Stepped wedge designs: insights from a design of experiments perspective.

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.

Inconsistent treatment estimates from mis-specified logistic regression analyses of randomized trials.

When the difference between treatments in a clinical trial is estimated by a difference in means, then it is well known that randomization ensures unbiassed estimation, even if no account is taken of important baseline covariates. However, when the treatment effect is assessed by other summaries, for example by an odds ratio if the outcome is binary, then bias can arise if some covariates are omitted, regardless of the use of randomization for treatment allocation or the size of the trial. We present accurate closed-form approximations for this asymptotic bias when important normally distributed covariates are omitted from a logistic regression. We compare this approximation with ones in the literature and derive more convenient forms for some of these existing results. The expressions give insight into the form of the bias, which simulations show is usable for distributions other than the normal. The key result applies even when there are additional binary covariates in the model.

Comparison of analgesic effects and patient tolerability of nabilone and dihydrocodeine for chronic neuropathic pain: randomised, crossover, double blind study.

OBJECTIVE: To compare the analgesic efficacy and side effects of the synthetic cannabinoid nabilone with those of the weak opioid dihydrocodeine for chronic neuropathic pain. DESIGN: Randomised, double blind, crossover trial of 14 weeks' duration comparing dihydrocodeine and nabilone. SETTING: Outpatient units of three hospitals in the United Kingdom. PARTICIPANTS: 96 patients with chronic neuropathic pain, aged 23-84 years. MAIN OUTCOME MEASURES: The primary outcome was difference between nabilone and dihydrocodeine in pain, as measured by the mean visual analogue score computed over the last 2 weeks of each treatment period. Secondary outcomes were changes in mood, quality of life, sleep, and psychometric function. Side effects were measured by a questionnaire. INTERVENTION: Patients received a maximum daily dose of 240 mg dihydrocodeine or 2 mg nabilone at the end of each escalating treatment period of 6 weeks. Treatment periods were separated by a 2 week washout period. Results Mean baseline visual analogue score was 69.6 mm (range 29.4-95.2) on a 0-100 mm scale. 73 patients were included in the available case analysis and 64 patients in the per protocol analysis. The mean score was 6.0 mm longer for nabilone than for dihydrocodeine (95% confidence interval 1.4 to 10.5) in the available case analysis and 5.6 mm (10.3 to 0.8) in the per protocol analysis. Side effects were more frequent with nabilone. CONCLUSION: Dihydrocodeine provided better pain relief than the synthetic cannabinoid nabilone and had slightly fewer side effects, although no major adverse events occurred for either drug. TRIAL REGISTRATION: Current Controlled Trials ISRCTN15330757 controlled-trials.com] .

Children's estimates of food portion size: the development and evaluation of three portion size assessment tools for use with children.

A number of methods have been developed to assist subjects in providing an estimate of portion size but their application in improving portion size estimation by children has not been investigated systematically. The aim was to develop portion size assessment tools for use with children and to assess the accuracy of children's estimates of portion size using the tools. The tools were food photographs, food models and an interactive portion size assessment system (IPSAS). Children (n 201), aged 4-16 years, were supplied with known quantities of food to eat, in school. Food leftovers were weighed. Children estimated the amount of each food using each tool, 24 h after consuming the food. The age-specific portion sizes represented were based on portion sizes consumed by children in a national survey. Significant differences were found between the accuracy of estimates using the three tools. Children of all ages performed well using the IPSAS and food photographs. The accuracy and precision of estimates made using the food models were poor. For all tools, estimates of the amount of food served were more accurate than estimates of the amount consumed. Issues relating to reporting of foods left over which impact on estimates of the amounts of foods actually consumed require further study. The IPSAS has shown potential for assessment of dietary intake with children. Before practical application in assessment of dietary intake of children the tool would need to be expanded to cover a wider range of foods and to be validated in a 'real-life' situation.

Children's estimates of food portion size: the effect of timing of dietary interview on the accuracy of children's portion size estimates.

For food intakes to be converted into nutrient intakes a measure or estimate of the amount of food consumed is required. A number of methods have been developed to assist subjects in providing an estimate of portion size. Children's ability to use perception, conceptualisation and memory skills to estimate food portion size has not been investigated systematically. The aim of the present study was to test the effect of the timing of a dietary interview on the accuracy of estimates of food portion sizes made by children, using food photographs, food models and an interactive portion size assessment system, developed for use with children and based on portion sizes of foods consumed by children. Children (n 108) aged 4-14 years were supplied with known quantities of foods and asked to estimate the portion size of each food using each of the three portion size assessment tools. Interviews took place (a) with the food in view, (b) just after the child had eaten the food or (c) 24 h after the child had eaten the food. There were no significant differences in children's ability to estimate food portion size (either as served or as eaten) with timing of interview. That is, children were as accurate in their estimates of portion size 24 h after consuming the food as when the food was in view. Under these conditions many children were able to estimate food portion size utilising perception, conceptualisation and memory skills.

Changes in consumption of sugars by English adolescents over 20 years.

