The primary reference for the generalized linear model using pseudo-observations is Per Kragh Andersen, Klein, and Rosthøj (2003). A more accesible review and summary of the method is Per Kragh Andersen and Pohar Perme (2010). The theoretical properties of the models have been studied by Graw, Gerds, and Schumacher (2009), Jacobsen and Martinussen (2016), and Overgaard et al. (2017). The methods for dealing with covariate dependent censoring are described in Binder, Gerds, and Andersen (2014), Overgaard, Parner, and Pedersen (2019), and Schoenenberger López (2018).

Various other extensions and uses of pseudo observations have been proposed (but this list is not comprehensive): relative survival (Pavlič and Pohar Perme 2019), causal inference (Per K. Andersen, Syriopoulou, and Parner 2017), case-cohort studies (Parner, Andersen, and Overgaard 2020), model checking (Perme and Andersen 2008), the illness-death model (Sabathé et al. 2020), parametric pseudo-observations (Nygård Johansen, Lundbye-Christensen, and Thorlund Parner 2020), goodness of fit (Pavlič, Martinussen, and Andersen 2019), recurrent events with death as a competing risk (Per Kragh Andersen, Angst, and Ravn 2019), joint models with recurrent events (Furberg et al. 2021).

Bibliography

Andersen, Per Kragh, Jules Angst, and Henrik Ravn. 2019. “Modeling Marginal Features in Studies of Recurrent Events in the Presence of a Terminal Event.” Lifetime Data Analysis 25 (4): 681–95.
Andersen, Per Kragh, John P. Klein, and Susanne Rosthøj. 2003. “Generalised Linear Models for Correlated Pseudo‐observations, with Applications to Multi‐state Models.” Biometrika 90 (1): 15–27. https://doi.org/10.1093/biomet/90.1.15.
Andersen, Per Kragh, and Maja Pohar Perme. 2010. “Pseudo-Observations in Survival Analysis.” Statistical Methods in Medical Research 19 (1): 71–99. https://doi.org/10.1177/0962280209105020.
Andersen, Per K, Elisavet Syriopoulou, and Erik T Parner. 2017. “Causal Inference in Survival Analysis Using Pseudo-Observations.” Statistics in Medicine 36 (17): 2669–81.
Binder, Nadine, Thomas A Gerds, and Per Kragh Andersen. 2014. “Pseudo-Observations for Competing Risks with Covariate Dependent Censoring.” Lifetime Data Analysis 20 (2): 303–15.
Furberg, Julie K, Per K Andersen, Sofie Korn, Morten Overgaard, and Henrik Ravn. 2021. “Bivariate Pseudo-Observations for Recurrent Event Analysis with Terminal Events.” Lifetime Data Analysis, 1–32.
Graw, Frederik, Thomas A Gerds, and Martin Schumacher. 2009. “On Pseudo-Values for Regression Analysis in Competing Risks Models.” Lifetime Data Analysis 15 (2): 241–55.
Jacobsen, Martin, and Torben Martinussen. 2016. “A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo-Observations.” Scandinavian Journal of Statistics 43 (3): 845–62.
Nygård Johansen, Martin, Søren Lundbye-Christensen, and Erik Thorlund Parner. 2020. “Regression Models Using Parametric Pseudo-Observations.” Statistics in Medicine.
Overgaard, Morten, Erik Thorlund Parner, Jan Pedersen, et al. 2017. “Asymptotic Theory of Generalized Estimating Equations Based on Jack-Knife Pseudo-Observations.” The Annals of Statistics 45 (5): 1988–2015.
Overgaard, Morten, Erik Thorlund Parner, and Jan Pedersen. 2019. “Pseudo-Observations Under Covariate-Dependent Censoring.” Journal of Statistical Planning and Inference 202: 112–22.
Parner, Erik T, Per K Andersen, and Morten Overgaard. 2020. “Cumulative Risk Regression in Case–Cohort Studies Using Pseudo-Observations.” Lifetime Data Analysis, 1–20.
Pavlič, Klemen, Torben Martinussen, and Per Kragh Andersen. 2019. “Goodness of Fit Tests for Estimating Equations Based on Pseudo-Observations.” Lifetime Data Analysis 25 (2): 189–205.
Pavlič, Klemen, and Maja Pohar Perme. 2019. “Using Pseudo-Observations for Estimation in Relative Survival.” Biostatistics 20 (3): 384–99.
Perme, Maja Pohar, and Per Kragh Andersen. 2008. “Checking Hazard Regression Models Using Pseudo-Observations.” Statistics in Medicine 27 (25): 5309–28.
Sabathé, Camille, Per K Andersen, Catherine Helmer, Thomas A Gerds, Hélène Jacqmin-Gadda, and Pierre Joly. 2020. “Regression Analysis in an Illness-Death Model with Interval-Censored Data: A Pseudo-Value Approach.” Statistical Methods in Medical Research 29 (3): 752–64.
Schoenenberger López, Andreu. 2018. “Modeling Pseudo-Observations with Covariate Dependent Censoring: Robustness of the Method Against Misspecified Censoring Models.” Master’s thesis, Universitat Politècnica de Catalunya.
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