Performance of mixed effects models and generalized estimating equations for continuous outcomes in partially clustered trials including both independent and paired data.

Many clinical trials involve partially clustered data, where some observations belong to a cluster and others can be considered independent. For example, neonatal trials may include infants from single or multiple births. Sample size and analysis methods for these trials have received limited attention. A simulation study was conducted to (1) assess whether existing power formulas based on generalized estimating equations (GEEs) provide an adequate approximation to the power achieved by mixed effects models, and (2) compare the performance of mixed models vs GEEs in estimating the effect of treatment on a continuous outcome. We considered clusters that exist prior to randomization with a maximum cluster size of 2, three methods of randomizing the clustered observations, and simulated datasets with uninformative cluster size and the sample size required to achieve 80% power according to GEE-based formulas with an independence or exchangeable working correlation structure. The empirical power of the mixed model approach was close to the nominal level when sample size was calculated using the exchangeable GEE formula, but was often too high when the sample size was based on the independence GEE formula. The independence GEE always converged and performed well in all scenarios. Performance of the exchangeable GEE and mixed model was also acceptable under cluster randomization, though under-coverage and inflated type I error rates could occur with other methods of randomization. Analysis of partially clustered trials using GEEs with an independence working correlation structure may be preferred to avoid the limitations of mixed models and exchangeable GEEs.

Categorisation of continuous covariates for stratified randomisation: How should we adjust?

To obtain valid inference following stratified randomisation, treatment effects should be estimated with adjustment for stratification variables. Stratification sometimes requires categorisation of a continuous prognostic variable (eg, age), which raises the question: should adjustment be based on randomisation categories or underlying continuous values? In practice, adjustment for randomisation categories is more common. We reviewed trials published in general medical journals and found none of the 32 trials that stratified randomisation based on a continuous variable adjusted for continuous values in the primary analysis. Using data simulation, this article evaluates the performance of different adjustment strategies for continuous and binary outcomes where the covariate-outcome relationship (via the link function) was either linear or non-linear. Given the utility of covariate adjustment for addressing missing data, we also considered settings with complete or missing outcome data. Analysis methods included linear or logistic regression with no adjustment for the stratification variable, adjustment for randomisation categories, or adjustment for continuous values assuming a linear covariate-outcome relationship or allowing for non-linearity using fractional polynomials or restricted cubic splines. Unadjusted analysis performed poorly throughout. Adjustment approaches that misspecified the underlying covariate-outcome relationship were less powerful and, alarmingly, biased in settings where the stratification variable predicted missing outcome data. Adjustment for randomisation categories tends to involve the highest degree of misspecification, and so should be avoided in practice. To guard against misspecification, we recommend use of flexible approaches such as fractional polynomials and restricted cubic splines when adjusting for continuous stratification variables in randomised trials.

Association of cord blood vitamin D with child neurodevelopment at 7 years of age.

AIM: The role of fetal vitamin D [25-hydroxyvitamin D (25(OH)D)], one of the nuclear steroid transcription regulators, and brain development is unclear. We previously found a weak but persistent association between cord blood 25(OH)D and child language abilities at 18 months and 4 years of age, but no association with cognition or behaviour. The aim of this study was to investigate the association between cord blood 25(OH)D and a range of neurodevelopmental outcomes in these same children at 7 years of age. METHODS: Cord blood samples from 250 Australian mother-child pairs were analysed for 25(OH)D by mass spectroscopy. Children underwent tests of cognition, language, academic abilities and executive functions with a trained assessor at 7 years of age. Caregivers completed questionnaires to rate their child's behaviour and executive functioning in the home environment. Associations between standardised 25(OH)D and outcomes were assessed using regression models, taking into account possible social and demographic confounders. RESULTS: Standardised 25(OH)D in cord blood was not associated with any test or parent-rated scores. Nor was there any association with the risk of having a poor test or parent-rated score. Likewise, cord blood 25(OH)D categorised as <25, 25-50 and >50 nmol/L was not associated with test scores or parent-rated scores. CONCLUSIONS: There was no evidence that cord blood vitamin D concentration or deficiency was associated with cognition, language, academic abilities, executive functioning or behaviour at 7 years of age.