OBJECTIVE: Dietary surveys of 11- to 12-year-old Northumbrian children in 1980 and 1990 revealed that consumption of non-milk extrinsic sugars (NMES) was 16-17% of energy intake. This study reports dietary sugars consumption in 2000 and compares it with data collected in 1980 and 1990, using identical methods. DESIGN: A repeat cross-sectional dietary survey of children aged 1-12 years attending the same schools as in the 1980 and 1990 surveys. SETTING: Seven middle schools in south Northumberland. SUBJECTS: All children aged 11-12 years old attending the seven schools. METHOD: Food consumption was recorded using two 3-day diet diaries. Food composition tables were used to calculate energy and nutrient intakes. NMES, and milk and intrinsic sugars were calculated using previously described methods. RESULTS: The numbers of children completing the surveys in 1980, 1990 and 2000 were 405, 379 and 424, respectively; approximately 60-70% of eligible children. Total sugars provided 22% of energy consistently over the three surveys. NMES consumption in 2000 provided 16% of energy compared with 16% in 1980 and 17% in 1990. Sources of NMES changed over the three surveys. NMES from soft drinks doubled from 15 to 31 g day(-1), and from breakfast cereals increased from 2 to 7 g day(-1) over the 20 years. Confectionery and soft drinks provided 61% of NMES. Over 20 years, the proportion of energy from fat decreased by 5% and from starch increased by 4%, creating a welcome tilt in the fat-starch see-saw, without an adverse effect on sugars intake. CONCLUSIONS: Consumption of NMES in 2000 was substantially higher than recommended, and there has been little change over 20 years. Continued and coordinated efforts are required at a national, community and individual level to reduce the intake of NMES.

Removal of acetabular bone in resurfacing arthroplasty of the hip: a comparison with hybrid total hip arthroplasty.

Resurfacing arthroplasty of the hip is being performed more frequently in the United Kingdom. The majority of these patients are younger than 55 years of age, and in this group the key benefits include conservation of femoral bone stock and the potential reduction in the rate of dislocation afforded by the larger resurfacing head. Early aseptic loosening is well recognised in patients younger than 55 years of age, and proponents of resurfacing believe that the improved wear characteristics of the metal-on-metal bearing may improve the long-term survival of this implant. There has been some concern, however, that resurfacing may not be conservative of acetabular bone. We compared a series of 33 consecutive patients who had a hybrid total hip arthroplasty with an uncemented acetabular component and a cemented femoral implant, with 35 patients undergoing a Birmingham hip resurfacing arthroplasty. We compared the diameter of the implanted acetabulum in both groups and, because they were not directly comparable, we corrected for patient size by measuring the diameter of the contralateral femoral head. The data were analysed using unpaired t-tests and analysis of covariance. There was a significantly larger acetabulum in the Birmingham arthroplasty group (mean diameter 56.6 mm vs 52.0 mm; p < 0.001). However, this group had a significantly larger femoral head diameter on the contralateral side (p = 0.03). Analysis of covariance revealed a significant difference between the mean size of the acetabular component implanted in the two operations. The greatest difference in the size of acetabulum was in those patients with a larger diameter of the femoral head. This study shows that more bone is removed from the acetabulum in hip resurfacing than during hybrid total hip arthroplasty, a difference which is most marked in larger patients.

A stable isotope titration method to determine the contribution of acetate disproportionation and carbon dioxide reduction to methanogenesis.

A novel stable isotope titration approach was developed to determine the contributions to total methane production made by CO(2) reduction and the disproportionation of acetate in anoxic environments. (13)CH(4), (12)CH(4), (13)CO(2) and (12)CO(2) production rates were measured in the head space of replicate anaerobic microcosms titrated with increasing amounts of (13)C-labelled substrates. The contribution of CO(2) reduction was calculated from the linear relationship between ratios of labelled and total CH(4) production and ratios of labelled and total CO(2) after the addition of (13)C-bicarbonate. In the case of acetoclastic methanogenesis rates of (13)CH(4) and (12)CH(4) production were fitted to a model based on an assumption that the relationship between the concentration of (13)C-labelled acetate and the rates of labelled and unlabelled methane production followed Michaelis-Menten kinetics. A comparison of the raw data with the model supported the assumption and provided both an estimate of the contribution of acetate to methane production and an estimate of the size of the indigenous acetate pool without the need to measure acetate directly. The method was applied to a freshwater sediment in the English Lake District where it was found that 66.3% (se 4.9) of methane production was due to acetate disproportionation and 28.9% (se 1.9) of methane production resulted from CO(2) reduction. This is in agreement with theoretical predictions and other empirical measurements of methanogenesis.

Does antenatal pelvic dilation predict renal scarring?

Moderate antenatal renal pelvic dilation (5-15 mm) may suggest vesicoureteric reflux, but it is not known to predict renal scarring. Dimercaptosuccinic acid scans on such children aged over 4 years showed a scarring rate (0/133 boys, 1/56 girls) similar to our local population. Investigation and treatment of moderate dilation may not be required.

A case control study to examine the pharmacological factors underlying ventricular septal defects in the North of England.

