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Fitting Parametric Counting Processes by Using Log‐Linear Models

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  • J. K. Lindsey

Abstract

Counting processes constitute a means of describing how and when a series of events occurs to individuals. The risk or intensity of events, which may vary over time, can depend on any aspects of the previous history of the individual. Standard log‐linear regression modelling techniques are used to choose from the explanatory variables those which are appropriate to describe this dependence on the past. Details are given on how to set up such repeated measurements of duration among events as log‐linear models. Two examples show how the technique can be used, even for simple survival data, to choose between models of different complexity and highlight the importance of dependence on the past for repeated events such as infection due to chronic granulotomous disease in the study of the effect of gamma interferon treatment.

Suggested Citation

  • J. K. Lindsey, 1995. "Fitting Parametric Counting Processes by Using Log‐Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(2), pages 201-212, June.
    • Handle: RePEc:bla:jorssc:v:44:y:1995:i:2:p:201-212
    DOI: 10.2307/2986345
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    Cited by:

    1. Bremhorst, Vincent & Lambert, Philippe, 2013. "Flexible estimation in cure survival models using Bayesian P-splines," LIDAM Discussion Papers ISBA 2013039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Helene C. W. Rytgaard & Frank Eriksson & Mark J. van der Laan, 2023. "Estimation of time‐specific intervention effects on continuously distributed time‐to‐event outcomes by targeted maximum likelihood estimation," Biometrics, The International Biometric Society, vol. 79(4), pages 3038-3049, December.
    3. Junichiro Yoshida & Nakahiro Yoshida, 2024. "Penalized estimation for non-identifiable models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 765-796, October.
    4. Lambert, Philippe & Kreyenfeld, Michaela, 2023. "Exogenous time-varying covariates in double additive cure survival model with application to fertility," LIDAM Discussion Papers ISBA 2023006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Oliver Lunding Sandqvist, 2023. "A multistate approach to disability insurance reserving with information delays," Papers 2312.14324, arXiv.org.

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