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. This happens, for example, when we have a measuring instrument that cannot detect values below a certain level. 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. 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-truncated when individuals below a threshold are not present in the sample. Let’s begin by defining left-truncation and left-censoring: Truncation or censoring happens during the sampling process. If we ignore truncation or censoring when analyzing our data, our estimates of population parameters will be inconsistent. These phenomena arise in medical sciences, engineering, social sciences, and other research fields. ![]() Truncation and censoring are two distinct phenomena that cause our samples to be incomplete.
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