Handling misclassified stratification variables in the analysis of randomised trials with continuous outcomes.

Many trials use stratified randomisation, where participants are randomised within strata defined by one or more baseline covariates. While it is important to adjust for stratification variables in the analysis, the appropriate method of adjustment is unclear when stratification variables are affected by misclassification and hence some participants are randomised in the incorrect stratum. We conducted a simulation study to compare methods of adjusting for stratification variables affected by misclassification in the analysis of continuous outcomes when all or only some stratification errors are discovered, and when the treatment effect or treatment-by-covariate interaction effect is of interest. The data were analysed using linear regression with no adjustment, adjustment for the strata used to perform the randomisation (randomisation strata), adjustment for the strata if all errors are corrected (true strata), and adjustment for the strata after some errors are discovered and corrected (updated strata). The unadjusted model performed poorly in all settings. Adjusting for the true strata was optimal, while the relative performance of adjusting for the randomisation strata or the updated strata varied depending on the setting. As the true strata are unlikely to be known with certainty in practice, we recommend using the updated strata for adjustment and performing subgroup analyses, provided the discovery of errors is unlikely to depend on treatment group, as expected in blinded trials. Greater transparency is needed in the reporting of stratification errors and how they were addressed in the analysis.

Partially clustered designs for clinical trials: Unifying existing designs using consistent terminology.

INTRODUCTION: Clinical trial designs based on the assumption of independent observations are well established. Clustered clinical trial designs, where all observational units belong to a cluster and outcomes within clusters are expected to be correlated, have also received considerable attention. However, many clinical trials involve partially clustered data, where only some observational units belong to a cluster. Examples of such trials occur in neonatology, where participants include infants from both singleton and multiple births, and ophthalmology, where one or two eyes per participant may need treatment. Partial clustering can also arise in trials of group-based treatments (e.g. group education or counselling sessions) or treatments administered individually by a discrete number of health care professionals (e.g. surgeons or physical therapists), when this is compared to an unclustered control arm. Trials involving partially clustered data have received limited attention in the literature and the current lack of standardised terminology may be hampering the development and dissemination of methods for designing and analysing these trials. METHODS AND EXAMPLES: In this article, we present an overarching definition of partially clustered trials, bringing together several existing trial designs including those for group-based treatments, clustering due to facilitator effects and the re-randomisation design. We define and describe four types of partially clustered trial designs, characterised by whether the clustering occurs pre-randomisation or post-randomisation and, in the case of pre-randomisation clustering, by the method of randomisation that is used for the clustered observations (individual randomisation, cluster randomisation or balanced randomisation within clusters). Real life examples are provided to highlight the occurrence of partially clustered trials across a variety of fields. To assess how partially clustered trials are currently reported, we review published reports of partially clustered trials. DISCUSSION: Our findings demonstrate that the description of these trials is often incomplete and the terminology used to describe the trial designs is inconsistent, restricting the ability to identify these trials in the literature. By adopting the definitions and terminology presented in this article, the reporting of partially clustered trials can be substantially improved, and we present several recommendations for reporting these trial designs in practice. Greater awareness of partially clustered trials will facilitate more methodological research into their design and analysis, ultimately improving the quality of these trials.

A Randomized Trial of Prenatal n-3 Fatty Acid Supplementation and Preterm Delivery.

