Modelling seizure rates rather than time to an event within clinical trials of antiepileptic drugs

Background Predictive models within epilepsy are frequently developed via Cox's proportional hazards models. These models estimate risk of a specified event such as 12-month remission. They are relatively simple to produce, have familiar output, and are useful to answer questions about short-term prognosis. However, the Cox model only considers time to first event rather than all seizures after starting treatment for example. This makes assessing change in seizure rates over time difficult. Variants to the Cox model exist enabling recurrent events to be modelled. One such variant is the Prentice, Williams and Peterson - Total Time (PWP-TT) model. An alternative is the negative binomial model for event counts. This study aims to demonstrate the differences between the three approaches, and to consider the benefits of the PWP-TT approach for assessing change in seizure rates over time. Methods Time to 12-month remission and time to first seizure after randomisation were modelled using the Cox model. Risk of seizure recurrence was modelled using the PWP-TT model, including all seizures across the whole follow-up period. Seizure counts were modelled using negative binomial regression. Differences between the approaches were demonstrated using participants recruited to the UK-based multi-centre Standard versus New Antiepileptic Drug (SANAD) study. Results Results from the PWP-TT model were similar to those from the conventional Cox and negative binomial models. In general, the direction of effect was consistent although the variables included in the models and the significance of the predictors varied. The confidence intervals obtained via the PWP-TT model tended to be narrower due to the increase in statistical power of the model. Conclusions The Cox model is useful for determining the initial response to treatment and potentially informing when the next intervention may be required. The negative binomial model is useful for modelling event counts. The PWP-TT model extends the Cox model to all included events. This is useful in determining the longer-term effects of treatment policy. Such a model should be considered when designing future clinical trials in medical conditions typified by recurrent events to improve efficiency and statistical power as well as providing evidence regarding changes in event rates over time.