condSURV:A package for nonparametric estimation of the survival functions for ordered multivariate failure time data.

Description

Newly developed methods for the estimation of the conditional survival function are implemented in this package. The condSURV package implements nonparametric and semiparametric estimators for these quantities. The package also implements feasible estimation methods for these quantities conditionally on current or past covariate measures. Other related estimators are also implemented in the package. One of these estimators is the Kaplan-Meier estimator typically assumed to estimate the survival function. A modification of the Kaplan-Meier estimator, based on a preliminary estimation (presmoothing) of the censoring probability for the survival time, given the available information is also implemented.

Author(s)

Luis Meira-Machado and Marta Sestelo.

Maintainer: Marta Sestelo, sestelo@uvigo.es

References

L. Meira-Machado, M. Sestelo, and A. Goncalves (2016). Nonparametric estimation of the survival function for ordered multivariate failure time data: a comparative study. Biometrical Journal, 58(3), 623–634.

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
)

Arguments

Details

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

Author(s)

Luis Meira-Machado and Marta Sestelo

References

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

Examples

obj <- with(colonCS, survCS(time1, event1, Stime, event))

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

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

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)

Arguments

Author(s)

Luis Meira-Machado and Marta Sestelo

References

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

See Also

PKM

Examples

require(survival)
obj <- with(colonCS, survCS(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)

Arguments

Value

Vector with Kaplan-Meier weights.

Author(s)

Luis Meira-Machado and Marta Sestelo

References

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

See Also

PKMW

Examples

obj <- with(colonCS, survCS(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)

Arguments

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 and Marta Sestelo

See Also

NWW

Examples

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

Nadaraya-Watson weights.

Description

Computes the Nadaraya-Watson weights.

Usage

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

Arguments

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 and Marta Sestelo

See Also

LLW

Examples

NWW(covariate = colonCS$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)

Arguments

Author(s)

Luis Meira-Machado and Marta Sestelo

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.

See Also

KM

Examples

obj <- with(colonCS, survCS(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)

Arguments

Value

Vector with presmoothed Kaplan-Meier weights.

Author(s)

Luis Meira-Machado and Marta Sestelo

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.

See Also

KMW

Examples

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

Bladder Cancer Recurrences.

Description

bladderCS 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.

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(bladderCS)
  head(bladderCS)

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.

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(colonCS)
head(colonCS)

German Breast Cancer Study Data.

Description

gbcsCS is a data frame with 16 variables and 686 observations. Cancer clinical trials are a rich source for examples of applications of methods for the analysis of time to event. Willi Sauerbrei and Patrick Royston have graciously provided us with data obtained from the German Breast Cancer Study Group, which they used to illustrate methods for building prognostic models (Sauerbrei and Royston, 1999). In the main study, a total of 720 patients with primary node positive breast cancer were recruited between July 1984, and December 1989, (see Schmoor, Olschweski and Schumacher M. 1996 and Schumacher et al. (1994)).

Format

A data frame with 686 observations on the following 16 variables. Below a brief description is given for some of these variables.

rectime

Time to recurrence/censoring, whichever occurs first.

censrec

Recurrence/censoring indicator (recurrence=1, alive=0).

survtime

Time to censoring/death, whichever occurs first.

censdead

Death/censoring indicator (death=1, alive=0).

age

Age in years.

size

Tumour size.

#'

deathdate

diagdateb

estrg_recp

grade

hormone

id

nodes

prog_recp

recdate

menopause

References

Schmoor, C., Sauerbrei, W. Bastert, G., Schumacher, M. (2000). Role of Isolated Locoregional Recurrence of Breast Cancer: Results of Four Prospective Studies. Journal of Clinical Oncology, 18(8), 1696-1708.

Schumacher, M., Bastert, G., Bojar, H., Hiibner, K., Olschewski, M., Sauerbrei, W., Schmoor, C., Beyerle, C., Neumann, R.L.A. and Rauschecker, H.F. for the German Breast Cancer Study Group (GBSG) (1994). A randomized 2 x 2 trial evaluating hormonal treatment and the duration of chemotherapy in node-positive breast cancer patients. Journal of Clinical Oncology, 12, 2086-2093.

Hosmer, D.W. and Lemeshow, S. and May, S. (2008). Applied Survival Analysis: Regression Modeling of Time to Event Data: Second Edition, John Wiley and Sons Inc., New York, NY

Examples

data(gbcsCS)
head(gbcsCS)

Plot for an object of class "survCS".

