Asymptotics for a class of dynamic recurrent event models

ABSTRACT Asymptotic properties, both consistency and weak convergence, of estimators arising in a general class of dynamic recurrent event models are presented. The class of models take into account the impact of interventions after each event occurrence, the impact of accumulating event occurrences, the induced informative and dependent right-censoring mechanism due to the data-accrual scheme, and the effect of covariate processes on the recurrent event occurrences. The class of models subsumes as special cases many of the recurrent event models that have been considered in biostatistics, reliability, and in the social sciences. The asymptotic properties presented have the potential of being useful in developing goodness-of-fit and model validation procedures, confidence intervals and confidence bands constructions, and hypothesis testing procedures for the finite- and infinite-dimensional parameters of a general class of dynamic recurrent event models, albeit the models without frailties.

[1]  Edsel A. Peña,et al.  Recurrent events and the exploding Cox model , 2010, Lifetime data analysis.

[2]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[3]  A. V. Peterson,et al.  On the regression analysis of multivariate failure time data , 1981 .

[4]  N. Breslow,et al.  A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship , 1974 .

[5]  L. J. Wei,et al.  Regression analysis of multivariate incomplete failure time data by modeling marginal distributions , 1989 .

[6]  Edsel A. Pefia,et al.  MODELS FOR RECURRENT EVENTS IN RELIABILITY AND SURVIVAL ANALYSIS , 2004 .

[7]  Ørnulf Borgan,et al.  Maximum likelihood estimation in parametric counting process models, with applications to censored failure time data , 1984 .

[8]  O. Aalen,et al.  Survival and Event History Analysis: A Process Point of View , 2008 .

[9]  R. Prentice,et al.  Commentary on Andersen and Gill's "Cox's Regression Model for Counting Processes: A Large Sample Study" , 1982 .

[10]  R. Gill,et al.  A Survey of Product-Integration with a View Toward Application in Survival Analysis , 1990 .

[11]  Robert L. Strawderman,et al.  A Weak Convergence Result Relevant in Recurrent and Renewal Models , 2000 .

[12]  J. Cavanaugh,et al.  Partial Likelihood , 2018, Wiley StatsRef: Statistics Reference Online.

[13]  Edsel A. Peña,et al.  Nonparametric Estimation With Recurrent Event Data , 2001 .

[14]  Thomas A. Mazzuchi,et al.  Mathematical reliability :: an expository perspective , 2004 .

[15]  Thomas Sellke,et al.  Weak Convergence of the Aalen Estimator for a Censored Renewal Process , 1988 .

[16]  O. Aalen.  Nonparametric Inference for a Family of Counting Processes , 1978 .

[17]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[18]  A. V. D. Vaart,et al.  Asymptotic Statistics: Frontmatter , 1998 .

[19]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[20]  Edsel A Peña,et al.  Semiparametric Inference for a General Class of Models for Recurrent Events. , 2007, Journal of statistical planning and inference.