View Submission - COMPSTAT2022

A0417
**Title: **Bias induced by ignoring double truncation
**Authors: **Carla Moreira - University of Minho (Portugal) **[presenting]**

**Abstract: **Truncation is a well-known phenomenon in some observational studies of time-to-event data. For example, when the sample restricts to those individuals with events falling between two particular dates, they are subject to selection bias due to the simultaneous presence of left and right truncation, also known as interval sampling, leading to a double truncation. When time-to-event data is doubly truncated, the sampling information includes the variable of interest $X$ and left-truncation and right-truncation variables $U$ and $V$, but the observable population reduces to those individuals for which the variable of interest lies between left-truncation and right-truncation variables. In this case, both large and small values of $X$ are observed in principle with a relatively small probability. The observational bias for $X$ varies from application to application, depending on the joint distribution of $(X, U, V)$. For a particular $x$, the probability of sampling a value $x$ may be roughly constant, inducing no observational bias; or it may be not constant, indicating bias induced by double truncation. We present the problem of estimating the distribution of $X$ and other related curves, using nonparametric and semiparametric approaches, from a set of iid triplets with the distribution of $(X, U, V)$ given the double truncation condition. We present several scenarios where double truncation appears in practice and analyse the effect of ignoring double truncation in such cases.