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Stepped wedge and cluster randomised crossover trials are examples of cluster randomised designs conducted over multiple time periods that are being used with increasing frequency in health research. Recent systematic reviews of both of these designs indicate that the within-cluster correlation is typically taken account of in the analysis of data using a random intercept mixed model, implying a constant correlation between any two individuals in the same cluster no matter how far apart in time they are measured: within-period and between-period intra-cluster correlations are assumed to be identical. Recently proposed extensions allow the within- and between-period intra-cluster correlations to differ, although these methods require that all between-period intra-cluster correlations are identical, which may not be appropriate in all situations. Motivated by a proposed intensive care cluster randomised trial, we propose an alternative correlation structure for repeated cross-sectional multiple-period cluster randomised trials in which the between-period intra-cluster correlation is allowed to decay depending on the distance between measurements. We present results for the variance of treatment effect estimators for varying amounts of decay, investigating the consequences of the variation in decay on sample size planning for stepped wedge, cluster crossover and multiple-period parallel-arm cluster randomised trials. We also investigate the impact of assuming constant between-period intra-cluster correlations instead of decaying between-period intra-cluster correlations. Our results indicate that in certain design configurations, including the one corresponding to the proposed trial, a correlation decay can have an important impact on variances of treatment effect estimators, and hence on sample size and power. An R Shiny app allows readers to interactively explore the impact of correlation decay. [ABSTRACT FROM AUTHOR]

Background: In order to obtain a measure of nutrient intake, a measure or estimate of the amount of food consumed is required. Weighing foods imposes a large burden on subjects, often resulting in underreporting. Tools are available to assist subjects in providing an estimate of portion size and these include food photographs. The application of these tools in improving portion size estimation by children has not been investigated systematically.Objectives: To assess the accuracy with which children are able to estimate food portion sizes using food photographs designed for use with adults, and to determine whether the accuracy of estimates is improved when age-appropriate portion size photographs are provided.Design: Original data from three separate studies, on the accuracy of portion size estimates by adults using food photographs, by children using adult photographs and by children using age-appropriate photographs, are analysed and compared.Subjects: One hundred and thirty-five adults aged 18 to 90 years and 210 children aged 4 to 11 years.Results: Children's estimates of portion sizes using age-appropriate food photographs were significantly more accurate (an underestimate of 1% on average) than estimates using photographs designed for use with adults (an overestimate of 45% on average). Accuracy of children's estimates of portion size using age-appropriate photographs was not significantly different from that of adults. Children overestimated a food's weight by 18% on average and adults underestimated by 5%.Conclusions: Providing children with food photographs depicting age-appropriate portion sizes greatly increases the accuracy of portion size estimates compared with estimates using photographs designed for use with adults. [ABSTRACT FROM AUTHOR]

The importance of education in the management of diabetes is recognised but has rarely been assessed in children. In a longitudinal controlled study we have examined the effect of a programme of education on the knowledge, diet, and concentration of glycated haemoglobin A1c in a group of diabetics. The programme took the form of two packages of education each consisting of four weekly meetings, in which small groups of parents and older children were led in a discussion of different aspects of diabetes. Only one of the 119 families who began the study failed to complete it. Family knowledge about diabetes improved as a result of the programme, although this was poorly retained in the fathers. A trend to improvement in several aspects of diet was noted but did not reach significance. A significant fall in glycated haemoglobin A1c was apparent seven months after the education in children aged 11 years and over. Those whose initial control was poor improved most. We conclude that such meetings should be considered as a useful adjunct to regular diabetic clinics. [ABSTRACT FROM AUTHOR]