Description

It draws the estimated conditional survival probabilities.

Usage

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

Arguments

Value

No value is returned.

Author(s)

Luis Meira-Machado and Marta Sestelo

Examples

fit1 <- survCOND(survCS(time1, event1, Stime, event) ~ 1, x = 365,
   data = colonCS, method = "LDM", conf = TRUE)

plot(fit1, xlab = "Time (days)", ylab = "S(y|365)", ylim = c(0.5, 1))

fit4 <- survCOND(survCS(time1, event1, Stime, event) ~ rx,
   x = 365, data = colonCS, method = "LDM")

plot(fit4, xlab = "Time (days)", ylab = "S(y|365)", ylim = c(0.5, 1))

Summarizing fits of survCS class

Description

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

Usage

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

Arguments

Value

A data frame or a list containing the following components:

Author(s)

Luis Meira-Machado and Marta Sestelo

References

L. Meira-Machado, M. Sestelo, and A. Goncalves (2016). Nonparametric estimation of the survival function for ordered multivariate failure time data: a comparative study. Biometrical Journal, 58(3), 623–634.

Examples

fit <- survCOND(survCS(time1, event1, Stime, event) ~ 1, x = 365,
data = colonCS, method = "LDM", conf = TRUE, n.boot = 50, cluster = FALSE)
summary(fit)
summary(fit, times = c(400, 1000, 2900))

Conditional survival probabilities based on the Kaplan-Meier weights, Landmark approaches and Inverse probability of censoring weighted.

Description

Provides estimates for the conditional survival probabilities based on Kaplan-Meier weighted estimators, the Landmark approaches and Inverse probability of censoring weighted.

Usage

survCOND(
  formula,
  x,
  y,
  lower.tail = FALSE,
  method = "LDM",
  presmooth = FALSE,
  conf = TRUE,
  n.boot = 200,
  data,
  conf.level = 0.95,
  z.value,
  bw = "dpik",
  window = "gaussian",
  method.weights = "NW",
  cluster = FALSE,
  ncores = NULL,
  na.rm = TRUE
)

Arguments

Details

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

Value

An object of class "survCS" and one of the following four classes: "KMW", "LMD", "PLDM" and "IPCW". Objects are implemented as a list with elements:

Author(s)

Luis Meira-Machado and Marta Sestelo

References

L. Meira-Machado, M. Sestelo, and A. Goncalves (2016). Nonparametric estimation of the survival function for ordered multivariate failure time data: a comparative study. Biometrical Journal, 58(3), 623–634.

Examples

   fit <- survCOND(survCS(time1, event1, Stime, event) ~ 1, x = 365, y = 730,
   data = colonCS, method = "KMW", conf = FALSE)

   fit1 <- survCOND(survCS(time1, event1, Stime, event) ~ 1, x = 365,
   data = colonCS, method = "LDM", conf = FALSE)

   fit2 <- survCOND(survCS(time1, event1, Stime, event) ~ 1, x = 365,
   data = colonCS, method = "LDM", lower.tail = TRUE, conf = FALSE)

   fit3 <- survCOND(survCS(time1, event1, Stime, event) ~ 1, x = 365,
   y = c(730, 1095, 1460), data = colonCS, method = "LDM", presmooth = TRUE,
   lower.tail = TRUE, conf = TRUE, n.boot = 100, conf.level = 0.95,
   cluster = FALSE)

   fit4 <- survCOND(survCS(time1, event1, Stime, event) ~ rx, x = 365,
   data = colonCS, method = "LDM", conf = FALSE)

   fit5 <- survCOND(survCS(time1, event1, Stime, event) ~ factor(sex),
   x = 365, data = colonCS, method = "LDM", conf = FALSE)

  ## Not run: 
   fit6 <- survCOND(survCS(time1, event1, Stime, event) ~ age,
   x = 365, y = 730, z.value = 48, data = colonCS, conf = TRUE)
   
## End(Not run)

Create a survCS object.

Description

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

Usage

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

Arguments

Details

Arguments in this function must be introduced in the following order: time1, event1, time2, ..., Stime and event, where time1, time2, ..., Stime are ordered event times and event1, event2,..., event their corresponding indicator statuses.

Value

An object of class "survCS" and of class "surv". "survCS" objects are implemented as a single dataframe.

Author(s)

Luis Meira-Machado and Marta Sestelo

Examples

with(colonCS, survCS(time1, event1, Stime, event))