Interval-Censored Data

Definition

Suppose that $T_1,T_2,\dots ,T_n$ are i.i.d. random variables represent survival times. Interval censored data is given as an interval, not an exact point of time. We only observe the interval $(L_i,R_i]$ that includes $T_i$ Interval-censored data is divided into four cases.

Case 1 Interval-Censored Data (Current Status Data)

Data is given the form of $[0,C_i]$ or $(C_i,\infty )$, where $C_i$ is a fixed time point.

Case 2 Interval-Censored Data

Data is given the form of $(L_i,R_i]$ where $0<L_i<R_i<\infty$.

Double Censored Data

Data is given the form of $(L_i,R_i]$ where $0\le L_i\le R_i\le \infty$.

If $R_i=\infty$, then it is right-censored data, if $L_i=0$, then it is left-censored data, and if $L_i=R_i$, then it is uncensored data.

Panel Data

Observations are made at discrete time points. The period between these observations can be viewed as an interval.