Comparison of sample size formulae for 2x2 cross-over designs applied to bioequivalence studies

We consider the comparison of two formulations in terms of average bioequivalence using the 2 × 2 cross-over design. In a bioequivalence study, the primary outcome is a pharmacokinetic measure, such as the area under the plasma concentration by time curve, which is usually assumed to have a lognormal distribution. The criterion typically used for claiming bioequivalence is that the 90% confidence interval for the ratio of the means should lie within the interval (0.80, 1.25), or equivalently the 90% confidence interval for the differences in the means on the natural log scale should be within the interval (-0.2231, 0.2231). We compare the gold standard method for calculation of the sample size based on the non-central t distribution with those based on the central t and normal distributions. In practice, the differences between the various approaches are likely to be small. Further approximations to the power function are sometimes used to simplify the calculations. These approximations should be used with caution, because the sample size required for a desirable level of power might be under- or overestimated compared to the gold standard method. However, in some situations the approximate methods produce very similar sample sizes to the gold standard method. Copyright © 2005 John Wiley & Sons, Ltd.

A case study of sample design for longitudinal research: young lives

This paper presents a case study to illustrate the range of decisions involved in designing a sampling strategy for a complex, longitudinal research study. It is based on experience from the Young Lives project and identifies the approaches used to sample children for longitudinal follow-up in four less developed countries (LDCs). The rationale for decisions made and the resulting benefits, and limitations, of the approaches adopted are discussed. Of particular importance is the choice of sampling approach to yield useful analysis; specific examples are presented of how this informed the design of the Young Lives sampling strategy.

Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

Survival, Pb-uptake and behaviour of three species of earthworm in Pb treated soils determined using an OECD-style toxicity test and a soil avoidance test

Mature (clitellate) Eisenia andrei Bouche (ultra epigeic), Lumbricus rubellus Hoffmeister (epigeic), and Aporrectodea caliginosa (Savigny) (endogeic) earthworms were placed in soils treated with Pb(NO3)(2) to have concentrations in the range 1000 to 10 000 mg Pb kg(-1). After 28 days LC50(-95%confidence limit) (+95%confidence limit) values were E. andrei 5824(-361)(+898) mg Pb kg(-1), L. rubellus 2867(-193)(+145) mg Pb kg(-1) and A. caliginosa 2747(-304)(+239) mg Pb kg(-1) and EC50s for weight change were E. andrei 2841(-68)(+150) Pb kg(-1), L. rubellus 1303(-201)(+204) mg Pb kg(-1) and A. caliginosa 1208(-206)(+212) Mg Pb kg(-1). At any given soil Pb concentration, Pb tissue concentrations after 28 days were the same for all three earthworm species. In a soil avoidance test there was no difference between the behaviour of the different species. The lower sensitivity to Pb exhibited by E. andrei is most likely due to physiological adaptations associated with the modes of life of the earthworms, and could have serious implications for the use of this earthworm as the species of choice in standard toxicological testing. (c) 2005 Elsevier Ltd. All rights reserved.

Donepezil for the symptomatic treatment of patients with mild to moderate Alzheimer's disease: a meta-analysis of individual patient data from randomised controlled trials

Background: The objective was to evaluate the efficacy and tolerability of donepezil (5 and 10 mg/day) compared with placebo in alleviating manifestations of mild to moderate Alzheimer's disease (AD). Method: A systematic review of individual patient data from Phase II and III double-blind, randomised, placebo-controlled studies of up to 24 weeks and completed by 20 December 1999. The main outcome measures were the ADAS-cog, the CIBIC-plus, and reports of adverse events. Results: A total of 2376 patients from ten trials were randomised to either donepezil 5 mg/day (n = 821), 10 mg/day (n = 662) or placebo (n = 893). Cognitive performance was better in patients receiving donepezil than in patients receiving placebo. At 12 weeks the differences in ADAS-cog scores were 5 mg/day-placebo: - 2.1 [95% confidence interval (CI), - 2.6 to - 1.6; p < 0.001], 10 mg/day-placebo: - 2.5 ( - 3.1 to - 2.0; p < 0.001). The corresponding results at 24 weeks were - 2.0 ( - 2.7 to - 1.3; p < 0.001) and - 3.1 ( - 3.9 to - 2.4; p < 0.001). The difference between the 5 and 10 mg/day doses was significant at 24 weeks (p = 0.005). The odds ratios (OR) of improvement on the CIBIC-plus at 12 weeks were: 5 mg/day-placebo 1.8 (1.5 to 2.1; p < 0.001), 10 mg/day-placebo 1.9 (1.5 to 2.4; p < 0.001). The corresponding values at 24 weeks were 1.9 (1.5 to 2.4; p = 0.001) and 2.1 (1.6 to 2.8; p < 0.001). Donepezil was well tolerated; adverse events were cholinergic in nature and generally of mild severity and brief in duration. Conclusion: Donepezil (5 and 10 mg/day) provides meaningful benefits in alleviating deficits in cognitive and clinician-rated global function in AD patients relative to placebo. Increased improvements in cognition were indicated for the higher dose. Copyright © 2004 John Wiley & Sons, Ltd.

