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Efficient Estimation of Fixed and Time‐varying Covariate Effects in Multiplicative Intensity Models
Author(s) -
MARTINUSSEN TORBEN,
SCHEIKE THOMAS H.,
SKOVGAARD IB M.
Publication year - 2002
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00060
Subject(s) - covariate , mathematics , estimator , multiplicative function , martingale (probability theory) , parametric statistics , additive model , semiparametric model , parametric model , monte carlo method , statistics , econometrics , mathematical analysis
The proportional hazards assumption of the Cox model does sometimes not hold in practise. An example is a treatment effect that decreases with time. We study a general multiplicative intensity model allowing the influence of each covariate to vary non‐parametrically with time. An efficient estimation procedure for the cumulative parameter functions is developed. Its properties are studied using the martingale structure of the problem. Furthermore, we introduce a partly parametric version of the general non‐parametric model in which the influence of some of the covariates varies with time while the effects of the remaining covariates are constant. This semiparametric model has not been studied in detail before. An efficient procedure for estimating the parametric as well as the non‐parametric components of this model is developed. Again the martingale structure of the model allows us to describe the asymptotic properties of the suggested estimators. The approach is applied to two different data sets, and a Monte Carlo simulation is presented.

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