Cluster Randomized Trials with a Pretest and Posttest: Equivalence of Three-, Two- and One-Level Analyses, and Sample Size Calculation.

In a cluster randomized trial clusters of persons, for instance, schools or health centers, are assigned to treatments, and all persons in the same cluster get the same treatment. Although less powerful than individual randomization, cluster randomization is a good alternative if individual randomization is impossible or leads to severe treatment contamination (carry-over). Focusing on cluster randomized trials with a pretest and post-test of a quantitative outcome, this paper shows the equivalence of four methods of analysis: a three-level mixed (multilevel) regression for repeated measures with as levels cluster, person, and time, and allowing for unstructured between-cluster and within-cluster covariance matrices; a two-level mixed regression with as levels cluster and person, using change from baseline as outcome; a two-level mixed regression with as levels cluster and time, using cluster means as data; a one-level analysis of cluster means of change from baseline. Subsequently, similar equivalences are shown between a constrained mixed model and methods using the pretest as covariate. All methods are also compared on a cluster randomized trial on mental health in children. From these equivalences follows a simple method to calculate the sample size for a cluster randomized trial with baseline measurement, which is demonstrated step-by-step.

Pragmatic Uncontrolled Study of Specialized Cognitive Behavioral Therapy for Adults With Chronic Tinnitus.

OBJECTIVES: Tinnitus is the perception of sound without an external source, affecting quality of life that can cause severe distress in approximately 1 to 3% of the population of people with tinnitus. Randomized controlled trials of cognitive behavioral therapy for tinnitus have demonstrated its effectiveness in improving quality of life, but the effects of their implementation on a large scale in routine practice remains unknown. Therefore, the main purpose of this study was to examine the effects of stepped-care cognitive behavioral therapy for tinnitus delivered in a tertiary audiological center of a regional hospital. Second, we wished to examine predictors of favorable outcome. DESIGN: Four hundred three adults with chronic tinnitus were enrolled in this prospective observational study (at 3 months, N=334, 8 months, N=261; 12 months, N=214). The primary outcome was health-related quality of life as measured by the Health Utilities Index III (HUI-III) at 12 months. Secondary outcomes were self-reported levels of tinnitus-related distress, disability, affective distress and tinnitus-related negative beliefs and fear. Measures were completed pre-intervention at 3 months, 8 months, and 12 months. Multilevel modeling was used to examine effects and their predictors. RESULTS: Younger participants with lower levels of tinnitus distress were more likely to dropout while those with higher tinnitus distress at baseline and quality of life were more likely to receive step 2 of treatment. MLM analyses revealed, with one exception, no relation between any baseline variable and outcome change over time. Most participants' improvement exceeded minimally clinical important difference criteria for quality of life, tinnitus-related handicap, and tinnitus distress. CONCLUSIONS: Results from this large pragmatic study complements those from randomized controlled trials of cognitive behavioral therapy for chronic tinnitus distress and supports its implementation under "real-world" conditions.

Imputation of Missing Covariates in Randomized Controlled Trials with Continuous Outcomes: Simple, Unbiased and Efficient Methods.

The literature on dealing with missing covariates in nonrandomized studies advocates the use of sophisticated methods like multiple imputation (MI) and maximum likelihood (ML)-based approaches over simple methods. However, these methods are not necessarily optimal in terms of bias and efficiency of treatment effect estimation in randomized studies, where the covariate of interest (treatment group) is independent of all baseline (pre-randomization) covariates due to randomization. This has been shown in the literature, but only for missingness on a single baseline covariate. Here, we extend the situation to multiple baseline covariates with missingness and evaluate the performance of MI and ML compared with simple alternative methods under various missingness scenarios in RCTs with a quantitative outcome. We first derive asymptotic relative efficiencies of the simple methods under the missing completely at random (MCAR) scenario and then perform a simulation study for non-MCAR scenarios. Finally, a trial on chronic low back pain is used to illustrate the implementation of the methods. The results show that all simple methods give unbiased treatment effect estimation but with increased mean squared residual. It also turns out that mean imputation and the missing-indicator method are most efficient under all covariate missingness scenarios and perform at least as well as MI and LM in each scenario.