Rapid and reliable determination of blood glucose concentration is essential during the neonatal period to prevent adverse neurodevelopmental outcome from hypoglycaemia. Despite their unreliability, reagent strip methods continue to be used extensively in neonatal nurseries due to their rapidity and convenience. Recently, a new portable laboratory standard technique has been introduced (HemoCue B-Glucose system) for whole blood glucose determination. It is particularly suitable for near-patient testing in neonatal units. This new method, as well as other established methods of whole blood (Yellow Springs Instrument (YSI) and a hexokinase method on Cobas Bio), and plasma (Kodak Ektachem) glucose measurement, were therefore evaluated for their accuracy and concordance of measurements taken in the neonatal period. There were substantial discrepancies among the four methods of glucose measurement with wide limits of agreement between these methods. The glucose concentrations measured by HemoCue and YSI (n = 206), HemoCue and hexokinase (n = 113), HemoCue and plasma glucose on Ektachem (n = 69) and hexokinase and Ektachem (n = 66) were likely to differ by -29 to +61%, -23 to +56%, -36 to +65%, and -19 to +30%, respectively. Even the laboratory methods of blood glucose determination, therefore, can not be used interchangeably. Using a model based approach, the probabilities of "discordant" classification as hypo- or normo-glycaemia were estimated to be 6.8%, 6.5%, and 7.1% between HemoCue and YSI, HemoCue and hexokinase on Cobas Bio, and HemoCue and Ektachem analysers, respectively. In view of these low probabilities of discordant classification with other glucose analysers, the HemoCue system may offer a reasonable compromise between bedside and laboratory blood glucose estimations in neonates. [ABSTRACT FROM AUTHOR]

Background: Pathogenic mitochondrial DNA (mtDNA) mutations are found in at least one in 8000 individuals. No effective treatment for mtDNA disorders is available, making disease prevention important. Many patients with mtDNA disease harbour a single pathogenic mtDNA deletion, but the risk factors for new cases and disease recurrence are not known.Methods: We did a multicentre study of 226 families in which a single mtDNA deletion had been identified in the proband, including patients with chronic progressive external ophthalmoplegia, Kearns Sayre syndrome, or Pearson's syndrome. We studied the relation between maternal age and the risk of unaffected mothers having an affected child, and determined the recurrence risks among the siblings and offspring of affected individuals.Findings: We noted no relation between maternal age and the risk of unaffected mothers having children with an mtDNA deletion disorder. None of the 251 siblings of the index cases developed clinical features of mtDNA disease. Risk of recurrence among the offspring of affected women was 4.11% (95% CI 0.86-11.54, or one in 117 to one in nine births). Only one of the mothers who had an affected child had a duplication of mtDNA in skeletal muscle.Interpretation: Unlike nuclear chromosomal rearrangements, incidence of mtDNA deletion disorders does not increase with maternal age, and unaffected mothers are unlikely to have more than one affected child. Affected women were previously thought to have a negligible chance of having clinically affected offspring, but the actual risk is, on average, about one in 24 births. [ABSTRACT FROM AUTHOR]