BACKGROUND: Amphetamine exposure is associated with congenital cardiac abnormalities in animals. We previously reported an association between recreational use of 2,4-methylenedioxymethamphetamine (ecstasy, MDMA) and ventricular septal defect in babies born to users. We have carried out a case control study to investigate risks in the occurrence of ventricular septal defect in a cohort of babies born in the North East of England. METHODS: Cases were identified from paediatric cardiology units in Newcastle upon Tyne and Leeds, and controls were recruited from the mothers of babies born in the same hospital as the index case. Research nurses carried out interviews using a structured questionnaire. RESULTS: A total of 296 case control pairs were studied. There was insufficient exposure to ecstasy to test the primary hypothesis. Increased risk of ventricular septal defect was found to be associated with consumption of cough and cold remedies [pre-conception OR 2.2, 95% CI 1.41, 3.51; pregnancy OR 5.1, 95% CI 2.56, 11.27; exposure in either OR 2.83, 95% CI 1.85, 4.45; P<0.005] and in the case of non-steroidals for exposures in pregnancy (OR 4.2, 95% CI 1.54, 14.26; P<0.005). CONCLUSIONS: These findings suggest that ventricular septal defect is associated with consuming the medications identified. They are also compatible with the hypothesis that sympathomimetics (pseudoephedrine, phenylephrine and phenylpropanolamine) present in cough mixtures cause the increased risk, and with our original hypothesis that sympathomimetics and amphetamines are potentially cardiotoxic in utero.

Changes over 20 years in macronutrient intake and body mass index in 11- to 12-year-old adolescents living in Northumberland.

Monitoring adolescent diets over time enables the assessment of the effectiveness of public health messages which are particularly important in vulnerable groups such as adolescents. In 2000, 424 children aged 11-12 years old completed two 3 d estimated dietary records. On the fourth day one nutritionist interviewed each child to clarify the information in the diary and foods were quantified with the aid of food models. Nutrient intake was calculated using computerised food tables. These children attended the same seven schools in the same Northumberland area as the 11- to 12-year-old children who recorded their diet using the same method in 1980 (n 405) and 1990 (n 379), respectively. Height and weight, and parental occupation were recorded in all three surveys for each child. Height and weight were used to calculate BMI, weight was used to estimate BMR and parental occupation was used to determine social class. Comparing the macronutrient intakes in 2000 with 1980 and 1990, energy intakes (EI) fell in boys (to 8.45 MJ) and girls (to 7.60 MJ). This fall may, at least in part, be due to an increase in low energy reporting. For 1980, 1990 and 2000 the percentage of boys with EI:BMR below 1.1 was 6, 15 and 23 %, respectively; for girls, 3, 14 and 18 %, respectively. Percentage energy from fat was unchanged between 1980 and 1990 but fell to 35 % (about 76 g/d) in 2000, alongside a 3 % increase in percentage energy from starch (30 %). Percentage energy from non-milk extrinsic sugars remained above recommendations (16 %; about 82 g/d). The number of overweight and obese children increased from 11 % to 30 % between 1980 and 2000. Positive changes have occurred in the Northumbrian adolescent diet but social inequalities, reported in previous surveys, remain.

The effect of otitis media with effusions on balance in children.

There is increasing interest in the effect, otitis media with effusions (OME) has on the balance in children. The aim of our investigation was to determine whether a universal effect on balance could be demonstrated in children with OME by using sway posturography. Assessment was made in 20 children with proven OME before and after the insertion of bilateral ventilation tubes. Sway posturography was performed on each occasion in each of the four recording conditions in the presence and absence of both reduced optic fixation and reduced proprioception. The pathlength traversed during the recording interval was measured and analysed by a split-unit anova. The results demonstrate an overall improvement in mean pathlength of 20% following treatment of the effusions (P < 0.001) (95% CI 14-25%). The effect of reduced optic fixation and of reduced proprioception were similar when increasing the mean pathlength by 22% (P < 0.001). These results demonstrate that OME has a universal effect on balance in all recording conditions.

Optimal designs for Michaelis-Menten kinetic studies.

Many reactions in enzymology are governed by the Michaelis-Menten equation. Characterising these reactions requires the estimation of the parameters K(M) and V(max) which determine the Michaelis-Menten equation and this is done by observing rates of reactions at a set of substrate concentrations. The choice of substrate concentrations is investigated by determining Bayesian D-optimal designs for a model in which residuals have a normal distribution with constant variance. Designs which focus on alternative quantities, such as K(M) or the ratio V(max)/K(M) are also considered. The effect on the optimal designs of alternative error distributions is also considered.

Methods for the analysis and design of limiting dilution assays.

Limiting dilution assays are a useful device for extracting quantitative information when the underlying analytical tool can only provide information on presence or absence. Analysis by maximum likelihood is advocated and some alternative methods are discussed. Several interval estimators, including one based directly on the log-likelihood are presented. Methods for determining designs which permit efficient estimation are considered and some of their weaknesses are mentioned. Opportunities for further methodological development are outlined.