Statistical models for censored point processes with cure fractions

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Abstract

We consider the analysis of data from the MRC Multicentre Trial for Early
Epilepsy and Single Seizures (MESS), which was undertaken to assess the differences
between two policies: immediate, or deferred treatment for patients
in early epilepsy. In studies of recurrent events, like epileptic seizures, there is
typically lots of information about individuals’ seizure patterns over a period
of time, which is often not fully utilised in analysis. We develop methodology
that allows pre-randomisation seizure counts and post-randomisation times to
first seizure, and from first to second seizure, to be jointly modelled, assuming
that these outcomes are predicted by (unobserved) seizure rates.
The joint model was found to be superior to standard survival methods. The
model had more power to detect statistically significant covariate effects not
found by standard survival analysis, however, interesting characteristics within
the data, not present in the model were also highlighted. The simple joint
model was extended to acknowledge these characteristics.
The results suggested that the identically distributed assumption for the survival
times may not be accurate. Instead we adjusted the model to allow for
changes in seizure rate both at randomisation and following a seizure postrandomisation.
There is evidence to suggest that there may be a substantial subset of the
MESS sample containing individuals who we would not expect to experience
seizures post-randomisation. If survival data has a proportion that are immune
to the event of interest, a model that ignores this may give misleading
results. We considered a cure rate model that allows the separation of individuals
who will never experience seizure recurrence and those who are at
risk of future seizures. We can then formulate probabilistic models for the
'at risk' individuals. These modifications to the simple joint model have been
considered both in isolation and together in a full model.

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