TY - JOUR

T1 - Targeted estimation of state occupation probabilities for the non-Markov illness-death model

AU - Munch, Anders

AU - Breum, Marie Skov

AU - Martinussen, Torben

AU - Gerds, Thomas A. A.

PY - 2023

Y1 - 2023

N2 - We use semi-parametric efficiency theory to derive a class of estimators for the state occupation probabilities of the continuous-time irreversible illness-death model. We consider both the setting with and without additional baseline information available, where we impose no specific functional form on the intensity functions of the model. We show that any estimator in the class is asymptotically linear under suitable assumptions about the estimators of the intensity functions. In particular, the assumptions are weak enough to allow the use of data-adaptive methods, which is important for making the identifying assumption of coarsening at random plausible in realistic settings. We suggest a flexible method for estimating the transition intensity functions of the illness-death model based on penalized Poisson regression. We apply this method to estimate the nuisance parameters of an illness-death model in a simulation study and a real-world application.

AB - We use semi-parametric efficiency theory to derive a class of estimators for the state occupation probabilities of the continuous-time irreversible illness-death model. We consider both the setting with and without additional baseline information available, where we impose no specific functional form on the intensity functions of the model. We show that any estimator in the class is asymptotically linear under suitable assumptions about the estimators of the intensity functions. In particular, the assumptions are weak enough to allow the use of data-adaptive methods, which is important for making the identifying assumption of coarsening at random plausible in realistic settings. We suggest a flexible method for estimating the transition intensity functions of the illness-death model based on penalized Poisson regression. We apply this method to estimate the nuisance parameters of an illness-death model in a simulation study and a real-world application.

KW - data-adaptive methods

KW - efficient estimation

KW - illness-death model

KW - state-dependent censoring

KW - targeted learning

KW - INTEGRATED TRANSITION HAZARDS

KW - NONPARAMETRIC-ESTIMATION

U2 - 10.1111/sjos.12644

DO - 10.1111/sjos.12644

M3 - Journal article

VL - 50

SP - 1532

EP - 1551

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

IS - 3

ER -