# transIPCW: Inverse probability of censoring weighted transition... In TPmsm: Estimation of Transition Probabilities in Multistate Models

## Description

Provides estimates for the transition probabilities based on inverse probability of censoring weighted estimators, IPCW.

## Usage

 1 2 3 transIPCW(object, s, t, x, bw="dpik", window="normal", method.weights="NW", state.names=c("1", "2", "3"), conf=FALSE, n.boot=1000, conf.level=0.95, method.boot="percentile", method.est=1, ...) 

## Arguments

 object An object of class ‘survTP’. s The first time for obtaining estimates for the transition probabilities. If missing, 0 will be used. t The second time for obtaining estimates for the transition probabilities. If missing, the maximum of Stime will be used. x Covariate values for obtaining estimates for the conditional transition probabilities. If missing, unconditioned transition probabilities will be computed. bw A character string indicating a function to compute a kernel density bandwidth. Defaults to “dpik” from package KernSmooth. Alternatively a single numeric value can be specified. window A character string specifying the desired kernel. See details below for possible options. Defaults to “normal” 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”. state.names A vector of characters giving the state names. conf Provides pointwise confidence bands. Defaults to FALSE. n.boot The number of bootstrap samples. Defaults to 1000 samples. conf.level Level of confidence. Defaults to 0.95 (corresponding to 95%). method.boot The method used to compute bootstrap confidence bands. Possible options are “percentile” and “basic”. Defaults to “percentile”. method.est The method used to compute the estimate. Possible options are 1 or 2. ... Further arguments. Typically these arguments are passed to the function specified by argument bw.

## Details

If bw="dpik" then possible options for argument window are “normal”, “box”, “epanech”, “biweight” or “triweight”. When argument bw is numeric then argument window accepts the same options as when bw="dpik" plus one of “tricube”, “triangular” or “cosine”.

If method.est=1 then p_{11}(s,t|X), p_{12}(s,t|X) and p_{22}(s,t|X) are estimated according to the following expressions:

p_{11}(s,t|X)=\frac{1-P(Z ≤q t|X)}{1-P(Z ≤q s|X)},

p_{12}(s,t|X)=\frac{P(Z ≤q t|X)-P(Z ≤q s|X)-P(s<Z ≤q t, T ≤q t|X)}{1-P(Z ≤q s|X)},

p_{22}(s,t|X) =\frac{P(Z ≤q s|X)-P(Z ≤q s,T ≤q t|X)}{P(Z ≤q s|X)-P(T ≤q s|X)}.

Then, p_{13}(s,t|X)=1-p_{11}(s,t|X)-p_{12}(s,t|X) and p_{23}(s,t|X)=1-p_{22}(s,t|X).

If method.est=2 then p_{11}(s,t|X), p_{12}(s,t|X) and p_{22}(s,t|X) are estimated according to the following expressions:

p_{11}(s,t|X)=\frac{P(Z>t|X)}{P(Z>s|X)},

p_{12}(s,t|X)=\frac{P(s<Z ≤q t,T>t|X)}{P(Z>s|X)},

p_{22}(s,t|X) =\frac{P(Z ≤q s,T>t|X)}{P(Z ≤q s, T>s|X)}.

Then, p_{13}(s,t|X)=1-p_{11}(s,t|X)-p_{12}(s,t|X) and p_{23}(s,t|X)=1-p_{22}(s,t|X).

## Value

If argument x is missing or if argument object doesn't contain a covariate, an object of class ‘TPmsm’ is returned. There are methods for contour, image, print and plot. ‘TPmsm’ objects are implemented as a list with elements:

 method A string indicating the type of estimator used in the computation. est A matrix with transition probability estimates. The rows being the event times and the columns the 5 possible transitions. inf A matrix with the lower transition probabilities of the confidence band. The rows being the event times and the columns the 5 possible transitions. sup A matrix with the upper transition probabilities of the confidence band. The rows being the event times and the columns the 5 possible transitions. time Vector of times where the transition probabilities are computed. s Start of the time interval. t End of the time interval. h The bandwidth used. If the estimator doesn't require a bandwidth, it's set to NULL. state.names A vector of characters giving the states names. n.boot Number of bootstrap samples used in the computation of the confidence band. conf.level Level of confidence used to compute the confidence band.

If argument x is specified and argument object contains a covariate, an object of class ‘TPCmsm’ is returned. There are methods for print and plot. ‘TPCmsm’ objects are implemented as a list with elements:

 method A string indicating the type of estimator used in the computation. est A 3 dimensional array with transition probability estimates. The first dimension being the event times, the second the covariate values and the last one the 5 possible transitions. inf A 3 dimensional array with the lower transition probabilities of the confidence band. The first dimension being the event times, the second the covariate values and the last one the 5 possible transitions. sup A 3 dimensional array with the upper transition probabilities of the confidence band. The first dimension being the event times, the second the covariate values and the last one the 5 possible transitions. time Vector of times where the transition probabilities are computed. covariate Vector of covariate values where the conditional transition probabilities are computed. s Start of the time interval. t End of the time interval. x Additional covariate values where the conditional transition probabilities are computed, which may or may not be present in the sample. h The bandwidth used. state.names A vector of characters giving the states names. n.boot Number of bootstrap samples used in the computation of the confidence band. conf.level Level of confidence used to compute the confidence band.

## Author(s)

Artur Araújo, Javier Roca-Pardiñas and Luís Meira-Machado

## References

Meira-Machado L., de Uña-Álvarez J., Datta S. Conditional Transition Probabilities in a non-Markov Illness-death Model. Discussion Papers in Statistics and Operation Research n 11/03, 2011. Department of Statistics and Operations Research, University of Vigo (ISSN: 1888-5756, Deposito Legal VG 1402 - 2007). This file can be downloaded from: http://webs.uvigo.es/depc05/reports/12_05.pdf

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

Davison, A. C., Hinkley, D. V. (1997) Bootstrap Methods and their Application Chapter 5, Cambridge University Press.

transAJ, transKMPW, transKMW, transLIN, transLS, transPAJ.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 # Set the number of threads nth <- setThreadsTP(2) # Create survTP object with age as covariate data(heartTP) heartTP_obj <- with(heartTP, survTP(time1, event1, Stime, event, age=age)) # Compute unconditioned transition probabilities transIPCW(object=heartTP_obj, s=33, t=412) # Compute unconditioned transition probabilities with confidence band transIPCW(object=heartTP_obj, s=33, t=412, conf=TRUE, conf.level=0.9, method.boot="basic", method.est=2) # Compute conditional transition probabilities transIPCW(object=heartTP_obj, s=33, t=412, x=0) # Compute conditional transition probabilities with confidence band transIPCW(object=heartTP_obj, s=33, t=412, x=0, conf=TRUE, conf.level=0.95, n.boot=100, method.boot="percentile", method.est=2) # Restore the number of threads setThreadsTP(nth)