Turnbull function

Turnbull estimator

Computes the Turnbull estimator for the survival function of interval censored data.

Turnbull(x, L, R, censored, trunclower = 0, truncupper = Inf,
         conf.type = "plain", conf.int = 0.95)

Arguments

• x: Vector with points to evaluate the estimator in.
• L: Vector of length $n$ with the lower boundaries of the intervals.
• R: Vector of length $n$ with the upper boundaries of the intervals.
• censored: Vector of $n$ logicals indicating if an observation is interval censored.
• trunclower: Lower truncation point, default is 0.
• truncupper: Upper truncation point, default is Inf.
• conf.type: Type of confidence interval, see survfit.formula. Default is "plain".
• conf.int: Confidence level of the two-sided confidence interval, see survfit.formula. Default is 0.95.

Details

We consider the random interval censoring model where one observes $L \le R$

and where the variable of interest $X$ lies between $L$ and $R$.

Right censored data should be entered as L=l and R=truncupper, and right censored data should be entered as L=trunclower and R=r.

This function calls survfit.formula from survival.

See Section 4.3.2 in Albrecher et al. (2017) for more details.

Returns

A list with following components: - surv: A vector of length length(x) containing the Turnbull estimator evaluated in the elements of x.

• fit: The output from the call to survfit.formula, an object of class survfit.

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

Turnbull, B. W. (1974). "Nonparametric Estimation of a Survivorship Function with Doubly Censored Data." Journal of the American Statistical Association, 69, 169--173.

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, 290--295.

Author(s)

Tom Reynkens

See Also

survfit.formula, KaplanMeier

Examples

L <- 1:10
R <- c(1, 2.5, 3, 4, 5.5, 6, 7.5, 8.25, 9, 10.5)
censored <- c(0, 1, 0, 0, 1, 0, 1, 1, 0, 1)

x <- seq(0, 12, 0.1)


plot(x, Turnbull(x, L, R, censored)$cdf, type="s", ylab="Turnbull estimator")