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Understanding truncation and censoring

Truncation and censoring are two distinct phenomena that cause our samples to be incomplete. These phenomena arise in medical sciences, engineering, social sciences, and other research fields. If we ignore truncation or censoring when analyzing our data, our estimates of population parameters will be inconsistent.

Truncation or censoring happens during the sampling process. Let’s begin by defining left-truncation and left-censoring:

Our data are left-truncated when individuals below a threshold are not present in the sample. For example, if we want to study the size of certain fish based on the specimens captured with a net, fish smaller than the net grid won’t be present in our sample.

Our data are left-censored at \(\kappa\) if every individual with a value below \(\kappa\) is present in the sample, but the actual value is unknown. This happens, for example, when we have a measuring instrument that cannot detect values below a certain level.

We will focus our discussion on left-truncation and left-censoring, but the concepts we will discuss generalize to all types of censoring and truncation—right, left, and interval.

When performing estimations with truncated or censored data, we need to use tools that account for that type of incomplete data. For truncated linear regression, we can use the truncreg command, and for censored linear regression, we can use the intreg or tobit command.

In this blog post, we will analyze the characteristics of truncated and censored data and discuss using truncreg and tobit to account for the incomplete data. Read more…