BACKGROUND: Previous studies have suggested that maternal supplementation with n-3 long-chain polyunsaturated fatty acids may reduce the incidence of preterm delivery but may also prolong gestation beyond term; however, more data are needed regarding the role of n-3 long-chain polyunsaturated fatty acids in pregnancy. METHODS: We performed a multicenter, double-blind, randomized trial in which women who were pregnant with single or multiple fetuses were assigned to receive either fish-oil capsules that contained 900 mg of n-3 long-chain polyunsaturated fatty acids (n-3 group) or vegetable-oil capsules that contained trace n-3 long-chain polyunsaturated fatty acids (control group) daily, beginning before 20 weeks of gestation and continuing to 34 weeks of gestation or delivery, whichever occurred first. The primary outcome was early preterm delivery, defined as delivery before 34 completed weeks of gestation. Other pregnancy and neonatal outcomes were also assessed. RESULTS: A total of 5544 pregnancies in 5517 women were randomly assigned at six centers in Australia; 5486 pregnancies were included in the primary analysis. Early preterm delivery occurred in the case of 61 of 2734 pregnancies (2.2%) in the n-3 group and 55 of 2752 pregnancies (2.0%) in the control group; the between-group difference was not significant (adjusted relative risk, 1.13; 95% confidence interval [CI], 0.79 to 1.63; P = 0.50). There were no significant differences between the groups in the incidence of interventions in post-term (>41 weeks of gestation) deliveries, in adverse events, or in other pregnancy or neonatal outcomes, except that a higher percentage of infants born to women in the n-3 group than in the control group were very large for gestational age at birth (adjusted relative risk, 1.30; 95% CI, 1.02 to 1.65). Percentages of serious adverse events did not differ between the groups. Minor gastrointestinal disturbances were more commonly reported in the n-3 group than in the control group. CONCLUSIONS: Supplementation with n-3 long-chain polyunsaturated fatty acids from early pregnancy (<20 weeks of gestation) until 34 weeks of gestation did not result in a lower incidence of early preterm delivery or a higher incidence of interventions in post-term deliveries than control. (Funded by the Australian National Health and Medical Research Council and the Thyne Reid Foundation; ORIP Australian New Zealand Clinical Trials Registry number, ACTRN12613001142729.).

Multiple imputation for handling missing outcome data in randomized trials involving a mixture of independent and paired data.

Randomized trials involving independent and paired observations occur in many areas of health research, for example in paediatrics, where studies can include infants from both single and twin births. Multiple imputation (MI) is often used to address missing outcome data in randomized trials, yet its performance in trials with independent and paired observations, where design effects can be less than or greater than one, remains to be explored. Using simulated data and through application to a trial dataset, we investigated the performance of different methods of MI for a continuous or binary outcome when followed by analysis using generalized estimating equations to account for clustering due to the pairs. We found that imputing data separately for independent and paired data, with paired data imputed in wide format, was the best performing MI method, producing unbiased point and standard error estimates for the treatment effect throughout. Ignoring clustering in the imputation model performed well in settings where the design effect due to the inclusion of paired data was close to one, but otherwise led to moderately biased variance estimates. Including a random cluster effect in the imputation model led to slightly biased point estimates for binary outcome data and variance estimates that were too small in some settings. Based on these results, we recommend researchers impute independent and paired data separately where feasible to do so. The exception is if the design effect due to the inclusion of paired data is close to one, where ignoring clustering may be appropriate.

Associations between newborn thyroid-stimulating hormone concentration and neurodevelopment and growth of children at 18 months.

The study aimed to assess the associations between newborn thyroid-stimulating hormone (TSH) concentration, a marker of iodine nutrition in early life, and childhood neurodevelopment and growth using data collected from two pregnancy studies, one in a borderline iodine-deficient setting (DHA to Optimize Mother Infant Outcome (DOMInO) Study) and one in an iodine-sufficient setting (Pregnancy Iodine and Neurodevelopment in Kids (PINK) Study). TSH data were obtained from routine newborn screening. Neurodevelopment was assessed at 18 months using the Bayley Scales of Infant and Toddler Development, third edition (Bayley-III). Weight, height and head circumference were measured at 18 months. In total, 1467 children were included in the analysis. Comparing the highest with the lowest TSH quartile, the mean differences (MD) in the Bayley-III scores ranged from -2·0 (95 % CI -4·7, 0·7) to -2·2 (95 % CI -5·8, 1·3) points in DOMInO and 1·0 (95 % CI -1·6, 3·6) to 2·0 (95 % CI -0·4, 4·4) points in PINK in the cognitive, language and motor scales; the MD in the anthropometric z scores ranged from -0·01 (95 % CI -0·5, 0·5) to -0·5 (95 % CI -0·9, -0·1) in both studies. A 1 mIU/l increase in TSH was associated with -0·3 (95 % CI -0·9, 0·2) point and 0·2 (95 % CI -0·3, 0·7) point changes in the mean cognitive score in the DOMInO and PINK, respectively. A null association between TSH and growth was also observed in both studies. Longitudinal studies that utilise newborn TSH data and examine neurodevelopmental outcomes at later ages are warranted, as neurodevelopmental assessments in older children are more predictive of later achievement.

