Path analysis for survival data with recurrent events

We propose a method for path analysis of survival data with recurrent events. By applying an additive model for the intensity, concepts like direct, indirect and total effects may be defined in an analogous way as for traditional path analysis. The focus is on understanding how to analyze the effect of a dynamic covariate, e.g. the number of previous events, and at the same ensuring that the effect of a fixed covariate is unbiasedly estimated. Theoretical considerations as well as simulations are presented. A dataset on recurrent tumors in rats is used for illustration.

[1]  J. Robins,et al.  Estimating the causal effect of zidovudine on CD4 count with a marginal structural model for repeated measures , 2002, Statistics in medicine.

[2]  O. Aalen.  A linear regression model for the analysis of life times. , 1989, Statistics in medicine.

[3]  Thomas H Scheike,et al.  The Additive Nonparametric and Semiparametric Aalen Model as the Rate Function for a Counting Process , 2002, Lifetime data analysis.

[4]  J. Robins,et al.  Marginal Structural Models and Causal Inference in Epidemiology , 2000, Epidemiology.

[5]  Judea Pearl,et al.  Direct and Indirect Effects , 2001, UAI.

[6]  O. Aalen,et al.  Further results on the non-parametric linear regression model in survival analysis. , 1993, Statistics in medicine.

[7]  Myles Hollander,et al.  Models for Recurrent Events in Reliability and Survival Analysis , 2004 .

[8]  Axel Gandy,et al.  A non‐parametric approach to software reliability , 2004 .

[9]  Marvin H. J. Gruber.  Improving Efficiency by Shrinkage: The James--Stein and Ridge Regression Estimators , 1998 .

[10]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[11]  S. Keleş,et al.  Recurrent events analysis in the presence of time‐dependent covariates and dependent censoring , 2004 .

[12]  T. Santner,et al.  An analysis of comparative carcinogenesis experiments based on multiple times to tumor. , 1980, Biometrics.

[13]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[14]  M. Hernán,et al.  Causal knowledge as a prerequisite for confounding evaluation: an application to birth defects epidemiology. , 2002, American journal of epidemiology.

[15]  Nobuoki Eshima,et al.  PATH ANALYSIS WITH LOGISTIC REGRESSION MODELS : EFFECT ANALYSIS OF FULLY RECURSIVE CAUSAL SYSTEMS OF CATEGORICAL VARIABLES , 2001 .

[16]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[17]  J. Robins,et al.  Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. , 2000, Epidemiology.

[18]  John D. Kalbfleisch,et al.  The Statistical Analysis of Failure Data , 1986, IEEE Transactions on Reliability.

[19]  Odd O Aalen,et al.  Dynamic Analysis of Multivariate Failure Time Data , 2004, Biometrics.

[20]  Odd Aalen,et al.  A Model for Nonparametric Regression Analysis of Counting Processes , 1980 .