Seizure Counts Research Articles

Analysis of Longitudinal Data of Epileptic Seizure Counts – A Two‐State Hidden Markov Regression Approach

This paper discusses a two-state hidden Markov Poisson regression (MPR) model for analyzing longitudinal data of epileptic seizure counts, which allows for the rate of the Poisson process to depend on covariates through an exponential link function and to change according to the states of a two-state Markov chain with its transition probabilities associated with covariates through a logit link function. This paper also considers a two-state hidden Markov negative binomial regression (MNBR) model, as an alternative, by using the negative binomial instead of Poisson distribution in the proposed MPR model when there exists extra-Poisson variation conditional on the states of the Markov chain. The two proposed models in this paper relax the stationary requirement of the Markov chain, allow for over-dispersion relative to the usual Poisson regression model and for correlation between repeated observations. The proposed methodology provides a plausible analysis for the longitudinal data of epileptic seizure counts, and the MNBR model fits the data much better than the MPR model. Maximum likelihood estimation using the EM and quasi-Newton algorithms is discussed. A Monte Carlo study for the proposed MPR model investigates the reliability of the estimation method, the choice of probabilities for the initial states of the Markov chain, and some finite sample behaviors of the maximum likelihood estimates, suggesting that (1) the estimation method is accurate and reliable as long as the total number of observations is reasonably large, and (2) the choice of probabilities for the initial states of the Markov process has little impact on the parameter estimates.

Proof of efficacy trials: crossover versus parallel-group studies

These have been a source of controversy for many years as different aspects of their design, conduct, and analysis have been subjected to close scrutiny. Vere (1979) dismissed them altogether ‘when a disorder presents in attacks it is probably better to rely on long periods of observation and large numbers to reduce variation, rather than a crossover design’ and the FDA discouraged their use. Despite this crossover trials have retained some popularity in the assessment of new antiepileptic drugs (AEDs) as add-on therapy compared with add-on placebo. One reason for this may be that with seizure counts in patients with drug-resistant, chronic epilepsy, between-patient variation is two, perhaps three, orders of magnitude greater than within-patient variation, exactly the situation in which crossover trials are much more economical than parallel-group studies. They are much less useful in newly diagnosed patients the majority of whom suffer far fewer, if any, seizures once AED treatment is commenced. The crosso er design in epilepsy is universally thought of from the very restricted viewpoint of the two-treatment, two-period design; here there may be problems of interpretation resulting from 1. lack of difference of a new AED from placebo in patients who may respond to neither — one solution is use of a two-period, three-treatment trial, which incorporates an established AED as a calibrator (Johnson, 1991); 2. interactions of new AED with (some of) those already taken-solution is to restrict entry or perhaps stratify on maintenance AEDs; 3. statistical tests for carryover effect of treatment from one period to the next are useless and anyway the statistical model of the carryover effect is pharmacologically naive (Senn, 1993) — solution is to include a washout period of sufficient duration to guarantee no carryover; 4. there may be a treatment by period interaction arising from sources other than the ‘carryover effect’ (Millar, 1983); 5. loss of patients during the first treatment or washout period, which could bias conclusions. The principal endpoints in crossover trials are seizure counts, seizure severity, and side effects; they are too short to assess changes in quality of life or cognition, and too small for reliable estimation of costs. * Tel.: +44-01223-330370; fax: +44-01223-330388. E-mail address: tony.johnson@mrc-bsu.cam.ac.uk (T. Johnson).

A double-blind comparison of lamotrigine and carbamazepine in newly diagnosed epilepsy with health-related quality of life as an outcome measure

The aim of this study was to compare the effect of treatment with lamotrigine (LTG) or carbamazepine (CBZ) on health-related quality of life (HRQOL) and to demonstrate the use of the SEALS Inventory as a comparative tool in clinical trials. Two hundred and sixty patients with newly diagnosed epilepsy were randomized to 48 weeks of treatment with LTG (n= 131) or CBZ (n= 129). HRQOL was measured at baseline and weeks 4, 12, 24, and 48 using the modified Side Effect and Life Satisfaction (SEALS) Inventory—a 38-item questionnaire divided into five subscales: Worry, Temper, Cognition, Dysphoria, and Tiredness. Overall, SEALS scores in the LTG group decreased (improved) significantly from baseline (P= 0.001). The LTG group had improvement in all five subscales over the 48 weeks of the study. CBZ patients had significantly worse SEALS scores than LTG patients at week 4 (P< 0.038). There was no significant change (positive or negative) in subsequent SEALS assessments. Analysis of SEALS data by subscale showed that the the CBZ group experienced more cognitive side-effects in general and more general changes in energy levels and affect during the first 4 weeks of treatment. These changes may help explain the difference in study completion rate: LTG 65%, CBZ 51% (P= 0.018). LTG offers the patient with newly diagnosed epilepsy significant benefits of greater tolerability and better health-related quality of life compared with CBZ. The SEALS Inventory is an effective tool for use in clinical trials of AEDs; it was a better predictor of trial completion than seizure counts, and used as a covariate enabled better detection of treatment effects. In general practice, the use of the SEALS Inventory to assess HRQOL has the potential to improve quality of care for people with epilepsy.