DHA supplementation in infants born preterm and the effect on attention at 18 months' corrected age: follow-up of a subset of the N3RO randomised controlled trial.

Infants born preterm miss out on the peak period of in utero DHA accretion to the brain during the last trimester of pregnancy which is hypothesised to contribute to the increased prevalence of neurodevelopmental deficits in this population. This study aimed to determine whether DHA supplementation in infants born preterm improves attention at 18 months' corrected age. This is a follow-up of a subset of infants who participated in the N3RO randomised controlled trial. Infants were randomised to receive an enteral emulsion of high-dose DHA (60 mg/kg per d) or no DHA (soya oil - control) from within the first days of birth until 36 weeks' post-menstrual age. The assessment of attention involved three tasks requiring the child to maintain attention on toy/s in either the presence or absence of competition or a distractor. The primary outcome was the child's latency of distractibility when attention was focused on a toy. The primary outcome was available for seventy-three of the 120 infants that were eligible to participate. There was no evidence of a difference between groups in the latency of distractibility (adjusted mean difference: 0·08 s, 95 % CI -0·81, 0·97; P = 0·86). Enteral DHA supplementation did not result in improved attention in infants born preterm at 18 months' corrected age.

Conducting Clinical Trials in Twin Populations: A Review of Design, Analysis, Recruitment and Ethical Issues for Twin-Only Trials.

Although twins often participate in medical research, few clinical trials are conducted entirely in twin populations. The purpose of this review is to demonstrate the substantial benefits and address the key challenges of conducting clinical trials in twin populations, or 'twin-only trials'. We consider the unique design, analysis, recruitment and ethical issues that arise in such trials. In particular, we describe the different approaches available for randomizing twin pairs, highlight the similarity or correlation that exists between outcomes of twins, and discuss the impact of this correlation on sample size calculations and statistical analysis methods for estimating treatment effects. We also consider the role of both monozygotic and dizygotic twins for studying variation in outcomes, the factors that may affect recruitment of twins, and the ethics of conducting trials entirely in twin populations. The advantages and disadvantages of conducting twin-only trials are also discussed. Finally, we recommend that twin-only trials should be considered more often.

Comparison of iodine status pre- and post-mandatory iodine fortification of bread in South Australia: a population study using newborn thyroid-stimulating hormone concentration as a marker.

OBJECTIVE: The present study aimed to evaluate the effect of mandatory iodine fortification of bread on the iodine status of South Australian populations using newborn thyroid-stimulating hormone (TSH) concentration as a marker. DESIGN: The study used an interrupted time-series design. SETTING: TSH data collected between 2005 and 2016 (n 211 033) were extracted from the routine newborn screening programme in South Australia for analysis. Iodine deficiency is indicated when more than 3 % of newborns have TSH > 5 mIU/l. PARTICIPANTS: Newborns were classified into three groups: the pre-fortification group (those born before October 2009); the transition group (born between October 2009 and June 2010); and the post-fortification group (born after June 2010). RESULTS: The percentage of newborns with TSH > 5 mIU/l was 5·1, 6·2 and 4·6 % in the pre-fortification, transition and post-fortification groups, respectively. Based on a segmented regression model, newborns in the post-fortification period had a 10 % lower risk of having TSH > 5 mIU/l than newborns in the pre-fortification group (incidence rate ratio (IRR) = 0·90; 95 % CI 0·87, 0·94), while newborns in the transitional period had a 22 % higher risk of having TSH > 5 mIU/l compared with newborns in the pre-fortification period (IRR = 1·22; 95 % CI 1·13, 1·31). CONCLUSIONS: Using TSH as a marker, South Australia would be classified as mild iodine deficiency post-fortification in contrast to iodine sufficiency using median urinary iodine concentration as a population marker. Re-evaluation of the current TSH criteria to define iodine status in populations is warranted in this context.