A randomized controlled trial comparing community lifestyle interventions to improve adherence to diet and physical activity recommendations: the VitalUM study.

Worldwide, adherence to national guidelines for physical activity (PA), and fruit and vegetable consumption is recommended to promote health and reduce the risk for (chronic) disease. This study reports on the effectiveness of various social-cognitive interventions to improve adherence to guidelines and the revealed adherence predictors. Participants (n = 1,629), aged 45-70 years, randomly selected and recruited in 2005-2006 from 23 Dutch general practices, were randomized (centralized stratified allocation) to four groups to receive a 12-month lifestyle intervention targeting guideline adherence for PA and fruit and vegetable consumption. Study groups received either four computer-tailored print communication (TPC) letters (n = 405), four telephone motivational interviewing (TMI) sessions (n = 407), a combined intervention (two TPC letters and two TMI sessions, n = 408), or no intervention (control group, n = 409). After the baseline assessment, all parties were aware of the treatment groups. Outcomes were measured with self-report postal questionnaires at baseline, 25, 47 and 73 weeks. For PA, all three interventions were associated with better guideline adherence than no intervention. Odds ratios for TPC, TMI and the combined intervention were 1.82 (95% CI 1.31; 2.54), 1.57 (95% CI 1.13; 2.18), and 2.08 (95% CI 1.50; 2.88), respectively. No pedometer effects were found. For fruit and vegetable consumption, TPC seemed superior to those in the other groups. Odd ratio for fruit and vegetable consumption were 1.78 (95% CI 1.32; 2.41) and 1.73 (95% CI 1.28; 2.33), respectively. For each behaviour, adherence was predicted by self-efficacy expectations, habit strength and stages of change, whereas sex, awareness and the number of action plans predicted guideline adherence for fruit and vegetable intake. The season predicted the guideline adherence for PA and fruit consumption. The odds ratios revealed were equivalent to modest effects sizes, although they were larger than those reported in systematic reviews. This study indicated that less resource intensive interventions might have the potential for a large public health impact when widely implemented. The strengths of this study were the participation of lower educated adults and evaluation of maintenance effects. (Trial NL1035, 2007-09-06).

Maximin design of cluster randomized trials with heterogeneous costs and variances.

Cluster randomized trials evaluate the effect of a treatment on persons nested within clusters, with clusters being randomly assigned to treatment. The optimal sample size at the cluster and person level depends on the study cost per cluster and per person, and the outcome variance at the cluster and the person level. The variances are unknown in the design stage and can differ between treatment arms. As a solution, this paper presents a Maximin design that maximizes the minimum relative efficiency (relative to the optimal design) over the variance parameter space, for trials with two treatment arms and a quantitative outcome. This maximin relative efficiency design (MMRED) is compared with a published Maximin design which maximizes the minimum efficiency (MMED). Both designs are also compared with the optimal designs for homogeneous costs and variances (balanced design) and heterogeneous costs and homogeneous variances (cost-conscious design), for a range of variances based upon three published trials. Whereas the MMED is balanced under high uncertainty about the treatment-to-control variance ratio, the MMRED then tends towards a balanced budget allocation between arms, leading to an unbalanced sample size allocation if costs are heterogeneous, similar to the cost-conscious design. Further, the MMRED corresponds to an optimal design for an intraclass correlation (ICC) in the lower half of the assumed ICC range (optimistic), whereas the MMED is the optimal design for the maximum ICC within the ICC range (pessimistic). Attention is given to the effect of the Welch-Satterthwaite degrees of freedom for treatment effect testing on the design efficiencies.

Aquatic Cycling Improves Knee Pain and Physical Functioning in Patients With Knee Osteoarthritis: A Randomized Controlled Trial.

