Description Usage Arguments Details Value References See Also Examples
Fit a Cox model to a progressive Markov illness-death process observed under right-censored survival times and interval- or right-censored progression times.
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formula |
an expression of the form |
data |
an optional data frame in which to interpret the variables named in
the arguments |
subset |
expression specifying which rows of |
init |
a named list of the vector |
formula.coxph |
an optional formula specifying a model to fit with
|
init.coxph |
a logical value indicating that |
control |
a named list of parameters controlling the model fit, returned by
the function |
... |
additional arguments to be passed to |
A valid formula
argument can be expressed
as
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where (<start>
, <stop>
] is largest known time
interval over which individual <id>
is at risk for a transition
between the states <from>
and <to>
. The variable
<status>
indicates whether or not a transition is observed to
occur at <stop>
.
Under dual censoring (Boruvka and Cook, 2014), both the originating
state and the left endpoint of an at-risk interval may be unknown.
This case is handled with <start> = NA
, <from> = NA
,
<to>
equal to the index of the terminal state, and any
transition-type–specific covariates taking on the values assumed when
<from>
is equal to the intermediate state index. Under
discrete observation of non-terminal events, the right-endpoint of
some at-risk intervals may be unknown. For these <start>
is
the initial observation time (zero, unless left-truncated),
<stop> = NA
and <from>
is equal to the initial state
index. Missing values are retained by the NA
action
na.coxdual
. The default NA
action is used to
handle any missing values passed to coxph
via
the arguments formula.coxph
or init.coxph
.
Dual censoring typically arises in two scenarios: (1) dual
right-censoring, where intermediate events are right-censored before
terminal events, and (2) interval-censored intermediate events.
For examples of these refer to dualrc
and
dualic
, respectively.
A consequence of dual censoring is that any discrete maximum
likelihood estimator has ambiguous support at any failure times
associated with these NA
values. To resolve this, the
cumulative baseline transition intensities are restricted to piecewise
linear functions on a sieve partition with size controlled by
arguments passed to coxdual.control
. This approach
requires that both types of transitions to the terminal state are, at
least for some subjects, observed exactly.
An object of the classes "coxinterval"
and "coxdual"
,
which is a list with the following components.
call |
the matched call to |
censor |
a string indicating the dual censoring type. The value "right" corresponds to strictly dual-right–censored data. All other cases return "interval". |
n |
size of the sample used in the model fit. |
m |
number of at-risk intervals used in the model fit. |
p |
number of regression coefficients. |
coef |
a named |
var |
a named |
basehaz |
a data frame giving the cumulative baseline transition intensities evaluated over the sieve partition. |
init |
list of initial values used in the model fit. |
loglik |
a vector giving the log-likelihood at initiation and each iteration. |
iter |
number of iterations needed to reach the stopping criteria. |
gradnorm |
the maximum norm of the score scaled by the parameter value at the final iteration. |
maxnorm |
the maximum norm of the difference between the penultimate and final parameter values. |
cputime |
the processing time used for parameter and variance estimation. |
fit.coxph |
the |
na.action |
the |
censor.rate |
a named vector of censoring rates. |
control |
a list of arguments passed to |
data |
a list containing the data relevant to the model fit, if the
|
Boruvka, A. and Cook, R. J. (2014) Sieve estimation in a Markov illness-death process under dual censoring.
cluster
, dualic
,
dualrc
, Surv
,
trans
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | # Fit Cox model to dual-right--censored data
fit <- coxdual(Surv(start, stop, status) ~ cluster(id) + trans(from, to)
+ I(z * (to == 1)) + I(z * (from %in% 0 & to == 2))
+ I(z * (from %in% c(NA, 1) & to == 2)), data = dualrc,
sieve.rate = 2/5)
fit
par(mfrow = c(1, 3))
by(fit$basehaz, fit$basehaz$trans, function(x) plot(x[, 2:1],
type = "l", main = paste(x[1, 3]), xlim = c(0, 2), ylim = c(0, 4)))
# Fit Cox model to data with interval-censored progression times
fit <- coxdual(Surv(start, stop, status) ~ cluster(id) + trans(from, to)
+ I(z * (to == 1)) + I(z * (from %in% 0 & to == 2))
+ I(z * (from %in% c(NA, 1) & to == 2)), data = dualic)
fit
par(mfrow=c(1, 3))
by(fit$basehaz, fit$basehaz$trans, function(x) plot(x[, 2:1],
type = "l", main = paste(x[1, 3]), xlim = c(0, 2), ylim = c(0, 4)))
|
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