Many chronic conditions, such as epilepsy and asthma, are typified by recurrent events—repeated acute deterioration events of a similar type. Statistical models for these conditions often focus on evaluating the time to the first event. They therefore do not make use of data available on all events. Statistical models for recurrent events exist, but it is not clear how best to evaluate their performance. We compare the relative performance of statistical models for analysing recurrent events for epilepsy and asthma. We studied two clinical exemplars of common and infrequent events: asthma exacerbations using the Optimum Patient Clinical Research Database, and epileptic seizures using data from the Standard versus New Antiepileptic Drug Study. In both cases, count-based models (negative binomial and zero-inflated negative binomial) and variants on the Cox model (Andersen-Gill and Prentice, Williams and Peterson) were used to assess the risk of recurrence (of exacerbations or seizures respectively). Performance of models was evaluated via numerical (root mean square prediction error, mean absolute prediction error, and prediction bias) and graphical (calibration plots and Bland–Altman plots) approaches. The performance of the prediction models for asthma and epilepsy recurrent events could be evaluated via the selected numerical and graphical measures. For both the asthma and epilepsy exemplars, the Prentice, Williams and Peterson model showed the closest agreement between predicted and observed outcomes. Inappropriate models can lead to incorrect conclusions which disadvantage patients. Therefore, prediction models for outcomes associated with chronic conditions should include all repeated events. Such models can be evaluated via the promoted numerical and graphical approaches alongside modified calibration measures.

Recent innovations in evidence based medicine methods, in particular instruments assessing risk of bias in randomised trials, have focused on methodological rigour at the expense of simplicity and practicability. Such a focus could lead to challenges in application and loss of reliability of instruments. To deal with these shortcomings, the Risk Of Bias instrument for Use in SysTematic reviews-for Randomised Controlled Trials (ROBUST-RCT) was created—a rigorously developed, simply structured, and user friendly instrument for assessing risk of bias of randomised controlled trials included in systematic reviews. This paper describes the development of ROBUST-RCT and provides associated documents and a manual of instructions.

Confidence in the justice system relies on it being both impartial and being seen to be impartial. It is therefore troubling that there are well-documented disparities between men and women and between ethnic groups at various stages of the criminal justice process. We report statistical analysis of existing data to (1) better understand the existing disparities, (2) investigate what information is available that might be useful in drawing a distinction between causation (discrimination) and association, (3) consider what statistical tools could be used to quantitatively investigate these relationships. Two datasets were investigated, looking at two different ends of the justice system. The first dataset describes the Metropolitan Police Force’s stop and search practices, an entry point into the criminal justice system. The second dataset describes sentencing, the final stage of that system, focusing on shoplifting offences dealt with by a sample of magistrates' courts.

ObjectiveTo evaluate the effectiveness of adjuvant levetiracetam in drug-resistant focal epilepsy. This is an update to the 2001 and 2012 reviews.MethodsThe search included the Cochrane Register of Studies and MEDLINE to 09/2018 for randomised, placebo-controlled trials of add-on levetiracetam in drug-resistant focal epilepsy. Two authors indepen- dently performed study selection, data extraction, and risk of bias assessments. Outcomes included≥50% reduction in seizure frequency (response) and adverse effects. We performed Mantel-Haenszel meta-analyses for risk ratios (RR), with 95% CI (99% for adverse effects). We assessed heterogeneity using I².ResultsThis update includes 14 trials (three more than the previous update), assessing 2,452 participants (296 children). Risks of bias were predominantly low. There were important levels of heterogeneity across multiple comparisons. There were two new findings: 1) Levetiracetam at either 500 mg/day or 4000 mg/day did not perform better than placebo for response (500 mg: RR 1.60, CI 0.71–3.62; 4000 mg: RR 1.64, CI 0.59–4.57). Levetiracetam was significantly better than placebo at all other individual doses (1000–3000 mg). 2) Odds of achieving response were increased by nearly 40% (odds ratio 1.39, CI 1.23–1.58) for each 1000 mg increase in dose of levetiracetam. Somnolence remained the most common adverse effect, and changes in behaviour were negligible overall.ConclusionsIt seems reasonable to continue using levetiracetam in drug-resistant focal epilepsy,10a2lthough a 500-mg dose may be no more effective than placebo.mbizvogkm@gmail.com