OBJECTIVE: To assess the efficacy of a 12-week aquatic cycling training program for improving knee pain and physical functioning in patients with knee osteoarthritis (OA). DESIGN: Two-arm, single-blind, parallel-group randomized controlled trial. SETTINGS: OA outpatient clinic of the Maastricht University Medical Center+. PARTICIPANTS: Patients (N=111, 50-70y) with unilateral mild-to-moderate knee OA. INTERVENTIONS: Participants (aquatic cycling [AC] group, n=55) received AC sessions of 45 min each 2 times per week. Each session combined upright seated cycling with out-of-saddle positions and exercises for the upper and lower body. The usual care (UC) group (n=47) continued with UC and was offered 12 AC sessions in a local swimming pool after their trial participation. MAIN OUTCOME MEASURES: The Knee Injury and Osteoarthritis Outcome Score (KOOS) on knee pain and physical function was assessed at baseline, postintervention, and at 24-wk follow-up. Multilevel (mixed regression) analysis examined the effects. RESULTS: Average attendance rate for the AC sessions was 80%. Statistically significant differences at postintervention and follow-up were found for knee pain in mean ± SD (UC pretest, 57.89±15.26; posttest, 55.90±18.04; follow-up, 57.24±19.16; and AC pretest, 56.96±12.96; posttest, 63.55±15.33; follow-up, 64.35±17.26; estimate, 8.16; SE, 3.27; 95% confidence interval [CI], 1.67-14.64; effect size [ES], 0.50) and physical functioning (UC pretest, 66.32±16.28; posttest, 66.80±19.04; follow-up, 65.42±17.98; and AC pretest, 61.89±17.151; posttest, 70.14±17.52; follow-up, 69.00±16.84; estimate, 7.16; SE, 3.19; 95% CI, 0.83-13.49; ES, 0.43) in favor of the aquatic group. CONCLUSIONS: The results suggest that a 12-week AC training program improves self-reported knee pain and physical functioning in patients with mild-to-moderate knee OA compared to UC.

The perceived behavior and barriers of community care professionals in encouraging functional activities of older adults: the development and validation of the MAINtAIN-C questionnaire.

BACKGROUND: Community care professionals need to encourage older adults in performing functional activities to maintain independence. However, professionals often perform functional activities on behalf of older adults. To change this, insights into the behavior and barriers of professionals in encouraging activities are required. In the current study, the MAINtAIN questionnaire, which was developed for nursing homes, was adopted. The objective was to create a modified version that is suitable for measuring behavior and barriers of community care professionals in encouraging functional activities of clients in the community care setting. The overall aims were to assess the content validity, construct validity, and internal consistency of the modified version. METHODS: Data was collected by qualitative and quantitative methods in two phases. During phase one, the MAINtAIN was assessed on appropriateness and feasibility by community nurses (N = 7), and the adapted questionnaire was assessed on content validity by research experts (N = 9) and community care professionals (N = 18). During phase two, the psychometric properties of the adapted MAINtAIN-C were assessed in community care professionals (N = 80). Construct validity was evaluated by an Exploratory Factor Analysis (EFA), and internal consistency was determined by calculating Cronbach's alpha coefficients. RESULTS: The formulation, verbs, and wording of the MAINtAIN were adapted; some items were excluded and relevant items were added, resulting in the MAINtAIN-C with two scales, showing good content validity. The Behaviors scale (20 items) measures perceived behavior in encouraging functional activities, expressing good internal consistency (Cronbach's alpha: .92). The Barriers scale measures barriers in encouraging functional activities related to two dimensions: 1) the clients' context (7 items), with good internal consistency (.78); and 2) the professional, social, and organizational contexts (21 items), showing good internal consistency (.83). CONCLUSIONS: The MAINtAIN-C seems promising to assess the behavior and barriers of community care professionals in encouraging functional activities. It can be used to display a possible difference between perceived and actual behavior, to develop strategies for removing barriers in encouraging activities to foster behavioral change. The results also provide guidance for further research in a larger sample to obtain more insight into the psychometric properties.

Imputation of missing covariate in randomized controlled trials with a continuous outcome: Scoping review and new results.

