A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo-observations
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A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo-observations. / Jacobsen, Martin; Martinussen, Torben.
I: Scandinavian Journal of Statistics, Bind 43, Nr. 3, 09.2016, s. 845-862.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo-observations
AU - Jacobsen, Martin
AU - Martinussen, Torben
PY - 2016/9
Y1 - 2016/9
N2 - Pseudo-values have proven very useful in censored data analysis in complex settings such as multi-state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second-order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo-values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U-statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies.
AB - Pseudo-values have proven very useful in censored data analysis in complex settings such as multi-state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second-order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo-values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U-statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies.
KW - pseudo-observations
KW - survival analysis
KW - U-statistic
KW - von Mises expansion
U2 - 10.1111/sjos.12212
DO - 10.1111/sjos.12212
M3 - Journal article
VL - 43
SP - 845
EP - 862
JO - Scandinavian Journal of Statistics
JF - Scandinavian Journal of Statistics
SN - 0303-6898
IS - 3
ER -
ID: 167129556