Modeling repeated count data subject to informative dropout.

In certain diseases, outcome is the number of morbid events over the course of follow-up. In epilepsy, e.g., daily seizure counts are often used to reflect disease severity. Follow-up of patients in clinical trials of such diseases is often subject to censoring due to patients dying or dropping out. If the sicker patients tend to be censored in such trials, estimates of the treatment effect that do not incorporate the censoring process may be misleading. We extend the shared random effects approach of Wu and Carroll (1988, Biometrics 44, 175-188) to the setting of repeated counts of events. Three strategies are developed. The first is a likelihood-based approach for jointly modeling the count and censoring processes. A shared random effect is incorporated to introduce dependence between the two processes. The second is a likelihood-based approach that conditions on the dropout times in adjusting for informative dropout. The third is a generalized estimating equations (GEE) approach, which also conditions on the dropout times but makes fewer assumptions about the distribution of the count process. Estimation procedures for each of the approaches are discussed, and the approaches are applied to data from an epilepsy clinical trial. A simulation study is also conducted to compare the various approaches. Through analyses and simulations, we demonstrate the flexibility of the likelihood-based conditional model for analyzing data from the epilepsy trial.

Evaluation of drug treatment outcome in epilepsy: a clinical perspective.

This article provides a comprehensive discussion of clinical outcome measures used in trials aimed at assessing the efficacy and safety of antiepileptic drugs. For efficacy, assessment still relies on careful documentation of changes in ictal activity as determined by seizure counts based on patients recall, direct clinical observation and (for absence seizures) EEG monitoring. In selected cases, assessment of seizure severity may also be indicated. The precise choice of outcome measures is largely dependent upon the specific trial design. In short-term regulatory trials, parameters such as time to nth seizure after randomization (or after achievement of target dosage) may be used as an index of antiepileptic efficacy, but the clinical relevance of such measures is questionable. In add-on trials in refractory patients, changes, in seizure counts and proportion of patients achieving 50%, 75% and 100% reduction in seizure frequency may be appropriate. For long-term monotherapy trials in newly diagnosed patients, proportion of patients achieving prolonged remission (1-year or longer) usually represents the most clinically meaningful efficacy outcome. Retention of patients on the allocated treatment over time is also a valuable measure, but it should be regarded as a composite endpoint because decision to continue treatment is dependent on both efficacy and tolerability. At present, there is no universally accepted method for evaluating side effects, particularly those which can not be documented objectively. Spontaneous reports of symptoms or use of specific checklists have advantages and disadvantages. Studies aimed at ensuring greater standardization in safety assessment should be encouraged, especially with respect to need of obtaining quantitative estimates, and information on both prevalence and incidence of side effects should be reported in all trials.

Modelling and analysis of count data using a renewal process

The Poisson process may be generalised by an ordinary renewal process with the times between renewals following a gamma distribution. Over- (under-) dispersion of the distribution of the number of renewals relative to the Poisson distribution is the result, according as the coefficient of variation of this gamma distribution is > 1 (< 1). This distribution of the number of renewals is then applied to analyse some data on seizure counts of epileptics.

Commissurotomies in Children

Although corpus callosotomy has been used since 1940 to treat severe, medically intractable seizure disorders, controversy remains as to when, or even if, the surgery should be performed. Unlike other types of surgical therapy of epilepsy where the epileptic focus is identified and removed, corpus callosotomy is used to interrupt the propagation of epileptic discharges. The procedure is primarily used in patients with secondarily generalized seizures in whom focal resections are not possible. Long-term follow-up studies of post-callosotomy patients are few and flawed by lack of accurate seizure counts and quality-of-life measures. Although it remains difficult to predict those patients who will benefit from the surgery, it appears that patients with "drop" attacks benefit the most from the procedure.

Exact Likelihood Evaluation in a Markov Mixture Model for Time Series of Seizure Counts

This paper provides an alternative to Albert's (1991), Biometrics 47, 1371-1381) approximation to the E-step when using the EM algorithm for parameter estimation in Markov mixture models. Use of a recursive algorithm of Baum et al. (1970, Annals of Mathematical Statistics 41, 164-171) results in exact evaluation of the likelihood, optimal parameter estimates, and very efficient computation. Applications to time series of seizure counts and fetal movements clearly show the advantages of this exact approach.

