Confidence bands for quantiles as a function of covariates in recurrent event models


  • Author: Statistics Views
  • Date: 12 June 2019
  • Copyright: Image copyright of Patrick Rhodes

In a paper published in The Canadian Journal of Statistics, the authors investigate the construction of various confidence bands for quantiles of the time between event recurrences when covariates and interventions performed after a recurrence are accounted for via a general Cox‐type model for recurrent events. They propose three types of bands: those based on the asymptotic properties of the properly standardized quantile; those based on a Khmaladze transformation of the original limiting distribution; and those based on bootstrap techniques.

The paper is available via the link below and the authors explain their findings in further detail below:

Confidence bands for quantiles as a function of covariates in recurrent event models

Akim Adekpedjou, Gayla R. Olbricht and Gideon K. D. Zamba

The Canadian Journal of Statistics, Volume 46, Issue 4, December 2018, pages 610-634

thumbnail image: Confidence bands for quantiles as a function of covariates in recurrent event models

Suppose we have a study where interest is the time to occurrence of a certain disease (biomedical studies), time until an item fails (reliability, engineering, warranty), time to next claim filing of a policyholder (insurance). All these events are subject to recurrence, that is can occur multiple times, and are encounter in our daily life. When an event occurs, some variables are recorded such as: (i) blood pressure, state of disease, temperature, and age in biomedical study, (ii) age, driver aggressiveness, car mileage, state of driver at time of event in actuarial science. Any of the variables recorded at event occurrence along with the types of treatment or malus/bonus received can have substantial impact on future event occurrences. It may be of interest to investigators to know how a certain treatment, repair, or reward/penalize affect the median time of future occurrences, or the time at which a certain percentage of units experience the event. This paper discusses techniques for obtaining a possible range of values that contain the real value of the median, or time at which a certain percentage of the units would fail.

We propose three techniques that incorporate the variables of interest while taking into account the type of treatment, repair, or penalty/reward after each event for determining such intervals. One is a model based and computationally intense, where it is assumed that the time to event has a certain form. It turns out that the model based is difficult to track because of all the unknowns in the model, which lead us to transform it and getting rid of the unknowns making it easier to obtain the numbers needed to obtain the intervals. The third is based on resampling the model, so-called bootstrap. The transformed approach turns out to be better as it reduces the variability as a result of the transformation. The transformed and computational intense intervals have a better coverage probability.

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