Natural variability in seizure frequency: Implications for trials and placebo

Abstract

Background: Changes in patient-reported seizure frequencies are the gold standard used to test efficacy of new treatments in randomized controlled trials (RCTs). Recent analyses of patient seizure diary data suggest that the placebo response may be attributable to natural fluctuations in seizure frequency, though the evidence is incomplete. Here we develop a data-driven statistical model and assess the impact of the model on interpretation of placebo response.

Methods: A synthetic seizure diary generator matching statistical properties seen across multiple epilepsy diary datasets was constructed. The model was used to simulate the placebo arm of 5000 RCTs. A meta-analysis of 23 historical RCTs was compared to the simulations.

Results: The placebo 50 %-responder rate (RR50) was 27.3 ± 3.6 % (simulated) and 21.1 ± 10.0 % (historical). The placebo median percent change (MPC) was 22.0 ± 6.0 % (simulated) and 16.7 ± 10.3 % (historical).

Conclusions: A statistical model of daily seizure count generation which incorporates quantities related to the natural fluctuations of seizure count data produces a placebo response comparable to those seen in historical RCTs. This model may be useful in better understanding the seizure count fluctuations seen in patients in other clinical settings.

Keywords: Clinical trials; Diary; Epidemiology; Seizures; Statistics.

Figure 6:

Graphical representation of NV model seizure diary generation via a flow diagram. For every patient, n and p are randomly generated according to the Gamma and Beta distributions, respectively, which are themselves parameterized by the group level parameters. The patient-specific n and p are then used to generate daily seizure counts from a Negative Binomial distribution via an equivalent Gamma-Poisson mixture. The default time scale is daily, but that can be modified by setting the T parameter to be anything other than 1.

Figure 7:

The base-10 log of the average two-week seizure count vs. the base 10 log of the standard deviation of the two-week seizure counts, with one point per patient, across three datasets (SeizureTracker, HEP, Neurovista)[8]. For each dataset, a line of best fit was plotted with correlation coefficients shown in the legend. Both the correlation coefficients and the plotted points for all three heterogeneous datasets strongly suggest that there is a generalizable relationship between the average seizure count and the standard deviation.

Figure 8:

(Left) 50%-responder rate (RR50) endpoints from one randomly simulated trial for placebo and drug arm, p-value calculated using Fisher exact test. (Right) Median percentage change (MPC) endpoints from one simulated trial for placebo and drug arm, p-value calculated using Wilcoxon Signed Rank Test. This graph shows the RR50 and MPC from one trial of the RCT simulations which are both within 1 standard deviation of the estimated RR50 and estimated MPC of 5000 simulated trials, i.e. typical of the larger simulated trial set (Figure 5).

Figure 1:

A) Flow diagram of generation of synthetic seizure diaries corresponding to a simulated patient population via utilization of NV model, shown with optimization over group level parameters. None of the 23 RCTs in the endpoint response comparison were used to optimize over the group level parameters. B) Flow diagram of the endpoint response comparison, where two statistical summarizations of the endpoint responses from 5000 simulated RCTs and 23 historical RCTs were compared against each other. ^†All four of these RCT design parameters (N, B, T, L) were taken from the ezogabine RCT [13].

Figure 2:

Histogram of monthly seizure frequencies of 10,000 simulated patients, shown with fitted median and historically derived target median of monthly seizure frequencies. The fitted median is 2.9, while the target median is 2.7. The fitted and target median are close to each other, suggesting that the seizure frequencies of the simulated and actual patient populations are similar.

Figure 3:

Base-10 logarithm of the standard deviation of seizures count per two-week period vs. base-10 logarithm of the average seizure count of two-week periods, shown with the line of best fit for the simulated patient population. The fitted slope is 0.68 with an R² value of 0.66, and the target slope, based on historical seizure diaries and intracranial seizure monitoring studies was 0.70. This shows that the simulated diaries have the “L relationship” on this plot that was noted in other datasets [8].

Figure 4:

Weekly seizure diary of a synthetic patient over 119 weeks (~30 months). This simulated diary is similar to those seen by clinicians. It is interesting to note that while some weeks show no seizures, others show more 6 or more seizures. The model did not explicitly include provisions for clusters, yet, they happened anyway due to random chance.

Figure 5:

Horizontal bar chart of RR50 (50% responder rate) and MPC (median percentage change) from 5000 simulated trials with an artificial drug effect of 20% compared to a meta-analysis of 23 historical trials. The bars show the mean of the trials, and the error bars show the standard deviation. This bar chart shows the similarity between the simulated and historical RCTs, suggesting that the model can make reasonable predictions about RCT outcomes.