Background Nausea and vomiting are experienced by most women during pregnancy. The onset is usually related to Last Menstrual Period (LMP) the date of which is often unreliable. This study describes the time to onset of nausea and vomiting symptoms from date of ovulation and compares this to date of last menstrual period Methods Prospective cohort of women seeking to become pregnant, recruited from 12 May 2014 to 25 November 2016, in the United Kingdom. Daily diaries of nausea and vomiting were kept by 256 women who were trying to conceive. The main outcome measure is the number of days from last menstrual period (LMP) or luteinising hormone surge until onset of nausea or vomiting. Results Almost all women (88%) had Human Chorionic Gonadotrophin rise within 8 to 10 days of ovulation; the equivalent interval from LMP was 20 to 30 days. Many (67%) women experience symptoms within 11 to 20 days of ovulation. Conclusions Onset of nausea and vomiting occurs earlier than previously reported and there is a narrow window for onset of symptoms. This indicates that its etiology is associated with a specific developmental stage at the foetal-maternal interface. Trial registration NCT01577147 . Date of registration 13 April 2012

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.

Discussion on the meeting on 'Signs and sizes: understanding and replicating statistical findings'

BackgroundNausea and vomiting in pregnancy is usually called ‘morning sickness’. This is felt by sufferers to trivialise the condition. Symptoms have been described as occurring both before and after noon, but daily symptom patterns have not been clearly described and statistically modelled to enable the term ‘morning sickness’ to be accurately analysed.AimTo describe the daily variation in nausea and vomiting symptoms during early pregnancy in a group of sufferers.Design and settingA prospective cohort study of females recruited from 15 May 2014 to 17 February 2017 by Swiss Precision Diagnostics (SPD) Development Company Limited, which was researching hormone levels in early pregnancy and extended its study to include the description of pregnancy symptoms.MethodDaily symptom diaries of nausea and vomiting were kept by females who were trying to conceive. They also provided daily urine samples, which when analysed enabled the date of ovulation to be determined. Data from 256 females who conceived during the first month of the study are included in this article. Daily symptom patterns and changes in daily patterns by week of pregnancy were modelled. Functional data analysis was used to produce estimated symptom probability functions.ResultsThere was a peak probability of nausea in the morning, a lower but sustained probability of nausea throughout the day, and a slight peak in the evening. Vomiting had a defined peak incidence in the morning.ConclusionReferring to nausea and vomiting in pregnancy as simply ‘morning sickness’ is inaccurate, simplistic, and therefore unhelpful.