Background Pulmonary function tests are central to diagnosis and monitoring of respiratory diseases but do not provide information on regional lung function heterogeneity. Fluorine 19 ( 19 F) MRI of inhaled perfluoropropane permits quantitative and spatially localized assessment of pulmonary ventilation properties without tracer gas hyperpolarization. Purpose To assess regional lung ventilation properties using 19 F MRI of inhaled perfluoropropane in participants with asthma, participants with chronic obstructive pulmonary disease (COPD), and healthy participants, including quantitative evaluation of bronchodilator response in participants with respiratory disease. Materials and Methods This prospective, dual-center study included participants with asthma or COPD from July 2019 to September 2022 and healthy participants from May 2018 to June 2019. Participants underwent conventional spirometry, proton MRI, and 19 F MRI following inhalation of a 79% perfluoropropane and 21% oxygen gas mixture. Three-dimensional 19 F MRI scans were acquired during a single breath hold. For participants with asthma or COPD, spirometric and MRI measurements were repeated following administration of nebulized salbutamol. Ventilation defect percentage (VDP) was calculated from perfluoropropane distribution. Linear mixed-effects models were used to assess differences in VDP between participant groups and before and after bronchodilator administration. Results Thirty-five participants with asthma (mean age, 50 years ± 18 [SD]; 21 male participants), 21 participants with COPD (mean age, 69 years ± 6; 14 male participants), and 38 healthy participants (mean age, 41 years ± 11; 20 male participants) were evaluated. 19 F MRI-derived VDP was elevated in participants with COPD (geometric mean, 27.2%) and participants with asthma (geometric mean, 8.3%) compared with healthy participants (geometric mean, 1.8%; geometric mean ratio, 15.2 [95% CI: 11.1, 20.6] for COPD and 4.6 [95% CI: 3.2, 6.6] for asthma; P < .001 for both). After bronchodilator administration, VDP was reduced by 33% in participants with asthma (from 8.3% to 5.6%) and 14% in participants with COPD (from 27.2% to 23.3%; P < .001 for both). Conclusion 19 F MRI of inhaled perfluoropropane was sensitive to changes in regional ventilation properties associated with lung disease and enabled quantification of changes following bronchodilator therapy. Published under a CC BY-NC-ND 4.0 license. Supplemental material is available for this article. See also the editorial by Unger in this issue.

Complete case analyses of complete crossover designs provide an opportunity to make comparisons based on patients who can tolerate all treatments. It is argued that this provides a means of estimating a principal stratum strategy estimand, something which is difficult to do in parallel group trials. While some trial users will consider this a relevant aim, others may be interested in hypothetical strategy estimands, that is, the effect that would be found if all patients completed the trial. Whether these estimands differ importantly is a question of interest to the different users of the trial results. This paper derives the difference between principal stratum strategy and hypothetical strategy estimands, where the former is estimated by a complete-case analysis of the crossover design, and a model for the dropout process is assumed. Complete crossover designs, that is, those where all treatments appear in all sequences, and which compare t treatments over p periods with respect to a continuous outcome are considered. Numerical results are presented for Williams designs with four and six periods. Results from a trial of obstructive sleep apnoea-hypopnoea (TOMADO) are also used for illustration. The results demonstrate that the percentage difference between the estimands is modest, exceeding 5% only when the trial has been severely affected by dropouts or if the within-subject correlation is low., (© 2021 The Authors. Biometrics published by Wiley Periodicals LLC on behalf of International Biometric Society.)

