Parametric models for response‐biased sampling

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A Semiparametric Estimation of Mean Functionals With Nonignorable Missing Data (2011, methodology): “Chen (2001) and Tang, Little, and Raghunathan (2003) discussed identifiability conditions only under some limited situations.”
An Instrumental Variable Approach for Identification and Estimation with Nonignorable Nonresponse (2014, background): “It has been studied in the case of parametric p(y|x) (Chen (2001)); Tang, Little, and Raghunathan (2003)) and some semiparametric p(y|x) (Rotnitzky and Robins (1997)), but it is not well studied in the case of nonparametric p(y|x).”
Identifiability of Normal and Normal Mixture Models with Nonignorable Missing Data (2015, methodology): “., there exists a variable that is associated with the outcome variable but independent of the missingness conditional on the outcome, identiability of some MNAR models can be achieved. For example, Chen (2001) shows identiability of a subset of the regression parameters with biased sampling data, W”
A New Instrumental Method for Dealing with Endogenous Selection (2010, methodology): “This assumption was also considered by Chen (2001), Tang et al. (2003), Hemvanich (2004) and Ramalho and Smith (2007) in a nonresponse framework.”