In this article, we first review the literature on dealing with missing values on a covariate in randomized studies and summarize what has been done and what is lacking to date. We then investigate the situation with a continuous outcome and a missing binary covariate in more details through simulations, comparing the performance of multiple imputation (MI) with various simple alternative methods. This is finally extended to the case of time-to-event outcome. The simulations consider five different missingness scenarios: missing completely at random (MCAR), at random (MAR) with missingness depending only on the treatment, and missing not at random (MNAR) with missingness depending on the covariate itself (MNAR1), missingness depending on both the treatment and covariate (MNAR2), and missingness depending on the treatment, covariate and their interaction (MNAR3). Here, we distinguish two different cases: (1) when the covariate is measured before randomization (best practice), where only MCAR and MNAR1 are plausible, and (2) when it is measured after randomization but before treatment (which sometimes occurs in nonpharmaceutical research), where the other three missingness mechanisms can also occur. The proposed methods are compared based on the treatment effect estimate and its standard error. The simulation results suggest that the patterns of results are very similar for all missingness scenarios in case (1) and also in case (2) except for MNAR3. Furthermore, in each scenario for continuous outcome, there is at least one simple method that performs at least as well as MI, while for time-to-event outcome MI is best.

Relative efficiencies of two-stage sampling schemes for mean estimation in multilevel populations when cluster size is informative.

In multilevel populations, there are two types of population means of an outcome variable ie, the average of all individual outcomes ignoring cluster membership and the average of cluster-specific means. To estimate the first mean, individuals can be sampled directly with simple random sampling or with two-stage sampling (TSS), that is, sampling clusters first, and then individuals within the sampled clusters. When cluster size varies in the population, three TSS schemes can be considered, ie, sampling clusters with probability proportional to cluster size and then sampling the same number of individuals per cluster; sampling clusters with equal probability and then sampling the same percentage of individuals per cluster; and sampling clusters with equal probability and then sampling the same number of individuals per cluster. Unbiased estimation of the average of all individual outcomes is discussed under each sampling scheme assuming cluster size to be informative. Furthermore, the three TSS schemes are compared in terms of efficiency with each other and with simple random sampling under the constraint of a fixed total sample size. The relative efficiency of the sampling schemes is shown to vary across different cluster size distributions. However, sampling clusters with probability proportional to size is the most efficient TSS scheme for many cluster size distributions. Model-based and design-based inference are compared and are shown to give similar results. The results are applied to the distribution of high school size in Italy and the distribution of patient list size for general practices in England.

A Longitudinal Study on the Relations Among Fear-Enhancing Parenting, Cognitive Biases, and Anxiety Symptoms in Non-clinical Children.

This longitudinal study explored the relations between fear-enhancing parenting behaviors (modeling and threat information transmission) and children's cognitive biases and anxiety symptoms on three subsequent time points over a one-year period. Participants were 216 children aged 7-12 years (114 boys and 102 girls), and their mothers (n = 199) and/or fathers (n = 117). On each time point, children and parents completed the Parental Enhancement of Anxious Cognitions scale, which measures parental modeling and threat information transmission. Furthermore, children filled in a measure of anxiety disorder symptoms. In addition, confirmation bias and interpretation bias were measured by means of a number of computerized tasks. The results yielded support for a circular model in which cognitive biases enhanced anxiety symptoms, which in turn promoted cognitive biases on each of the three time points. However, no evidence was found for longitudinal effects of cognitive biases on anxiety or vice versa. In contrast to what we expected, cognitive biases and anxiety appeared to promote parental modeling and threat information rather than the other way around. These findings extend research on the relations between parenting behaviors, cognitive biases, and childhood anxiety symptoms, and suggest valuable leads for assessment and intervention.

The course of fear of cancer recurrence: Different patterns by age in breast cancer survivors.

OBJECTIVE: To examine the time course and predictors of fear of cancer recurrence (FCR) in breast cancer survivors over a period of 18 months after initial surgery. METHODS: Breast cancer patients (n = 267) were followed until 18 months after primary breast surgery. Shortly after surgery, participants completed the Life Orientation Test-Revised to measure optimism and the Concerns about Recurrence Scale to measure FCR. Mixed regression analysis was performed with age, optimism, marital status, education, type of surgery, with or without lymphectomy, chemotherapy, hormonal therapy, or radiotherapy, time since surgery, and all interactions with time as predictors of FCR. RESULTS: The final model included a significant interaction between age and time since surgery and a main effect for optimism. CONCLUSION: These results suggest that the course of FCR depends on the age of breast cancer survivors. Younger survivors showed an increase of fear during the first 1.5 years after breast surgery, whereas older survivors showed stable levels during the first 6 months after which it declined. Also, less optimistic survivors reported higher levels of FCR. Health care providers should pay (extra) attention to FCR in younger and less optimistic patients and offer psychological help when needed.