Effects of an antenatal dietary intervention in overweight and obese women on 6 month infant outcomes: follow-up from the LIMIT randomised trial.

BACKGROUND: The immediate impact of providing an antenatal dietary intervention during pregnancy has been extensively studied, but little is known of the effects beyond the neonatal period. Our objective was to evaluate the effect of an antenatal dietary intervention in overweight or obese women on infant outcomes 6 months after birth. METHODS: We conducted a follow up study of infants born to women who participated in the LIMIT trial during pregnancy. Live-born infants at 6-months of age, and whose mother provided consent to ongoing follow-up were eligible. The primary follow-up study endpoint was the incidence of infant BMI z-score ≥90th centile for infant sex and age. Secondary study outcomes included a range of infant anthropometric measures, neurodevelopment, general health, and infant feeding. Analyses used intention to treat principles according to the treatment group allocated in pregnancy. Missing data were imputed and analyses adjusted for maternal early pregnancy BMI, parity, study centre, socioeconomic status, age, and smoking status. Outcome assessors were blinded to the allocated treatment group. RESULTS: A total of 1754 infants were assessed at age 6 months (Lifestyle Advice n = 869; Standard Care n = 885), representing 82.1% of the eligible sample (n = 2136). There were no statistically significant differences in the incidence of infant BMI z-score ≥90th centile for infants born to women in the Lifestyle Advice group, compared with the Standard Care group (Lifestyle Advice 233 (21.71%) vs. Standard Care 233 (21.90%); adjusted relative risk (aRR) 0.99; 95% confidence interval 0.82 to 1.18; p = 0.88). There were no other effects on infant growth, adiposity, or neurodevelopment. CONCLUSION: Providing pregnant women who were overweight or obese with an antenatal dietary and lifestyle intervention did not alter 6-month infant growth and adiposity. TRIAL REGISTRATION: Australian and New Zealand Clinical Trials Registry (ACTRN12607000161426).

Accounting for twin births in sample size calculations for randomised trials.

BACKGROUND: Including twins in randomised trials leads to non-independence or clustering in the data. Clustering has important implications for sample size calculations, yet few trials take this into account. Estimates of the intracluster correlation coefficient (ICC), or the correlation between outcomes of twins, are needed to assist with sample size planning. Our aims were to provide ICC estimates for infant outcomes, describe the information that must be specified in order to account for clustering due to twins in sample size calculations, and develop a simple tool for performing sample size calculations for trials including twins. METHODS: ICCs were estimated for infant outcomes collected in four randomised trials that included twins. The information required to account for clustering due to twins in sample size calculations is described. A tool that calculates the sample size based on this information was developed in Microsoft Excel and in R as a Shiny web app. RESULTS: ICC estimates ranged between -0.12, indicating a weak negative relationship, and 0.98, indicating a strong positive relationship between outcomes of twins. Example calculations illustrate how the ICC estimates and sample size calculator can be used to determine the target sample size for trials including twins. CONCLUSIONS: Clustering among outcomes measured on twins should be taken into account in sample size calculations to obtain the desired power. Our ICC estimates and sample size calculator will be useful for designing future trials that include twins. Publication of additional ICCs is needed to further assist with sample size planning for future trials.

Prevalence and reporting of recruitment, randomisation and treatment errors in clinical trials: A systematic review.

