The `longevity`

package includes an implementation of
Turnbull’s EM algorithm for the empirical distribution function for data
subject to arbitrary censoring and truncation patterns.

For example, we can consider the interval censored data considered in
Lindsey and Ryan (1998). The
`left`

and `right`

give respectively.

```
library(longevity)
left <- c(0,15,12,17,13,0,6,0,14,12,13,12,12,0,0,0,0,3,4,1,13,0,0,6,0,2,1,0,0,2,0)
right <- c(16, rep(Inf, 4), 24, Inf, 15, rep(Inf, 5), 18, 14, 17, 15,
Inf, Inf, 11, 19, 6, 11, Inf, 6, 12, 17, 14, 25, 11, 14)
test <- np_elife(time = left, # left bound for time
time2 = right, # right bound for time
type = "interval2", # data are interval censored
event = 3) # specify interval censoring, argument recycled
plot(test)
```

We can also extract the equivalence classes and compare them to Lindsey and Ryan (1998): these match the values
returned in the paper. The summary statistics reported by the
`print`

method include the restricted mean, which is computed
by calculating the area under the survival curve.

```
## left right
## [1,] 4 6
## [2,] 13 14
## [3,] 15 16
## [4,] 17 18
```

```
## Nonparametric maximum likelihood estimator
##
## Routine converged
## Number of equivalence classes: 4
## Restricted mean at upper bound 18 : 10.47143
## Quartiles of the survival function: 15.5 14 8
```

Lindsey, Jane C., and Louise M. Ryan. 1998. “Methods for
Interval-Censored Data.” *Statistics in Medicine* 17 (2):
219–38. https://doi.org/10.1002/(SICI)1097-0258(19980130)17:2<219::AID-SIM735>3.0.CO;2-O.