Psychiatric disorders in children with autism spectrum disorders: prevalence, comorbidity, and associated factors in a population-derived sample

Objective: Autism spectrum disorders are now recognized to occur in up to 1% of the population and to be a major public health concern because of their early onset, lifelong persistence, and high levels of associated impairment. Little is known about the associated psychiatric disorders that may contribute to impairment. We identify the rates and type of psychiatric comorbidity associated with ASDs and explore the associations with variables identified as risk factors for child psychiatric disorders. Method: A subgroup of 112 ten- to 14-year old children from a population-derived cohort was assessed for other child psychiatric disorders (3 months' prevalence) through parent interview using the Child and Adolescent Psychiatric Assessment. DSM-IV diagnoses for childhood anxiety disorders, depressive disorders, oppositional defiant and conduct disorders, attention-deficit/hyperactivity disorder, tic disorders, trichotillomania, enuresis, and encopresis were identified. Results: Seventy percent of participants had at least one comorbid disorder and 41% had two or more. The most common diagnoses were social anxiety disorder (29.2%, 95% confidence interval [CI)] 13.2-45.1), attention-deficit/hyperactivity disorder (28.2%, 95% CI 13.3-43.0), and oppositional defiant disorder (28.1%, 95% CI 13.9-42.2). Of those with attention/deficit/hyperactivity disorder, 84% received a second comorbid diagnosis. There were few associations between putative risk factors and psychiatric disorder. Conclusions: Psychiatric disorders are common and frequently multiple in children with autism spectrum disorders. They may provide targets for intervention and should be routinely evaluated in the clinical assessment of this group.

The prevalence and nature of prescribing and monitoring errors in English general practice – a retrospective case note review

Objective To determine the prevalence and nature of prescribing and monitoring errors in general practices in England. Design Retrospective case note review of unique medication items prescribed over a 12 month period to a 2% random sample of patients. Mixed effects logistic regression was used to analyse the data. Setting Fifteen general practices across three primary care trusts in England. Data sources Examination of 6048 unique prescription items prescribed over the previous 12 months for 1777 patients. Main outcome measures Prevalence of prescribing and monitoring errors, and severity of errors, using validated definitions. Results Prescribing and/or monitoring errors were detected in 4.9% (296/6048) of all prescription items (95% confidence interval 4.4 - 5.5%). The vast majority of errors were of mild to moderate severity, with 0.2% (11/6048) of items having a severe error. After adjusting for covariates, patient-related factors associated with an increased risk of prescribing and/or monitoring errors were: age less than 15 (Odds Ratio (OR) 1.87, 1.19 to 2.94, p=0.006) or greater than 64 years (OR 1.68, 1.04 to 2.73, p=0.035), and higher numbers of unique medication items prescribed (OR 1.16, 1.12 to 1.19, p<0.001). Conclusion Prescribing and monitoring errors are common in English general practice, although severe errors are unusual. Many factors increase the risk of error. Having identified the most common and important errors, and the factors associated with these, strategies to prevent future errors should be developed based on the study findings.

Do early father–infant interactions predict the onset of externalising behaviours in young children? Findings from a longitudinal cohort study

Background Factors related to parents and parenting capacities are important predictors of the development of behavioural problems in children. Recently, there has been an increasing research focus in this field on the earliest years of life, however, relatively few studies have addressed the role of fathers, despite this appearing to be particularly pertinent to child behavioural development. This study aimed to examine whether father–infant interactions at age 3 months independently predicted child behavioural problems at 1 year of age. Method A sample of 192 families was recruited from two maternity units in the United Kingdom. Father–infant interactions were assessed in the family home and coded using the Global Rating Scales. Child behaviour problems were assessed by maternal report. Hierarchical and logistic regression analyses were used to examine associations between father–infant interaction and the development of behavioural problems. Results Disengaged and remote interactions between fathers and their infants were found to predict externalising behavioural problems at the age of 1 year. The children of the most disengaged fathers had an increased risk of developing early externalising behavioural problems [disengaged (nonintrusive) interactions – adjusted Odds Ratio 5.33 (95% Confidence Interval; 1.39, 20.40): remote interactions adj. OR 3.32 (0.92, 12.05)] Conclusions Disengaged interactions of fathers with their infants, as early as the third month of life, predict early behavioural problems in children. These interactions may be critical factors to address, from a very early age in the child’s life, and offer a potential opportunity for preventive intervention.