Background/aims In clinical trials, it is not unusual for errors to occur during the process of recruiting, randomising and providing treatment to participants. For example, an ineligible participant may inadvertently be randomised, a participant may be randomised in the incorrect stratum, a participant may be randomised multiple times when only a single randomisation is permitted or the incorrect treatment may inadvertently be issued to a participant at randomisation. Such errors have the potential to introduce bias into treatment effect estimates and affect the validity of the trial, yet there is little motivation for researchers to report these errors and it is unclear how often they occur. The aim of this study is to assess the prevalence of recruitment, randomisation and treatment errors and review current approaches for reporting these errors in trials published in leading medical journals. Methods We conducted a systematic review of individually randomised, phase III, randomised controlled trials published in New England Journal of Medicine, Lancet, Journal of the American Medical Association, Annals of Internal Medicine and British Medical Journal from January to March 2015. The number and type of recruitment, randomisation and treatment errors that were reported and how they were handled were recorded. The corresponding authors were contacted for a random sample of trials included in the review and asked to provide details on unreported errors that occurred during their trial. Results We identified 241 potentially eligible articles, of which 82 met the inclusion criteria and were included in the review. These trials involved a median of 24 centres and 650 participants, and 87% involved two treatment arms. Recruitment, randomisation or treatment errors were reported in 32 in 82 trials (39%) that had a median of eight errors. The most commonly reported error was ineligible participants inadvertently being randomised. No mention of recruitment, randomisation or treatment errors was found in the remaining 50 of 82 trials (61%). Based on responses from 9 of the 15 corresponding authors who were contacted regarding recruitment, randomisation and treatment errors, between 1% and 100% of the errors that occurred in their trials were reported in the trial publications. Conclusion Recruitment, randomisation and treatment errors are common in individually randomised, phase III trials published in leading medical journals, but reporting practices are inadequate and reporting standards are needed. We recommend researchers report all such errors that occurred during the trial and describe how they were handled in trial publications to improve transparency in reporting of clinical trials.

Twins as Participants in Randomized Controlled Trials: A Review of Published Literature.

Monozygotic (MZ) and dizygotic (DZ) twins participate in research that partitions variance in health, disease, and behavior into genetic and environmental components. However, there are other innovative roles for twins in medical research. One such way is involving MZ and/or DZ twins in co-twin control-designed randomized controlled trials (RCTs). To our knowledge, no reviews have been conducted that summarizes the involvement of twins in RCTs. Therefore, we conducted a systematic literature search using the U.S. Clinical Trials Database, NHS electronic databases, MEDLINE, EMBASE, and PsychINFO for RCTs on publications involving MZ and/or DZ twins as RCT participants. Out of the 186,027 clinical trials registered in the U.S. clinical trial register ClinicaTrails.gov, only six RCTs used twins as participants. From 1,598 articles identified in our search, 50 peer-reviewed English language publications met our pre-defined inclusion criteria. Sample sizes for RCTs have ranged from a total number of participants from 2 to 1,162; however, 32 (64%) studies had a sample size of 100 or less, and of those, 12 (24%) had fewer than 10. Both MZ and DZ twins have been recruited to the RCTs. In most instances (33/50) each twin from a pair were assigned to different study arms. Most of those studies included MZ twins only. Despite the methodological advantages, the use of MZ and DZ twins as participants in interventional RCTs appeared limited. The continuous development of innovative twin designs, especially RCTs, indicates that twin research can extend beyond the more widely recognized heritability estimates.

The effect of an antenatal lifestyle intervention in overweight and obese women on circulating cardiometabolic and inflammatory biomarkers: secondary analyses from the LIMIT randomised trial.

