Description Usage Arguments Details Value References Examples
trSurvfit
estimates survival curves under dependent truncation and independent censoring via a structural transformation model.
1 2 3 4 5 6 7 8 9 | trSurvfit(
trun,
obs,
delta = NULL,
tFun = "linear",
plots = FALSE,
control = trSurv.control(),
...
)
|
trun |
left truncation time satisfying |
obs |
observed failure time, must be the same length as |
delta |
an optional 0-1 vector of censoring indicator (0 = censored, 1 = event) for |
tFun |
a character string specifying the transformation function or a user specified function indicating the relationship
between X, T, and a.
When
|
plots |
an optional logical value; if TRUE, a series of diagnostic plots as well as the survival curve for the observed failure time will be plotted. |
control |
controls the lower and upper bounds when |
... |
for future methods. |
A structural transformation model assumes there is a latent, quasi-independent truncation time that is associated with the observed dependent truncation time, the event time, and an unknown dependence parameter through a specified funciton. The dependence parameter is chosen to either minimize the absolute value of the restricted inverse probability weighted Kendall's tau or maximize the corresponding p-value. The marginal distribution for the truncation time and the event time are completely left unspecified.
The structure of the transformation model is of the form:
h(U) = (1 + a)^{-1} \times (h(T) + ah(X)),
where T is the truncation time, X is the observed failure time, U is the transformed truncation time that is quasi-independent from X and h(\cdot) is a monotonic transformation function. The condition, T < X, is assumed to be satisfied. The quasi-independent truncation time, U, is obtained by inverting the test for quasi-independence by either minimizing the absolute value of the restricted inverse probability weighted Kendall's tau or maximize the corresponding p-value.
At the current version, three transformation structures can be specified. trans = "linear"
corresponds to
h(X) = 1;
trans = "log"
corresponds to
h(X) = log(X);
trans = "exp"
corresponds to
h(X) = exp(X).
The output contains the following components:
surv
is a data.frame
contains the survival probabilities estimates.
byTau
a list contains the estimator of transformation parameter:
par
is the best set of transformation parameter found;
obj
is the value of the inverse probability weighted Kendall's tau corresponding to 'par'.
byP
a list contains the estimator of transformation parameter:
par
is the best set of transformation parameter found;
obj
is the value of the inverse probability weighted Kendall's tau corresponding to 'par'.
qind
a data frame consists of two quasi-independent variables:
trun
is the transformed truncation time;
obs
is the corresponding uncensored failure time.
Martin E. and Betensky R. A. (2005), Testing quasi-independence of failure and truncation times via conditional Kendall's tau, Journal of the American Statistical Association, 100 (470): 484-492.
Austin, M. D. and Betensky R. A. (2014), Eliminating bias due to censoring in Kendall's tau estimators for quasi-independence of truncation and failure, Computational Statistics & Data Analysis, 73: 16-26.
Chiou, S., Austin, M., Qian, J. and Betensky R. A. (2018), Transformation model estimation of survival under dependent truncation and independent censoring, Statistical Methods in Medical Research, 28 (12): 3785-3798.
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