Objectives: Renal replacement therapy (RRT) options are limited for small babies because of lack of available technology. We investigated the precision of ultrafiltration, biochemical clearances, clinical efficacy, outcomes, and safety profile for a novel non-Conformité Européenne-marked hemodialysis device for babies under 8 kg, the Newcastle Infant Dialysis Ultrafiltration System (NIDUS), compared with the current options of peritoneal dialysis (PD) or continuous venovenous hemofiltration (CVVH)., Design: Nonblinded cluster-randomized cross-sectional stepped-wedge design with four periods, three sequences, and two clusters per sequence., Setting: Clusters were six U.K. PICUs., Patients: Babies less than 8 kg requiring RRT for fluid overload or biochemical disturbance., Interventions: In controls, RRT was delivered by PD or CVVH, and in interventions, NIDUS was used. The primary outcome was precision of ultrafiltration compared with prescription; secondary outcomes included biochemical clearances., Measurements and Main Results: At closure, 97 participants were recruited from the six PICUs (62 control and 35 intervention). The primary outcome, obtained from 62 control and 21 intervention patients, showed that ultrafiltration with NIDUS was closer to that prescribed than with control: sd controls, 18.75, intervention, 2.95 (mL/hr); adjusted ratio, 0.13; 95% CI, 0.03-0.71; p = 0.018. Creatinine clearance was smallest and least variable for PD (mean, sd ) = (0.08, 0.03) mL/min/kg, larger for NIDUS (0.46, 0.30), and largest for CVVH (1.20, 0.72). Adverse events were reported in all groups. In this critically ill population with multiple organ failure, mortality was lowest for PD and highest for CVVH, with NIDUS in between., Conclusions: NIDUS delivers accurate, controllable fluid removal and adequate clearances, indicating that it has important potential alongside other modalities for infant RRT., Competing Interests: Drs. Lambert’s, Matthews’s, Holstein’s, Agbeko’s, Duncan’s, Mok’s, Ghose’s, Kennedy’s, McColl’s, Whitaker’s, Wightman’s, and Wilson’s institutions received funding from the U.K. National Institute for Health Research (NIHR) Efficacy and Mechanism Evaluation Program (EME). NIHR EME grant number 14/23/26 provided financial support to the organizations employing the co-authors except Mr. Boucher. Drs. Lambert, Coulthard, Holstein, Crosier, Duncan, Grant, Mok, Ghose, McColl, A. Steel, Smith, Whitaker, Wilson, and Wirz received support for article research from the NIHR EME. Drs. Lambert, Coulthard, Holstein, Agbeko, Duncan, Mok, Pappachan, Chisholm, Ghose, McColl, Parslow, Pattinson, A. Steel, Straker, Walker, Whitaker, Wightman, and Wood and Mr. Boucher disclosed the off-label product use of the Newcastle Infant Dialysis Ultrafiltration System (NIDUS) device. Dr. Coulthard disclosed that he is the inventor of the NIDUS device and is named on a patent submitted by Newcastle upon Tyne Hospitals NHS Trust. Dr. Coulthard has the possibility that he may receive royalties in the future from sales of the NIDUS. Mrs. Crosier disclosed the off-label product use of dialyzing babies less than 8 kg. Dr. McColl disclosed government work. Mr. Smith disclosed that he does medicolegal expert work in the field of pediatric anesthesia and PICU. Dr. Agbeko is editor for Archives of Disease in Childhood and received funding from BMJ Publishing. Dr. Lambert received Honorarium September 2022 for a case study presentation (not I-KID) at transplant educational event by Sandoz. Dr. Straker has medicolegal reports for court: none related to the area of pediatric dialysis/or dialysis devices and was the honorary treasurer of the European Extracorporeal Life Support Organisation until 2021. The remaining authors have disclosed that they do not have any potential conflicts of interest., (Copyright © 2023 The Author(s). Published by Wolters Kluwer Health, Inc. on behalf of the Society of Critical Care Medicine and the World Federation of Pediatric Intensive and Critical Care Societies.)

Limited research exists on the effectiveness of product placement in secondary schools. We explored the impact of re-positioning sweet-baked goods, fruit, sugar-sweetened beverages (SSBs) and water on pupil's lunchtime purchases in two secondary schools in North-East England. We employed a stepped-wedge design with two clusters and four time periods. The intervention(s) involved re-positioning selected food and drinks to increase and decrease accessibility of 'healthier' and 'less healthy' items, respectively. Unidentifiable smartcard data measured the change in number of pupil's purchasing the above items. McNemar tests were undertaken on paired nominal data in Stata(v15). In School A, pupils purchasing fruit pots from control to intervention increased ( n = 0 cf. n = 81; OR 0, 95% CI 0 to 0.04); post-intervention, this was not maintained. In School B, from control to intervention pupil's purchasing sweet-baked goods decreased ( n = 183 cf. n = 147; OR 1.2, 95% CI 1 to 1.6). This continued post-intervention ( n = 161 cf. n = 122; OR 1.3, 95% CI 1.0 to 1.7) and was similar for SSBs ( n = 180 cf. n = 79; OR 2.3, 95% CI 1.7 to 3.0). We found no evidence of other changes. There is some evidence that product placement may positively affect pupil's food and drink purchases. However, there are additional aspects to consider, such as, product availability, engaging canteen staff and the individual school context.

