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Stuart G. Baker, Letter to the Editor: “Comment on Hubbard and Miglioretti (2013), Consider Also a Selection Model for the Cumulative Risk of False Positive Screening Tests”, Biometrics, Volume 69, Issue 4, December 2013, Page 1084, https://doi.org/10.1111/biom.12116
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From the perspective of the missing-data literature (Little and Rubin, 2002), there are two types of models usually considered for estimating the cumulative probability of a false positive in k cancer screening tests based on data from persons receiving k or fewer cancer screening tests. One type is a pattern-mixture model in which the probability of a false positive is conditional on the observed number of screening tests. Hubbard and Miglioretti (2013) have improved this type of model. A second type of model is a selection model that combines (i) a logistic regression involving the false positive status on a screening test in the absence of censoring and (ii) a model for censoring of screening tests that depends only on observed baseline variables (and has different parameters from the aforementioned logistic regression) so that it can be ignored under likelihood-based inference (Baker, Erwin, and Kramer, 2003; Croswell et al., 2010; Baker, 2011). In a study involving both types of models, the estimated cumulative false positive rates were similar (Croswell et al., 2009).