BackgroundEpilepsy is an important neurological condition and drug resistance in epilepsy is particularly common in individuals with focal seizures. In this review, we summarise the current evidence regarding a new antiepileptic drug, levetiracetam, when used as add-on treatment for controlling drug-resistant focal epilepsy. This is an update to a Cochrane Review that was originally published in 2001.ObjectivesTo evaluate the effectiveness of levetiracetam, added on to usual care, in treating drug-resistant focal epilepsy.Search methodsWe searched the Cochrane Epilepsy Group's Specialized Register (August 2012), the Cochrane Central Register of Controlled Trials (CENTRAL, The Cochrane Library Issue 7, 2012), and MEDLINE (1946 to August week 1, 2012). We also contacted the manufacturers of levetiracetam and researchers in the field to seek any ongoing or unpublished trials.Selection criteriaRandomised, placebo-controlled trials of add-on levetiracetam treatment in people with drug-resistant focal epilepsy.Data collection and analysisTwo review authors independently selected trials for inclusion, assessed trials for bias, extracted data, and evaluated the overall quality of evidence. Outcomes investigated included 50% or greater reduction in focal seizure frequency (response); less than 50% reduction in focal seizure frequency (non-response); treatment withdrawal; adverse effects (including a specific analysis of changes in behaviour); cognitive effects and quality of life (QoL). Risk ratios (RR) with 95% confidence intervals (CIs) were used as measures of effect (99% CIs for adverse effects). Primary analyses were Intention-to-Treat (ITT). Dose response and inter-trial heterogeneity were evaluated in regression models.Main resultsEleven trials (1861 participants) were included. They predominantly possessed low risks of bias. Participants were adults in nine trials (1565 participants) and children in the remaining two trials (296 participants). The dose of levetiracetam tested was 1000 to 4000 mg/day in adults, and 60 mg/kg/day in children. Treatment ranged from 12 to 24 weeks. For the 50% or greater reduction in focal seizure frequency outcome, the RR was significantly in favour of levetiracetam at all doses. The naive estimates, ignoring dose, showed children (52% responded) as better responders than adults (39% responded) on levetiracetam. 25% of children and 16% of adults responded to placebo. The Number Needed to Treat for an additional beneficial outcome for children and adults was four (95% CI three to seven) and five (95% CI four to six), respectively. The significant levels of statistical heterogeneity between trials on adults precluded valid provision of an overall RR (ignoring dose). Results for the two trials that tested levetiracetam 2000 mg on adults were sufficiently similar to be combined to give an RR for 50% or greater reduction in focal seizure frequency of 4.91 (95% CI 2.75 to 8.77), with an RR of 0.68 (95% CI 0.60 to 0.77) for non-response. At this dose, 37% and 8% of adults were responders in the levetiracetam and placebo groups, respectively. Regression analysis demonstrated that much of the heterogeneity between adult trials was likely to be explained by different doses of levetiracetam tested and different years of trial publication. There was no evidence of statistical heterogeneity between trials on children. For these trials, the RR for 50% or greater reduction in focal seizure frequency was 1.91 (95% CI 1.38 to 2.63), with an RR of 0.68 (95% CI 0.56 to 0.81) for non-response. 27% of children responded. Participants were not significantly more likely to have levetiracetam withdrawn (RR 0.98; 95% CI 0.73 to 1.32 and RR 0.80; 95% CI 0.43 to 1.46 for adults and children, respectively). For adults, somnolence (RR 1.51; 99% CI 1.06 to 2.17) and infection (RR 1.76; 99% CI 1.03 to 3.02) were significantly associated with levetiracetam. Accidental injury was significantly associated with placebo (RR 0.60; 99% CI 0.39 to 0.92). No individual adverse effect was significantly associated with levetiracetam in children. Changes in behaviour were negligible in adults (1% affected; RR 1.79; 99% CI 0.59 to 5.41) but significant in children (23% affected; RR 1.90; 99% CI 1.16 to 3.11). Cognitive effect and QoL outcomes suggested that levetiracetam had a positive effect on cognition and some aspects of QoL in adults. In children, levetiracetam did not appear to alter cognitive function but there was evidence of worsening in certain aspects of child behaviour. The overall quality of evidence used was high.Authors' conclusionsThis update adds seven more trials to the original review, which contained four trials. At every dose analysed, levetiracetam significantly reduced focal seizure frequency relative to placebo. This indicates that levetiracetam can significantly reduce focal seizure frequency when it is used as an add-on treatment for both adults and children with drug-resistant focal epilepsy. As there was evidence of significant levels of statistical heterogeneity within this positive effect it is difficult to be precise about the relative magnitude of the effect. At a dose of 2000 mg, levetiracetam may be expected to be 3.9 times more effective than placebo; with 30% of adults being responders at this dose. At a dose of 60 mg/kg/day, levetiracetam may be expected to be 0.9 times more effective than placebo; with 25% of children being responders at this dose. When dose was ignored, children were better responders than adults by around 4% to 13%. The results grossly suggest that one child or adult may respond to levetiracetam for every four or five children or adults, respectively, that have received levetiracetam rather than placebo. The drug seems to be well tolerated in both adults and children although non-specific changes in behaviour may be experienced in as high as 20% of children. This aspect of the adverse-effect profile of levetiracetam was analysed crudely and requires further investigation and validation. It seems reasonable to continue the use of levetiracetam in both adults and children with drug-resistant focal epilepsy. The results cannot be used to confirm longer-term or monotherapy effects of levetiracetam or its effects on generalised seizures. The conclusions are largely unchanged from those in the original review. The most significant contribution of this update is the addition of paediatric data into the analysis.