Efficient design of cluster randomized trials with treatment-dependent costs and treatment-dependent unknown variances.

Cluster randomized trials evaluate the effect of a treatment on persons nested within clusters, where treatment is randomly assigned to clusters. Current equations for the optimal sample size at the cluster and person level assume that the outcome variances and/or the study costs are known and homogeneous between treatment arms. This paper presents efficient yet robust designs for cluster randomized trials with treatment-dependent costs and treatment-dependent unknown variances, and compares these with 2 practical designs. First, the maximin design (MMD) is derived, which maximizes the minimum efficiency (minimizes the maximum sampling variance) of the treatment effect estimator over a range of treatment-to-control variance ratios. The MMD is then compared with the optimal design for homogeneous variances and costs (balanced design), and with that for homogeneous variances and treatment-dependent costs (cost-considered design). The results show that the balanced design is the MMD if the treatment-to control cost ratio is the same at both design levels (cluster, person) and within the range for the treatment-to-control variance ratio. It still is highly efficient and better than the cost-considered design if the cost ratio is within the range for the squared variance ratio. Outside that range, the cost-considered design is better and highly efficient, but it is not the MMD. An example shows sample size calculation for the MMD, and the computer code (SPSS and R) is provided as supplementary material. The MMD is recommended for trial planning if the study costs are treatment-dependent and homogeneity of variances cannot be assumed.

Efficient treatment allocation in 2 × 2 multicenter trials when costs and variances are heterogeneous.

At the design stage of a study, it is crucial to compute the sample size needed for treatment effect estimation with maximum precision and power. The optimal design depends on the costs, which may be known at the design stage, and on the outcome variances, which are unknown. A balanced design, optimal for homogeneous costs and variances, is typically used. An alternative to the balanced design is a design optimal for the known and possibly heterogeneous costs, and homogeneous variances, called costs considering design. Both designs suffer from loss of efficiency, compared with optimal designs for heterogeneous costs and variances. For 2 × 2 multicenter trials, we compute the relative efficiency of the balanced and the costs considering designs, relative to the optimal designs. We consider 2 heterogeneous costs and variance scenarios (in 1 scenario, 2 treatment conditions have small and 2 have large costs and variances; in the other scenario, 1 treatment condition has small, 2 have intermediate, and 1 has large costs and variances). Within these scenarios, we examine the relative efficiency of the balanced design and of the costs considering design as a function of the extents of heterogeneity of the costs and of the variances and of their congruence (congruent when the cheapest treatment has the smallest variance, incongruent when the cheapest treatment has the largest variance). We find that the costs considering design is generally more efficient than the balanced design, and we illustrate this theory on a 2 × 2 multicenter trial on lifestyle improvement of patients in general practices.

Effects, costs and feasibility of the 'Stay Active at Home' Reablement training programme for home care professionals: study protocol of a cluster randomised controlled trial.

BACKGROUND: According to the principles of Reablement, home care services are meant to be goal-oriented, holistic and person-centred taking into account the capabilities and opportunities of older adults. However, home care services traditionally focus on doing things for older adults rather than with them. To implement Reablement in practice, the 'Stay Active at Home' programme was developed. It is assumed that the programme leads to a reduction in sedentary behaviour in older adults and consequently more cost-effective outcomes in terms of their health and wellbeing. However, this has yet to be proven. METHODS/ DESIGN: A two-group cluster randomised controlled trial with 12 months follow-up will be conducted. Ten nursing teams will be selected, pre-stratified on working area and randomised into an intervention group ('Stay Active at Home') or control group (no training). All nurses of the participating teams are eligible to participate in the study. Older adults and, if applicable, their domestic support workers (DSWs) will be allocated to the intervention or control group as well, based on the allocation of the nursing team. Older adults are eligible to participate, if they: 1) receive homecare services by the selected teams; and 2) are 65 years or older. Older adults will be excluded if they: 1) are terminally ill or bedbound; 2) have serious cognitive or psychological problems; or 3) are unable to communicate in Dutch. DSWs are eligible to participate if they provide services to clients who fulfil the eligibility criteria for older adults. The study consists of an effect evaluation (primary outcome: sedentary behaviour in older adults), an economic evaluation and a process evaluation. Data for the effect and economic evaluation will be collected at baseline and 6 and/or 12 months after baseline using performance-based and self-reported measures. In addition, data from client records will be extracted. A mixed-methods design will be applied for the process evaluation, collecting data of older adults and professionals throughout the study period. DISCUSSION: This study will result in evidence about the effectiveness, cost-effectiveness and feasibility of the 'Stay Active at Home' programme. TRIAL REGISTRATION: ClinicalTrials.gov: NCT03293303 , registered on 20 September 2017.