BACKGROUND: Maternal overweight and obesity during pregnancy is associated with insulin resistance, hyperglycaemia, hyperlipidaemia and a low-grade state of chronic inflammation. The aim of this pre-specified analysis of secondary outcome measures was to evaluate the effect of providing antenatal dietary and lifestyle advice on cardiometabolic and inflammatory biomarkers. METHODS: We conducted a multicentre trial in which pregnant women who were overweight or obese were randomised to receive either Lifestyle Advice or Standard Care. We report a range of pre-specified secondary maternal and newborn cardiometabolic and inflammatory biomarker outcomes. Maternal whole venous blood was collected at trial entry (mean 14 weeks gestation; non-fasting), at 28 weeks gestation (fasting), and at 36 weeks gestation (non-fasting). Cord blood was collected after birth and prior to the delivery of the placenta. A range of cardiometabolic and inflammatory markers were analysed (total cholesterol, triglycerides, non-esterified fatty acids, high-density lipoprotein cholesterol, insulin, glucose, leptin, adiponectin, C-reactive protein, granulocyte macrophage-colony stimulating factor, interferon gamma, TNF-α, and interleukins 1ß, 2, 4, 5, 6, 8, and 10). Participants were analysed in the groups to which they were randomised, and were included in the analyses if they had a measure at any time point. RESULTS: One or more biological specimens were available from 1951 women (989 Lifestyle Advice and 962 Standard Care), with cord blood from 1174 infants (596 Lifestyle Advice and 578 Standard Care). There were no statistically significant differences in mean cardiometabolic and inflammatory marker concentrations across pregnancy and in infant cord blood between treatment groups. Estimated treatment group differences were close to zero, with 95% confidence intervals spanning a range of differences that were short of clinical relevance. There was no evidence to suggest that the intervention effect was modified by maternal BMI category. CONCLUSIONS: Despite our findings, it will be worth considering potential relationships between cardiometabolic and inflammatory markers and clinical outcomes, including longer-term infant health and adiposity. TRIAL REGISTRATION: Australian and New Zealand Clinical Trials Registry ( ACTRN12607000161426 ; Date Registered 09/03/2007).

Sample size calculations for randomised trials including both independent and paired data.

Randomised trials including a mixture of independent and paired data arise in many areas of health research, yet methods for determining the sample size for such trials are lacking. We derive design effects algebraically assuming clustering because of paired data will be taken into account in the analysis using generalised estimating equations with either an independence or exchangeable working correlation structure. Continuous and binary outcomes are considered, along with three different methods of randomisation: cluster randomisation, individual randomisation and randomisation to opposite treatment groups. The design effect is shown to depend on the intracluster correlation coefficient, proportion of observations belonging to a pair, working correlation structure, type of outcome and method of randomisation. The derived design effects are validated through simulation and example calculations are presented to illustrate their use in sample size planning. These design effects will enable appropriate sample size calculations to be performed for future randomised trials including both independent and paired data. Copyright © 2017 John Wiley & Sons, Ltd.

Treatment of missing data in follow-up studies of randomised controlled trials: A systematic review of the literature.

BACKGROUND/AIMS: After completion of a randomised controlled trial, an extended follow-up period may be initiated to learn about longer term impacts of the intervention. Since extended follow-up studies often involve additional eligibility restrictions and consent processes for participation, and a longer duration of follow-up entails a greater risk of participant attrition, missing data can be a considerable threat in this setting. As a potential source of bias, it is critical that missing data are appropriately handled in the statistical analysis, yet little is known about the treatment of missing data in extended follow-up studies. The aims of this review were to summarise the extent of missing data in extended follow-up studies and the use of statistical approaches to address this potentially serious problem. METHODS: We performed a systematic literature search in PubMed to identify extended follow-up studies published from January to June 2015. Studies were eligible for inclusion if the original randomised controlled trial results were also published and if the main objective of extended follow-up was to compare the original randomised groups. We recorded information on the extent of missing data and the approach used to treat missing data in the statistical analysis of the primary outcome of the extended follow-up study. RESULTS: Of the 81 studies included in the review, 36 (44%) reported additional eligibility restrictions and 24 (30%) consent processes for entry into extended follow-up. Data were collected at a median of 7 years after randomisation. Excluding 28 studies with a time to event primary outcome, 51/53 studies (96%) reported missing data on the primary outcome. The median percentage of randomised participants with complete data on the primary outcome was just 66% in these studies. The most common statistical approach to address missing data was complete case analysis (51% of studies), while likelihood-based analyses were also well represented (25%). Sensitivity analyses around the missing data mechanism were rarely performed (25% of studies), and when they were, they often involved unrealistic assumptions about the mechanism. CONCLUSION: Despite missing data being a serious problem in extended follow-up studies, statistical approaches to addressing missing data were often inadequate. We recommend researchers clearly specify all sources of missing data in follow-up studies and use statistical methods that are valid under a plausible assumption about the missing data mechanism. Sensitivity analyses should also be undertaken to assess the robustness of findings to assumptions about the missing data mechanism.