Background The majority of people with epilepsy have a good prognosis and their seizures are controlled by a single antiepileptic drug. However, up to 20% of patients from population-based studies, and up to 30% from clinical series (not population-based), develop drug-resistant epilepsy, especially those with focal-onset seizures. In this review, we summarise the current evidence regarding topiramate, an antiepileptic drug first marketed in 1996, when used as an add-on treatment for drug-resistant focal epilepsy. This is an update of a Cochrane Review first published in 1999, and last updated in 2014. Objectives To evaluate the efficacy and tolerability of topiramate when used as an add-on treatment for people with drug-resistant focal epilepsy. Search methods For the latest update of this review we searched the following databases on 2 July 2018: Cochrane Register of Studies (CRS Web), which includes the Cochrane Epilepsy Group Specialized Register and the Cochrane Central Register of Controlled Trials (CENTRAL); MEDLINE (Ovid, 1946- ); ClinicalTriats.gov and the WHO International Clinical Trials Registry Platform (ICTRP). We imposed no language restrictions. We also contacted the manufacturers of topiramate and researchers in the field to identify any ongoing or unpublished studies. Selection criteria Randomised, placebo-controlled add-on trials of topiramate, recruiting people with drug-resistant focal epilepsy. Data collection and analysis Two review authors independently selected trials for inclusion and extracted the relevant data. We assessed the following outcomes: (1) 50% or greater reduction in seizure frequency; (2) seizure freedom; (3) treatment withdrawal (any reason); (4) adverse effects. Primary analyses were intention-to-treat (ITT), and summary risk ratios (RRs) with 95% confidence intervals (95% Cls) are presented. We evaluated dose-response in regression models. We carried out a 'Risk of bias' assessment for each included study using the Cochrane 'Risk of bias' tool and assessed the overall certainty of evidence using the GRADE approach. Main results We included 12 trials, representing 1650 participants. Baseline phases ranged from four to 12 weeks and double-blind phases ranged from 11 to 19 weeks. The RR for a 50% or greater reduction in seizure frequency with add-on topiramate compared to placebo was 2.71 (95% CI 2.05 to 3.59; 12 studies; high-certainty evidence). Dose regression analysis showed increasing effect with increasing topiramate dose demonstrated by an odds ratio (OR) of 1.45 (95% CI 1.28 to 1.64; P < 0.001) per 200 mg/d increase in topiramate dosage. The proportion of participants achieving seizure freedom was also significantly increased with add-on topiramate compared to placebo (RR 3.67, 95% CI 1.79 to 7.54; 8 studies; moderate-certainty evidence). Treatment withdrawal was significantly higher for add-on topiramate compared to placebo (RR 2.37, 95% CI 1.66 to 3.37; 12 studies; high-certainty evidence). The RRs for the following adverse effects indicate that they are significantly more prevalent with topiramate, compared to placebo: ataxia 2.29 (99% CI 1.10 to 4.77; 4 studies); concentration difficulties 7.81(99% CI 2.08 to 29.29; 6 studies; moderate-certainty evidence); dizziness 1.52 (99% CI 1.07 to 2.16; 8 studies); fatigue 2.08 (99% CI 1.37 to 3.15; 10 studies); paraesthesia 3.65 (99% CI 1.58 to 8.39; 7 studies; moderate-certainty evidence); somnolence 2.44 (99% CI 1.61 to 3.68; 9 studies); 'thinking abnormally' 5.70 (99% CI 2.26 to 14.38; 4 studies; high-certainty evidence); and weight loss 3.99 (99% CI 1.82 to 8.72; 9 studies; low-certainty evidence). Evidence of publication bias for the primary outcome was found (Egger test, P = 0.001). We rated all studies included in the review as having either low or unclear risk of bias. Overall, we assessed the evidence as moderate to high certainty due to the evidence of publication bias, statistical heterogeneity and imprecision, which was partially compensated for by large effect sizes. Authors' conclusions Topiramate has efficacy as an add-on treatment for drug-resistant focal epilepsy as it is almost three times more effective compared to a placebo in reducing seizures. The trials reviewed were of relatively short duration and provided no evidence for the long-term efficacy of topiramate. Short-term use of add-on topiramate was shown to be associated with several adverse events. The results of this review should only be applied to adult populations as only one study included children. Future research should consider further examining the effect of dose.