A Two-State Markov Mixture Model for a Time Series of Epileptic Seizure Counts

This paper discusses a model for a time series of epileptic seizure counts in which the mean of a Poisson distribution changes according to an underlying two-state Markov chain. The EM algorithm (Dempster, Laird, and Rubin, 1977, Journal of the Royal Statistical Society, Series B 39, 1-38) is used to compute maximum likelihood estimators for the parameters of this two-state mixture model and extensions are made allowing for nonstationarity. The model is illustrated using daily seizure counts for patients with intractable epilepsy and results are compared with a simple Poisson distribution and Poisson regressions. Some simulation results are also presented to demonstrate the feasibility of this model.

Seizure Frequency in Intractable Partial Epilepsy: A Statistical Analysis

We examined the seizure records of 13 patients (nine men and four women, ages 27-50 years) with intractable partial epilepsy, maintained with steady anti-epileptic drug dosages. Patients recorded daily seizure frequency on calendars. Periods of outpatient observation ranged from 99 to 1,710 days and the number of observed seizures ranged from 18 to over 400, with daily seizure rates of 0.1-4.3 per day. We used the quasi-likelihood regression model to examine the following four departures of the daily seizure counts from a Poisson (random) model: (1) linear increasing or decreasing time trends in expected seizure rates; (2) clustering, where the expected seizure rate on a given day depends on the number of seizures observed on the immediate prior days; (3) monthly cyclicity; and (4) increased variability (overdispersion). Linear time trends were seen in six patients (four increasing and two decreasing), clustering was seen in 10 patients, and a near-monthly cycle appeared in four patients (two of nine men and two of four women). A significant amount of extra variation (overdispersion) relative to a Poisson distribution was observed in all but one of the 13 patients. Departures from a Poisson (random) model appear more common in this population of patients with medically intractable epilepsy than is commonly recognized, and have clinical importance as well as implications for the design of clinical studies.

The development of a seizure severity scale as an outcome measure in epilepsy

In controlled trials of antiepileptic drugs (AEDs) seizure frequency is often the only variable considered. With little prospect of improving assessment of AEDs, using seizure counts as the only end-point, there is a need for the development of new outcome measures. Clinical experience indicates that seizure severity is equally important to the patient and, by preventing seizure spread, AEDs can influence seizure severity without necessarily reducing seizure frequency. A scale capable of measuring seizure severity and change of severity attributable to treatment could be a useful additional outcome measure. Such a scale should exhibit the basic properties of validity and reliability. An easily administrable 16-point scale, containing 2 subscales — perception of control and ictal/post-ictal effects — has been developed. This scale has been tested on a patient population (n = 159) representative of that seen in trials of novel AEDs. Using standardised statistical methods, the scale has been shown to be both reliable and valid.

A randomised double-blind placebo-controlled crossover add-on trial of lamotrigine in patients with treatment-resistant partial seizures

Efficacy and safety of lamotrigine (LTG) as add-on therapy was assessed in a randomised double-blind placebo-controlled trial of this drug in 23 adult patients with refractory partial seizures. Fifteen patients showed an improvement on LTG treatment, with a greater than 50% decrease in total seizure count in 7 patients. Fourteen patients experienced fewer simple and complex partial seizures, with 8 patients benefitting by more than a 50% decrease in seizure frequency. The drug was well tolerated over the 2 month treatment period. The plasma concentration of concomitant antiepileptic drugs remained. No haematological or chemical abnormalities were noted.

Some Covariance Models for Longitudinal Count Data with Overdispersion

A family of covariance models for longitudinal counts with predictive covariates is presented. These models account for overdispersion, heteroscedasticity, and dependence among repeated observations. The approach is a quasi-likelihood regression similar to the formulation given by Liang and Zeger (1986, Biometrika 73, 13-22). Generalized estimating equations for both the covariate parameters and the variance-covariance parameters are presented. Large-sample properties of the parameter estimates are derived. The proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures.

A randomized double-blind placebo-controlled add-on trial of lamotrigine in patients with severe epilepsy

The efficacy of lamotrigine (LTG), a new antiepileptic drug (AED) chemically unralated to drugs in current use, was evaluated in 21 in-patients (18 males, 3 females; mean age 34.6; range 23—42 years) with severe refractory epilepsy. An add-on double-blind place-bo-controlled crossover design was used, with 12 week treatment periods, and a 6 week washout period. Subjects were allocated to 1 of 2 dosing schedules according to their concomitant AEDs. Doses were increased according to clinical response. Although there was no significant reduction in total seizure count during the lamotrigine treatment period compared to placebo, there appears to be a drug effect as there was a marked reduction in generalized onic-clonic seizures in favour of lamotrigine in the last 4 weeks of the treatment period. There was no significant difference in volunteered adverse experiences during active and placebo treatment. Concomitant serum AED concentrations, biochemical and haematological parameters were unaffected by lamotrigine treatment.

