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Models and inference for on–off data via clipped Ornstein–Uhlenbeck processes

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  • Emil Aas Stoltenberg
  • Nils Lid Hjort

Abstract

We introduce a model for recurrent event data subject to left‐, right‐, and intermittent‐censoring. The observations consist of binary sequences (along with covariates) for each individual under study. These sequences are modeled as generated by latent Ornstein–Uhlenbeck processes being above or below certain thresholds. Features of the latent process and the thresholds are taken as functions of covariates, allowing the researcher to distinguish factors that have an effect on the frailty, from those that have an effect on the variability, of the observational unit. Inference is achieved by a quasi‐likelihood approach, for which consistency and asymptotic normality is established. An advantage of our model is that particularities regarding the censoring need not be taken actively into account, and that it is well suited for situations where the individuals under study are irregularly and asynchronously observed. The motivation for our model came from a dataset pertaining to the incidence of diarrhoea among Brazilian children growing up under rather harsh conditions. We analyze these data with our model and contrast the results with an intensity‐based counting process analysis of the same data.

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  • Emil Aas Stoltenberg & Nils Lid Hjort, 2021. "Models and inference for on–off data via clipped Ornstein–Uhlenbeck processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 908-929, September.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:3:p:908-929
    DOI: 10.1111/sjos.12472
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    References listed on IDEAS

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    3. Slud, Eric, 1989. "Clipped Gaussian processes are never M-step Markov," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 1-14, April.
    4. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, January.
    5. Ørnulf Borgan & Rosemeire L. Fiaccone & Robin Henderson & Mauricio L. Barreto, 2007. "Dynamic Analysis of Recurrent Event Data with Missing Observations, with Application to Infant Diarrhoea in Brazil," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 53-69, March.
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