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 -