Controlled Trial of Lamotrigine (Lamictar) for Refractory Partial Seizures

The antiepileptic effect of lamotrigine (LTG) was assessed in a double-blind, placebo-controlled crossover trial in 24 adult patients with refractory partial seizures. LTG or placebo was added to existing antiepileptic drugs (AEDs). The dose of LTG varied from 75 to 400 mg daily. Three patients did not complete the trial. One was withdrawn from the trial with ataxia, tiredness, dyspnea, and diplopia while receiving LTG and died 18 days later of invasive carcinoma involving the liver. A second patient was withdrawn during baseline for contravening admission criteria, and a third received LTG in error during both treatment periods. Twenty-one patients (12 men and 9 women) completed the trial. An analysis of seizure counts in the 12-week treatment period with LTG showed a statistically significant reduction in seizures as compared with placebo for total seizures (p less than 0.002), partial seizures (p less than 0.002), and secondarily generalized seizures (p less than 0.05). The analysis of total seizure days showed a significant reduction during LTG treatment (p less than 0.002). There were no statistically significant changes in plasma concentrations of phenytoin (PHT), carbamazepine (CBZ), primidone (PRM), or phenobarbital (PB) between the two treatment periods. The most common adverse events reported during the trial were diplopia, drowsiness, tiredness, ataxia, and headache, but although these were more frequent during LTG treatment, the differences from placebo were not statistically significant. No hematological or biochemical changes were noted.

Reliability of seizure diaries in adult epileptic patients.

Daily diaries are used widely in neurologic research and clinical practice to assess alterations in seizure frequency among patients with epilepsy. However, no formal tests of the reliability of this data collection method have been performed. We investigated the reliability of seizure recall in adult patients participating in a longitudinal study of stress, mood and seizure frequency. Patients maintained daily diaries for 10-36 weeks. The reliability study entailed completion of a single additional diary on the evening of a randomly selected day with reference to the preceding day. This design produced two diaries, completed 1 day apart, for the same 24-hour period. Measuring reliability with the Pearson correlation coefficient, overall reliability of seizure recall was 0.95 and was not markedly influenced by the subjects' sociodemographic characteristics, neurological or psychological status. In sum, the assumption in the literature that the daily diary is a reliable method for securing data on seizure counts appears warranted.

Seizures during barbiturate withdrawal: Relation to blood level

We studied 21 patients with complex partial seizures during phenobarbital (PB) or primidone withdrawal. Blood levels were measured daily, and seizure frequency was monitored by nursing staff and EEG-video telemetry. Patients were monitored for one week of baseline and for five weeks after PB tapering was initiated (withdrawal). Most were observed for at least one week after levels were undetectable. When ranked seizure counts were averaged, there was a tendency for seizure rates to be highest as PB levels passed through the range 15 to 20 mg/l, compared with rates at higher or lower PB levels. There was little or no relation between the rate of PB withdrawal, other drug therapy, or initial PB level and the ratio of highest seizure frequency to mean seizure frequency. Patients withdrawing from PB may be most likely to experience an increase in seizure frequency when their PB blood level falls below 20 mg/l.

An accurate assessment of the prevalence ratio of epilepsy adequately adjusted by influencing factors.

The prevalence of epilepsy was estimated by defining an initial prevalence ratio based on a population study and modifying this figure on the basis of various factors which influenced it. The definition required 3 seizures diagnosed by a doctor and the influencing factors included false-negative responses (where the diagnosis was confirmed), false reporting (where the diagnosis had not been established) and falsely low seizure counts (where therapy had reduced the number of seizure below the mandatory 3). As a result of these calculations the figure of approximately 1 in 50 was offered as a reliable and reasonable estimate of the true prevalence ratio of epilepsy within a well-defined Australian population.

A CATALOGUE OF R.C.S.'s PORTRAITS

Trials of antiseizure medications involve static group assignments for treatments with pre-specified durations. We propose a response-adaptive crossover design using basic statistical assumptions regarding both seizure count and duration of treatment to determine when a participant can change group assignment. We modelled seizure frequency as a Poisson process and estimated the likelihood that seizure frequency had decreased by 50% compares to baseline using both a Bayesian and maximum likelihood approach. We simulated trials to estimate the influence of this design on statistical power and observation duration with each treatment. For patients with 9 baseline seizures in 4 weeks who had no change in seizure frequency, the simulation identified non-response in a median of 16 days. The response-adaptive crossover design resulted in a modest increase in statistical power to identify an effective treatment while maximizing the time in a group producing a response. Only 8% of participants remained in the placebo group for all 90 days of the simulated trials. These example theoretical results can provide quantitative guidance regarding objective criteria to determine non-response in real-time during a controlled clinical trial without revealing the assigned treatment. Implementing a response-adaptive crossover design may both improve statistical power while minimizing participant risk.