| icfit {STAND} | R Documentation |
Calculates the Self-Consistent Estimate of Survival from Interval Censored Data
Description
This function calculates the self-consistent estimate of survival
for interval censored data.
(i.e., the nonparametric maximum likelihood estimate that generalizes
the Kaplan-Meier estimate to interval censored data).
The censoring is such that if the ith observation fails at x,
we only observe that L[i] < x \le R[i]. Data may be entered with
"exact" values, i.e., L[i] = x = R[i]. In that case the L[i] is
changed internally to L[i]* which is the next lower of any of the
observed endpoints (unless R[i] = 0 then an error results).
Usage
icfit(L, R, initp = NA, minerror = 1e-06, maxcount = 1000)
Arguments
L |
a vector of the left endpoints of the interval |
R |
a vector of the right endpoints of the interval |
initp |
a vector with an initial estimate of the density
function. This vector should sum to 1 and have a
length equal to the number of unique values of |
minerror |
The minimum error for convergence purposes. The
EM algorithm stops when |
maxcount |
the maximum number of iterations. Default is 10000. |
Details
The algorithm is basically an EM-algorithm applied to
interval censored data (see Turnbull, 1976); however,
first there is a primary reduction (See Aragon and
Eberly, 1992). Convergence is defined when the maximum
reduced gradient is less than minerror, and the
Kuhn-Tucker conditions are approximately met,
otherwise a warning will result. (see Gentleman and
Geyer, 1994). There may be other faster algorithms,
but they are more complicated (see Aragon and Eberly,
1992). The output for time is sort(unique(c(0,L,R,Inf)))
without the Inf. The output for p keeps the value
related to Inf so that p may be inserted into initp
for another run. The outputs for p and surv act as if
the jumps in the survival curve happen at the largest
of the possible times (see Gentleman and Geyer, 1994,
Table 2, for a more accurate way to present p).
Value
Returns a list with the following elements:
u |
a vector of Lagrange multipliers. If there are any
negative values of |
error |
this is the maximum of the reduced gradients. If
convergence is correct then |
count |
number of iterations of the self-consistent algorithm (i.e., EM-algorithm) |
time |
a vector of times (see details) |
p |
a vector of probabilities, all except the last
values are associated with the time
vector above, i.e., |
surv |
a vector of survival values associated with
the time vector above, i.e.,
|
Note
The functions icfit, icplot,
and ictest and documentation for these functions are from Michael P. Fay.
You are free to distribute these functions to whomever is
interested. They come with no warranty however.
Author(s)
Michael P. Fay
References
Aragon, J. and Eberly, D. (1992), "On Convergence of Convex Minorant Algorithms for Distribution Estimation with Interval-Censored Data," Journal of Computational and Graphical Statistics. 1: 129-140.
Gentleman, R. and Geyer, C. J. (1994), "Maximum Likelihood for Interval Censored Data: Consistency and Computation," Biometrika, 81, 618-623.
Turnbull, B. W. (1976), "The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data," Journal of the Royal Statistical Society, Series B,(Methodological), 38(3), 290-295.
See Also
Examples
# Calculate and plot a Kaplan-Meier type curve for interval censored data.
# This is S(x) = 1 - F(x) and is the sample estimate of the probability
# of exceeding x. The filmbadge data is used as an example.
data(filmbadge)
out <- icfit(filmbadge$dlow,filmbadge$dhigh)
icplot(out$surv, out$time,XLAB="Dose",YLAB="Exceedance Probability")