Importance of competing risks in the analysis of anti-epileptic drug failure

Patients with a new diagnosis of epilepsy are usually prescribed an antiepileptic drug (AED) as monotherapy [1, 2]. An AED would be considered successful if the person taking it becomes seizure free with few side effects. Treatments that cause unacceptable side effects are likely to be changed to an alternative, whilst a treatment that fails to control seizures will either be changed to an alternative, or a second drug will be added. In order to assess this measure of failure in randomised trials (RCTs) of AEDs, a primary outcome recommended by the International League Against Epilepsy is retention time on AED [3], a composite outcome [4, 5], defined as the time from randomisation to the withdrawal of the randomised AED or addition of another.

Overall retention on treatment, i.e. time to treatment failure for any reason, may be analysed using standard survival analysis methods [6] and such analyses are common in the AED field in both studies of monotherapy [7–14] and add-on therapy [15, 16]. However this approach fails to examine different reasons for treatment failure (such as inadequate seizure control or adverse events), and assumes that reasons for failure are of equal importance which may not be the case. For example the loss of a driving license due to continued seizures will have differing social and economic consequences to the more common side effects such as nausea, dizziness or rash. A situation could arise in which two AEDs are considered equivalent as a result of similar overall treatment failure when in fact the drugs have very different effects on withdrawal due to side effects and poor seizure control.

In the statistical literature, the situation where there are several reasons why an event can occur is known as 'competing risks'. Ignoring this aspect of an outcome by analysing events overall can result in misleading conclusions [6]. Some authors have examined separately the time to withdrawal due to side effects [16] and have censored patients whose allocated treatment is changed due to inadequate seizure control, which may give misleading results as analyses assume that the competing risks of withdrawal are independent [6]. This assumption is questionable for AED treatment where there may be an association between these two causes of treatment failure. Thus a full investigation of retention time should include statistical methods that do not assume the competing risks of withdrawal are independent.

This paper considers the implications of competing risks of treatment failure for the design, data collection and analysis of AED studies motivated by analysis of the SANAD (Standard And New Anti-epileptic Drugs) trial [17] and drawing on our experience of datasets from our programme of individual patient data meta-analyses (IPDMA). We make recommendations for improving research practice.

Failure to investigate the competing risks of anti-epileptic drug withdrawal can lead to important differences in the clinical effect profiles of AEDs being missed. Thus overall treatment failure could be similar for two AEDs when the drugs have very different effects on withdrawal due to side effects and poor seizure control. For a particular patient, it is best to summarise each of these two risks for AEDs individually, as well as considering the overall risk of withdrawing for any reason. Further research is needed however to ascertain the relative importance of these different outcomes to individuals with epilepsy.

Prior to analysis, the timescale for competing causes should always be investigated. Risks operating over different time periods are less of an issue for the analysis. However, as demonstrated here, there is overlap of the timescale for withdrawals due to the different reasons and this is likely to be true for all AED studies.

More attention is required in the choice of statistical methods employed for the analysis of the competing risks of drug withdrawal. Cumulative incidence estimation allows appropriate inference about the probability of failure of AEDs allowing for the presence of competing reasons for such failure. This contrasts with the inappropriate inference that is often made from one minus the Kaplan-Meier estimate for a single failure reason which can only be interpreted as a probability of failure in the hypothetical situation that other failure reasons are not possible. Further, as suggested by a recent simulation study [33], the cumulative incidence approach has greater power to detect treatment differences than a logrank analysis in particular circumstances. This holds true for a difference in one direction for one cause and no or an opposite difference for the other cause, a situation worthy of note for anti-epileptic drug trials particularly when new and standard AEDs are being compared. Although conclusions from the two methods of analysis were similar for both pairwise comparisons shown here, this will not always be the case.

The reliability of classification of the cause of drug failure must be assured before a competing risks analysis is undertaken. The analysis of overall withdrawal is safe since the information that a drug has been withdrawn is usually reliable. For a competing risks analysis however, the analyst must consider whether the classification of the reason for withdrawal is reliable. The trials reviewed in this paper varied in the level of detail collected. In particular, data on the reason for withdrawal needs to be as accurate as possible for more explanatory research questions such as those posed in pharmacogenetic studies.

The dataset used for illustration here contained only two patients for whom the reason for drug withdrawal was recorded as non-compliance. Censoring the outcome for these two individuals implicitly assumes that the reason for non-compliance was not related to either seizure control or side effects. The results are likely to be robust to such an assumption in this example due to the low number of cases involved. However in other datasets where this reason is recorded more frequently, some sort of sensitivity analysis would be required to establish the robustness of the conclusions to this assumption. One approach would be to first code the withdrawal due to non-compliance as an event then as a censored observation and assess the robustness of the conclusions to such extreme assumptions. Of course ideally, as is the thrust of this paper, one would wish to minimise such problems through improved data collection methods.

The majority of drug withdrawals occurred by one year in the SANAD dataset although two-year follow-up provides greater power since almost all drug withdrawals occurred by this time. Monotherapy studies need longer follow-up however to investigate seizure control. Studies with both treatment failure and remission outcomes should intend to follow up each patient for a minimum of one year, and ensure that a reasonable number of patients will provide longer term follow-up, particularly important for seizure outcomes. Finally, we recommend that this outcome be termed 'time to treatment failure' rather than retention time since the former better reflects the event of interest.

The non-parametric cause-specific hazard function for cause l is estimated by maximum likelihood via

$h_l(t_j)=\frac{d_{lj}}{n_j}$

where d _lj represents the number of failures of type l at time t _j and n _j is the number at risk at this time. The maximum likelihood estimator of the cause-specific incidence at time t _j is

I _l (t _j ) = P(T <t _j , L = l) = S(t _j-1)h _l (t _j )

where P(T <t _j , L = l) is the probability that an individual withdraws from drug due to cause l before t _j and S(t _j-1) denotes the overall survival function at time t _j-1i.e. the probability that an individual does not withdraw for any reason before t _j-1.

The cause-specific cumulative incidence function at time t is then

$I_l(t)=P(T<t,L=l)={\displaystyle \sum _{j=1}^r{I}_l(t_j)}$

where the summation is over each cause-specific event time up to time t.