Context: Remission rates in young people with Graves hyperthyroidism are less than 25% after 2 years of thionamide antithyroid drug (ATD)., Objective: We explored whether rituximab (RTX), a B-lymphocyte-depleting agent, would increase remission rates when administered with a short course of ATD., Methods: This was an open-label, multicenter, single-arm, phase 2 trial in young people (ages, 12-20 years) with Graves hyperthyroidism. An A'Hern design was used to distinguish an encouraging remission rate (40%) from an unacceptable rate (20%). Participants presenting with Graves hyperthyroidism received 500 mg RTX and 12 months of ATD titrated according to thyroid function. ATDs were stopped after 12 months and primary outcome assessed at 24 months. Participants had relapsed at 24 months if thyrotropin was suppressed and free 3,5,3'-triiodothyronine was raised; they had received ATD between months 12 and 24; or they had thyroid surgery/radioiodine., Results: A total of 27 participants were recruited and completed the trial with no serious side effects linked to treatment. Daily carbimazole dose at 12 months was less than 5 mg in 21 of 27 participants. Thirteen of 27 participants were in remission at 24 months (48%, 90% one-sided CI, 35%-100%); this exceeded the critical value (9) for the A'Hern design and provided evidence of a promising remission rate. B-lymphocyte count at 28 weeks, expressed as a percentage of baseline, was related to likelihood of remission., Conclusion: Adjuvant RTX, administered with a 12-month course of ATD, may increase the likelihood of remission in young people with Graves hyperthyroidism. A randomized trial of adjuvant RTX in young people with Graves hyperthyroidism is warranted., (© The Author(s) 2021. Published by Oxford University Press on behalf of the Endocrine Society.)

Introduction: The I-KID study aims to determine the clinical efficacy, outcomes and safety of a novel non-CE-marked infant haemodialysis machine, the Newcastle Infant Dialysis Ultrafiltration System (NIDUS), compared with currently available therapy in the UK. NIDUS is specifically designed for renal replacement therapy in small babies between 0.8 and 8 kg., Methods and Analysis: The clinical investigation is taking place in six UK centres. This is a randomised clinical investigation using a cluster stepped-wedge design. The study aims to recruit 95 babies requiring renal replacement therapy in paediatric intensive care units over 20 months., Ethics and Dissemination: The study has high parent and public involvement at all stages in its design and parents will be involved in dissemination of results to parents and professionals via publications, conference proceedings and newsletters. The study has has ethics permissions from Tyne and Wear South Research Ethics Committee., Trial Registration Numbers: IRAS ID number: 170 481MHRA Reference: CI/2017/0066ISRCT Number: 13 787 486CPMS ID number: 36 558NHS REC reference: 16/NE/0008Eudamed number: CIV-GB-18-02-023105Link to full protocol v6.0: https://fundingawards.nihr.ac.uk/award/14/23/26., Competing Interests: Competing interests: Dr Malcolm Coulthard is named on the patent and will receive some royalties if the NIDUS device goes into commercial production. The Newcastle upon Tyne NHS Foundation Trust will receive some royalties if the NIDUS device goes into commercial production.Allmed, the device manufacturers, are providing 17 NIDUS devices for loan to sites for the I-KID study and for potential compassionate use in the post-study period. NIDUS consumables are purchased as per normal clinical care. The rest of the authors have completed the COI form and have no competing interests to declare., (© Author(s) (or their employer(s)) 2021. Re-use permitted under CC BY. Published by BMJ.)