Association of cord blood vitamin D with early childhood growth and neurodevelopment.

AIM: The association between fetal vitamin D [25-hydroxyvitamin D (25(OH)D)] exposure and early child growth and neurodevelopment is controversial. The aim of this study was to investigate the association between cord blood 25(OH)D and birth size, childhood growth and neurodevelopment. METHODS: Cord blood samples from 1040 Australian women enrolled in a randomised trial of docosahexaenoic acid (DHA) supplementation during pregnancy were analysed for 25(OH)D using mass spectroscopy. Infant length, weight and head circumference were measured at delivery. A sub-sample of 337 infants with cord blood samples were selected for growth and neurodevelopment assessment at 18 months and 4 years of age. Associations between standardised 25(OH)D and outcomes were assessed, taking into account DHA treatment, social and demographic variables. RESULTS: Standardised 25(OH)D in cord blood was not associated with length, weight or head circumference at birth, 18 months or 4 years of age. 25(OH)D was not associated with cognitive, motor, social-emotional or adaptive behaviour scores at 18 months, or cognitive score at 4 years of age. A 10 nmol/L increase in cord blood 25(OH)D was associated with a modest increase in average Language scores of 0.60 points at 18 months (adjusted 95% CI 0.04-1.17, P = .04) and 0.68 points at 4 years (adjusted 95% CI 0.07-1.29, P = .03) of age. CONCLUSIONS: Cord blood vitamin D was modestly, positively associated with language development in early childhood in our sample, although the magnitude of the association was small. Randomised controlled trials are needed to confirm a causal association and establish the potential clinical significance of the relationship between vitamin D status and language development.

The effect of antenatal dietary and lifestyle advice for women who are overweight or obese on emotional well-being: the LIMIT randomized trial.

INTRODUCTION: Our aim was to evaluate the effect of dietary and lifestyle advice given to women who were overweight or obese during pregnancy on maternal quality of life, anxiety and risk of depression, and satisfaction with care. MATERIAL AND METHODS: We conducted a randomized trial, involving pregnant women with body mass index ≥25 kg/m(2) , recruited from maternity units in South Australia. Women were randomized to Lifestyle Advice or Standard Care, and completed questionnaires assessing risk of depression (Edinburgh Postnatal Depression Scale), anxiety (Spielberger State-Trait Anxiety Inventory), and quality of life (SF-36) at trial entry, 28 and 36 weeks' gestation, and 4 months postpartum. Secondary trial outcomes assessed for this analysis were risk of depression, anxiety, maternal quality of life, and satisfaction with care. RESULTS: One or more questionnaires were completed by 976 of 1108 (90.8%) women receiving Lifestyle Advice and 957 of 1104 (89.7%) women receiving Standard Care. The risk of depression [adjusted risk ratio 1.01; 95% confidence interval (CI) 0.82-1.24; p = 0.95], anxiety (adjusted risk ratio 1.09; 95% CI 0.93-1.27; p = 0.31), and health-related quality of life were similar between the two groups. Women receiving Lifestyle Advice reported improved healthy food choice [Lifestyle Advice 404 (68.9%) vs. Standard Care 323 (51.8%); p < 0.0001], and exercise knowledge [Lifestyle Advice 444 (75.8%) vs. Standard Care 367 (58.8%); p < 0.0001], and reassurance about their health [Lifestyle Advice 499 (85.3%) vs. Standard Care 485 (77.9%); p = 0.0112], and health of their baby [Lifestyle Advice 527 (90.2%) vs. Standard Care 545 (87.6%); p = 0.0143]. CONCLUSION: Lifestyle advice in pregnancy improved knowledge and provided reassurance without negatively impacting well-being.