My experience with forensic statistics is largely through providing reports for civil cases. This article introduces the type of cases with which I have been involved, and the issues which have arisen, in a few jurisdictions. I wish to encourage more involvement, and debate on the contribution statistics might make in civil litigation, and what might be learned from criminal forensic statistics.

AimHyperkinetic movement disorders (HMDs) can be assessed using impairment-based scales or functional classifications. The Burke-Fahn-Marsden Dystonia Rating Scale-movement (BFM-M) evaluates dystonia impairment, but may not reflect functional ability. The Gross Motor Function Classification System (GMFCS), Manual Ability Classification System (MACS), and Communication Function Classification System (CFCS) are widely used in the literature on cerebral palsy to classify functional ability, but not in childhood movement disorders. We explore the concordance of these three functional scales in a large sample of paediatric HMDs and the impact of dystonia severity on these scales.MethodChildren with HMDs (n=161; median age 10y 3mo, range 2y 6mo-21y) were assessed using the BFM-M, GMFCS, MACS, and CFCS from 2007 to 2013. This cross-sectional study contrasts the information provided by these scales.ResultsAll four scales were strongly associated (all Spearman's rank correlation coefficient r(s)>0.72, p<0.001), with worse dystonia severity implying worse function. Secondary dystonias had worse dystonia and less function than primary dystonias (p<0.001). A longer proportion of life lived with dystonia is associated with more severe dystonia (r(s)=0.42, p<0.001).InterpretationThe BFM-M is strongly linked with the GMFCS, MACS, and CFCS, irrespective of aetiology. Each scale offers interrelated but complementary information and is applicable to all aetiologies. Movement disorders including cerebral palsy can be effectively evaluated using these scales.

We propose a unified approach for multilevel sample selection models using a generalized result on skew distributions arising from selection. If the underlying distributional assumption is normal, then the resulting density for the outcome is the continuous component of the sample selection density and has links with the closed skew-normal distribution (CSN). The CSN distribution provides a framework which simplifies the derivation of the conditional expectation of the observed data. This generalizes the Heckman's two-step method to a multilevel sample selection model. Finite-sample performance of the maximum likelihood estimator of this model is studied through a Monte Carlo simulation.

Non‐random sampling is a source of bias in empirical research. It is common for the outcomes of interest (e.g. wage distribution) to be skewed in the source population. Sometimes, the outcomes are further subjected to sample selection, which is a type of missing data, resulting in partial observability. Thus, methods based on complete cases for skew data are inadequate for the analysis of such data and a general sample selection model is required. Heckman proposed a full maximum likelihood estimation method under the normality assumption for sample selection problems, and parametric and non‐parametric extensions have been proposed. We generalize Heckman selection model to allow for underlying skew‐normal distributions. Finite‐sample performance of the maximum likelihood estimator of the model is studied via simulation. Applications illustrate the strength of the model in capturing spurious skewness in bounded scores, and in modelling data where logarithm transformation could not mitigate the effect of inherent skewness in the outcome variable.

Singpurwalla addresses the important challenge of modelling a unique individual. He proposes "propensity" as an approach to describing the reliability or life time of "one of a kind". My view is that mathematical modelling is only possible when we assume that nonunique features provide sufficient information for statistical prediction to be useful. As far as possible, we should test our assumptions. However, contrary to a popular perception of Hume, we always rely on some beliefs.