Purpose: To assess the reproducibility of percentage ventilated lung volume (%VV) measurements in healthy volunteers acquired by fluorine ( 19 F)-MRI of inhaled perfluoropropane, implemented at two research sites., Methods: In this prospective, ethically approved study, 40 healthy participants were recruited (May 2018-June 2019) to one of two research sites. Participants underwent a single MRI scan session on a 3T scanner, involving periodic inhalation of a 79% perfluoropropane/21% oxygen gas mixture. Each gas inhalation session lasted about 30 seconds, consisting of three deep breaths of gas followed by a breath-hold. Four 19 F-MR ventilation images were acquired per participant, each separated by approximately 6 minutes. The value of %VV was determined by registering separately acquired 1 H images to ventilation images before semi-automated image segmentation, performed independently by two observers. Reproducibility of %VV measurements was assessed by components of variance, intraclass correlation coefficients, coefficients of variation (CoV), and the Dice similarity coefficient., Results: The MRI scans were well tolerated throughout, with no adverse events. There was a high degree of consistency in %VV measurements for each participant (CoV observer1 = 0.43%; CoV observer2 = 0.63%), with overall precision of %VV measurements determined to be within ± 1.7% (95% confidence interval). Interobserver agreement in %VV measurements revealed a high mean Dice similarity coefficient (SD) of 0.97 (0.02), with only minor discrepancies between observers., Conclusion: We demonstrate good reproducibility of %VV measurements in a group of healthy participants using 19 F-MRI of inhaled perfluoropropane. Our methods have been successfully implemented across two different study sites, supporting the feasibility of performing larger multicenter clinical studies., (© 2021 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals LLC on behalf of International Society for Magnetic Resonance in Medicine.)

Background: Technology has advanced bringing new cost-effective methods to measure food intake. The aim of the study was to compare food and drink portion estimates from a traditional portion estimation method using 3D food models with portion estimates using an online dietary recall tool, Intake24., Methods: 11-12 year old children were recruited from secondary schools in Newcastle upon Tyne. Each pupil completed a two-day food diary followed by an interview during which pupils estimated food portion sizes using a range of 3D food models. They also completed Intake24 for the same 2 days. Bland Altman analyses were used to compare mean intake for each method., Results: Seventy pupils completed both portion estimation methods. There was good agreement in food weight estimations between the two methods (geometric mean ratio 1.00), with limits of agreement ranging from minus 35% to plus 53%. Intake24 provided estimates of energy intake that were 1% lower on average than estimates of energy intake using the food models. Mean intakes of all macro and micronutrients using Intake24 were within 6% of the food model estimates., Conclusions: The findings suggest that there was little difference in portion estimations from the two methods, allowing comparisons to be made between Intake24 data and food diary data collected from same age pupils using 3D food models in previous years.

Objective: First-line treatment of thyrotoxicosis in young people is thionamide anti-thyroid drug (ATD) in a blocking dose with levothyroxine replacement (block and replace, BR) or in a smaller dose tailored to render the patient euthyroid (dose titration, DT). Our objective was to determine which regimen provides more stable biochemical control., Design: A multi-centre phase III, open-label randomised trial comparing BR with DT in patients aged 2-17 years with newly diagnosed thyrotoxicosis at 15 UK centres., Methods: Patients were randomised shortly after diagnosis and treated for 3 years. The primary outcome was the percentage of serum thyroid-stimulating hormone (TSH) levels in the reference range between 6 months and 3 years. Secondary outcomes included the proportion of Free thyroxine (FT4) levels in the reference range, adverse event frequency and 4 years outcome (remission/relapse)., Results: Eighty-two patients were randomised, with details on clinical course in 81 (62 Female); 40 were allocated to BR (41 DT). Three withdrew with one ineligible. The mean percentage of serum TSH within reference range was 60.2% in BR and 63.8% in DT patients; adjusted difference 4.3%, 95% CI (-7.8 to 16.4); P = 0.48. Proportions for FT4 were 79.2% in BR and 85.7% in DT patients; adjusted difference 6.8%, (-0.2 to 15.6); P = 0.13. Three patients developed neutropenia - all on BR. 6 BR and 10 DT patients were in remission at 4y., Conclusion: This randomised trial has shown no evidence to suggest that BR, when managing the young patient with thyrotoxicosis, is associated with improved biochemical stability when compared to DT.

