Logistic regression when the outcome is measured with uncertainty.

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Learning kernel logistic regression in the presence of class label noise (2014, background): “[28] studied logistic regression with known label flip probabilities and they reckon problems when these probabilities are unknown.”
Data mining for credit card fraud: A comparative study (2011, background): “Qualitative response models are appropriate when dependent variable is categorical [36].”
Partially Supervised Learning Using an EM‐Boosting Algorithm (2004, methodology): “Third, to make the model identiﬁable, Magder and Hughes (1997) ﬁxed sensitivity and speciﬁcity, while we ﬁxed the average log odds for having a cancer among BPH-labeled subjects at ln { P (0) / (1 − P (0) ) } where P 0 is a starting value.”
Label-Noise Robust Logistic Regression and Its Applications (2012, background): “[20] studied label-noise robust logistic regression with known label flipping probabilities but they reckon problems when these probabilities are unknown.”
Essential Medical Statistics (2003, methodology): “3 For a binary outcome variable, if the sensitivity and specificity with which it was measured are known then estimated odds ratios from logistic regression may be corrected, as described by Magder and Hughes (1997). 4 Measurement error in a numerical outcome variable does not lead to regression dil”