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In clinical and epidemiological research doubly truncated data often appear.This is the case, for instance, when the data registry is formed by intervalsampling. Double truncation generally induces a sampling bias on the targetvariable, so proper corrections of ordinary estimation and inference proceduresmust be used. Unfortunately, the nonparametric maximum likelihood estimator ofa doubly truncated distribution has several drawbacks, like potentialnon-existence and non-uniqueness issues, or large estimation variance.Interestingly, no correction for double truncation is needed when the samplingbias is ignorable, which may occur with interval sampling and other samplingdesigns. In such a case the ordinary empirical distribution function is aconsistent and fully efficient estimator that generally brings remarkablevariance improvements compared to the nonparametric maximum likelihoodestimator. Thus, identification of such situations is critical for the simpleand efficient estimation of the target distribution. In this paper we introducefor the first time formal testing procedures for the null hypothesis ofignorable sampling bias with doubly truncated data. The asymptotic propertiesof the proposed test statistic are investigated. A bootstrap algorithm toapproximate the null distribution of the test in practice is introduced. Thefinite sample performance of the method is studied in simulated scenarios.Finally, applications to data on onset for childhood cancer and Parkinson'sdisease are given. Variance improvements in estimation are discussed andillustrated.

Testing for an ignorable sampling bias under random double truncation