The stepped wedge design (SWD) is a form of cluster randomized trial, usually comparing two treatments, which is divided into time periods and sequences, with clusters allocated to sequences. Typically all sequences start with the standard treatment and end with the new treatment, with the change happening at different times in the different sequences. The clusters will usually differ in size but this is overlooked in much of the existing literature. This paper considers the case when clusters have different sizes and determines how efficient designs can be found. The approach uses an approximation to the variance of the treatment effect, which is expressed in terms of the proportions of clusters and of individuals allocated to each sequence of the design. The roles of these sets of proportions in determining an efficient design are discussed and illustrated using two SWDs, one in the treatment of sexually transmitted diseases and one in renal replacement therapy. Cluster-balanced designs, which allocate equal numbers of clusters to each sequence, are shown to have excellent statistical and practical properties; suggestions are made about the practical application of the results for these designs. The paper concentrates on the cross-sectional case, where subjects are measured once, but it is briefly indicated how the methods can be extended to the closed-cohort design., (© 2020 The International Biometric Society.)

Purpose: To report the vitamin D status in adults from seven European countries and to identify behavioural correlates., Methods: In total, 1075 eligible adult men and women from Ireland, Netherlands, Spain, Greece, UK, Poland and Germany, were included in the study., Results: Vitamin D deficiency and insufficiency, defined as 25-hydroxy vitamin D 3 (25-OHD 3 ) concentration of <30 and 30-49.9 nmol/L, respectively, were observed in 3.3 and 30.6% of the participants. The highest prevalence of vitamin D deficiency was found in the UK and the lowest in the Netherlands (8.2 vs. 1.1%, P < 0.05). In addition, the prevalence of vitamin D insufficiency was higher in females compared with males (36.6 vs. 22.6%, P < 0.001), in winter compared with summer months (39.3 vs. 25.0%, P < 0.05) and in younger compared with older participants (36.0 vs. 24.4%, P < 0.05). Positive dose-response associations were also observed between 25-OHD 3 concentrations and dietary vitamin D intake from foods and supplements, as well as with physical activity (PA) levels. Vitamin D intakes of ≥5 μg/day from foods and ≥5 μg/day from supplements, as well as engagement in ≥30 min/day of moderate- and vigorous-intensity PA were associated with higher odds (P < 0.05) for maintaining sufficient (≥50 nmol/L) 25-OHD 3 concentrations., Conclusions: The prevalence of vitamin D deficiency varied considerably among European adults. Dietary intakes of ≥10 μg/day of vitamin D from foods and/or supplements and at least 30 min/day of moderate- and vigorous-intensity PA were the minimum thresholds associated with vitamin D sufficiency.

Stepped wedge designs (SWDs) have received considerable attention recently, as they are potentially a useful way to assess new treatments in areas such as health services implementation. Because allocation is usually by cluster, SWDs are often viewed as a form of cluster-randomized trial. However, since the treatment within a cluster changes during the course of the study, they can also be viewed as a form of crossover design. This article explores SWDs from the perspective of crossover trials and designed experiments more generally. We show that the treatment effect estimator in a linear mixed effects model can be decomposed into a weighted mean of the estimators obtained from (1) regarding an SWD as a conventional row-column design and (2) a so-called vertical analysis, which is a row-column design with row effects omitted. This provides a precise representation of "horizontal" and "vertical" comparisons, respectively, which to date have appeared without formal description in the literature. This decomposition displays a sometimes surprising way the analysis corrects for the partial confounding between time and treatment effects. The approach also permits the quantification of the loss of efficiency caused by mis-specifying the correlation parameter in the mixed-effects model. Optimal extensions of the vertical analysis are obtained, and these are shown to be highly inefficient for values of the within-cluster dependence that are likely to be encountered in practice. Some recently described extensions to the classic SWD incorporating multiple treatments are also compared using the experimental design framework., (Copyright © 2017 John Wiley & Sons, Ltd.)