~ age, s =365,
              method = "breslow", conf.type='bootstrap', z.value=60, conf = TRUE, data =colonIDM)
summary(res8, time=365*1:6)
plot(res8)
res9 <- tprob(survIDM(time1, event1, Stime, event) ~ rx, s =365,
              method = "breslow", conf.type='bootstrap',  conf = TRUE, data =colonIDM)
summary(res9, time=365*1:6)
plot(res9, trans="02", ylim=c(0,0.5))
# more than a covariate (Breslow Method)
res10<- tprob(survIDM(time1, event1, Stime, event) ~ nodes + factor(rx), s =365,
              method = "breslow", conf = TRUE, data =colonIDM)
summary(res10,t=365*1:5)
autoplot(res10)
res11<- tprob(survIDM(time1, event1, Stime, event) ~ nodes + factor(rx), s =365,
              method = "breslow", z.value=c(10,'Obs'), conf = TRUE, data =colonIDM)
summary(res11,t=365*1:5)
autoplot(res11)
# more than a covariate for Non Linear Models (Breslow Method)
res12<- tprob(survIDM(time1, event1, Stime, event) ~ pspline(age)+ nodes + factor(rx), s =365,
              method = "breslow", conf = TRUE, data =colonIDM)
summary(res12,t=365*1:5)
autoplot(res12)
# Confidence intervals
res13 <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 365,
               method = "AJ", conf = TRUE, n.boot = 5, conf.level = 0.95,
               conf.type = "log", data = colonIDM)
summary(res13, time=365*1:7)
autoplot(res13)

## End(Not run)
## Not run: 
# Aalen-Johansen
res <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 0,
method = "AJ", conf = FALSE, data = colonIDM)
summary(res, time=365*1:6)
plot(res)
# Transition Probabilities Pij(t)=Pij(365,t)
# LIDA
res1 <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 365,
             method = "LIDA", conf = FALSE, data = colonIDM)

summary(res1, time=365*1:6)
plot(res1)
plot(res1, trans="01", ylim=c(0,0.15))
# Landmark (LM)
res2 <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 365,
              method = "LM", conf = FALSE, data = colonIDM)
summary(res2, time=365*1:6)
plot(res2)
# Presmoothed LM
res3 <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 365,
              method = "PLM", conf = TRUE, data = colonIDM)
summary(res3, time=365*1:6)
autoplot(res3, interactive = TRUE)
# Conditional transition probabilities
# With factor
res4 <- tprob(survIDM(time1, event1, Stime, event) ~ factor(sex), s = 365,
              method = "AJ", conf = TRUE, data = colonIDM)
summary(res4, time=365*1:6)
plot(res4, trans="02", ylim=c(0,0.5))
res5 <- tprob(survIDM(time1, event1, Stime, event) ~ rx, s =365,
              method = "breslow", z.value='Lev', conf = TRUE, data =colonIDM)
summary(res5, time=365*1:6)
plot(res5,trans="02", ylim=c(0,0.5))
# with continuous covariate (IPCW and Breslow Method)
res6 <- tprob(survIDM(time1, event1, Stime, event) ~ age, s = 365,
              method = "IPCW", z.value = 48, conf = FALSE, data = colonIDM,
              bw = "dpik", window = "gaussian", method.weights = "NW")
summary(res6, time=365*1:6)
plot(res6)
res7 <- tprob(survIDM(time1, event1, Stime, event) ~ age, s =365,
              method = "breslow", z.value=60, conf = FALSE, data =colonIDM)
summary(res7, time=365*1:6)
autoplot(res7, interactive=TRUE)
res8 <- tprob(survIDM(time1, event1, Stime, event) ~ age, s =365,
              method = "breslow", conf.type='bootstrap', z.value=60, conf = TRUE, data =colonIDM)
summary(res8, time=365*1:6)
plot(res8)
res9 <- tprob(survIDM(time1, event1, Stime, event) ~ rx, s =365,
              method = "breslow", conf.type='bootstrap',  conf = TRUE, data =colonIDM)
summary(res9, time=365*1:6)
plot(res9, trans="02", ylim=c(0,0.5))
# more than a covariate (Breslow Method)
res10<- tprob(survIDM(time1, event1, Stime, event) ~ nodes + factor(rx), s =365,
              method = "breslow", conf = TRUE, data =colonIDM)
summary(res10,t=365*1:5)
autoplot(res10)
res11<- tprob(survIDM(time1, event1, Stime, event) ~ nodes + factor(rx), s =365,
              method = "breslow", z.value=c(10,'Obs'), conf = TRUE, data =colonIDM)
summary(res11,t=365*1:5)
autoplot(res11)
# more than a covariate for Non Linear Models (Breslow Method)
res12<- tprob(survIDM(time1, event1, Stime, event) ~ pspline(age)+ nodes + factor(rx), s =365,
              method = "breslow", conf = TRUE, data =colonIDM)
summary(res12,t=365*1:5)
autoplot(res12)
# Confidence intervals
res13 <- tprob(survIDM(time1, event1, Stime, event) ~ 1, s = 365,
               method = "AJ", conf = TRUE, n.boot = 5, conf.level = 0.95,
               conf.type = "log", data = colonIDM)
summary(res13, time=365*1:7)
autoplot(res13)

## End(Not run)

Package 'survidm'

Help Index

survidm: Inference and Prediction in an Illness-Death Model

Description

Author(s)

References

Visualization of objects of class survIDM with ggplot2 graphics.

Description

Usage

Arguments

Value

Author(s)

Examples

Estimation of the conditional distribution function of the response, given the covariate under random censoring.

Description

Usage

Arguments

Details

Author(s)

References

Examples

Bladder Cancer Recurrences.

Description

Usage

Format

References

Examples

Nonparametric estimation of the Cumulative Incident Functions in the illness-death model

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Chemotherapy for Stage B/C colon cancer.

Description

Usage

Format

Source

References

Examples

Fit proportional hazards regression model in each transition of the Illness-Death Model.

Description

Usage

Arguments

Value

Author(s)

Examples

Kaplan-Meier product-limit estimate of survival

Description

Usage

Arguments

Author(s)

References

See Also

Examples

Kaplan-Meier weights

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Local linear weights

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

This function is used to test the markov assumption in the illness-death model.

Description

Usage

Arguments

Visualization of objects of class `survIDM` with ggplot2 graphics.

Summarizing fits of `cmm` class

Summarizing fits of `survIDM` class