Description Usage Arguments Details Value Note Author(s) References See Also Examples
This function calculates the selfconsistent estimate of survival for interval censored data. (i.e., the nonparametric maximum likelihood estimate that generalizes the KaplanMeier estimate to interval censored data). The censoring is such that if the ith observation fails at x, we only observe that L[i] < x ≤ 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).
1 
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. 
The algorithm is basically an EMalgorithm 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
KuhnTucker 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
).
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 selfconsistent algorithm (i.e., EMalgorithm) 
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., p[i] = Prob (X = time[i]). The last value is associated with time==Inf. (see details). 
surv 
a vector of survival values associated with the time vector above, i.e., surv[i] = Prob (X > time[i] ) 
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.
Michael P. Fay
Aragon, J. and Eberly, D. (1992), "On Convergence of Convex Minorant Algorithms for Distribution Estimation with IntervalCensored Data," Journal of Computational and Graphical Statistics. 1: 129140.
Gentleman, R. and Geyer, C. J. (1994), "Maximum Likelihood for Interval Censored Data: Consistency and Computation," Biometrika, 81, 618623.
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), 290295.
1 2 3 4 5 6  # Calculate and plot a KaplanMeier 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")

Loading required package: survival
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