Sampling Bias in Population Studies—How to Use the Lexis Diagram

Abstract

Modified versions of the lifetime distribution are often used in survival analysis. The modifications depend on how we choose individuals for the study and on the assumptions on the behaviour of the population. A rigorous point process description of the Lexis diagram is used to make the sampling mechanisms and the preconditions transparent. The point process description gives a framework to handle all possible sampling patterns. The set‐up is generalized so it can handle more complicated life descriptions than just lifetimes, and the diability model is used as an example. Two set‐ups can be used. Conditional on the birthtimes, the lifetime distribution is left truncated and subject to either right censoring or right truncation. Assuming that the birthtimes can be described by a Poisson process the modifications are length bias and the recurrence time distribution known from renewal theory.