SPEEK: effect evaluation of a Ghanaian school-based and peer-led sexual education programme.

In sub-Saharan Africa, theory and evidenced-based interventions that are systematically designed and using sound evaluation methods to report on effectiveness are limited. A sex education programme called SPEEK was developed, implemented and evaluated in Ghana using the Intervention Mapping approach. SPEEK aimed at delaying sexual initiation, reducing sexually transmitted infections (STIs) and preventing pregnancy, targeting junior high school students in a West African rural setting. The final programme included 11 (interactive) lessons using a diverse range of theory-based methods. In this article, we report on the effect evaluation of the programme. Participating schools were randomized to the intervention (N = 10 schools) and a waiting-list control group (N = 11 schools). The students completed survey questionnaires at baseline (N = 1822), at direct post-test (N = 1805) and at six months follow-up (N = 1959), measuring cognitive and affective psychosocial determinants of sexual delay, condom use and STI testing. Mixed regression models showed that at direct post-test, students having received the SPEEK programme scored significantly more positively on knowledge on condom use, pregnancy and STIs testing; attitude toward exercising sexual rights, condom availability and condom use; perceived behavioural control toward sexual delay, condom use and sexual intercourse; and perceived risk toward STIs (P's < 0.002). The results suggest that the programme may improve adolescent sexual health in Ghana or in similar cultures, but would need further study that include behavioural measures and a longer follow-up to make this assertion with more confidence.

Gamified working memory training in overweight individuals reduces food intake but not body weight.

Working Memory (WM) plays a crucial role in successful self-regulation of behavior, including weight regulation. Improving WM might therefore be a promising strategy to support weight loss. In the present study, overweight individuals with a desire to lose weight (N = 91) received an online lifestyle intervention, in conjunction with either 25 sessions of gamified WM training (experimental condition) or a sham training (control). Primary outcomes were Body Mass Index (BMI) and food intake at posttest. Secondary outcomes were executive functioning, self-control, eating style, eating psychopathology and healthy eating. Data were analyzed with mixed regression analyses with condition as between-subjects factor (experimental versus control) and time as within-subjects factor (baseline, posttest, FU1 after one month and FU2 after six months). Results revealed that the experimental condition increased their WM span more than control from pretest to posttest, and these gains were retained at FU1, though lost at FU2. No transfer effects of WM training to other executive functioning measures were found. During the bogus taste test at posttest, participants in the experimental condition consumed significantly less than participants in the control condition. However, both conditions showed a small reduction in BMI, improved eating style, reduced eating disorder pathology, and reported more self-control and a healthier eating pattern. In conclusion, the current results provide some evidence that WM training can improve eating behavior at the short term. However, the WM gains were short-lived, and the added value of WM training as an intervention to promote weight loss could not be established. Future studies should test the added value of WM training booster sessions to promote weight loss over a prolonged period of time.

Repairing the efficiency loss due to varying cluster sizes in two-level two-armed randomized trials with heterogeneous clustering.

In two-armed trials with clustered observations the arms may differ in terms of (i) the intraclass correlation, (ii) the outcome variance, (iii) the average cluster size, and (iv) the number of clusters. For a linear mixed model analysis of the treatment effect, this paper examines the expected efficiency loss due to varying cluster sizes based upon the asymptotic relative efficiency of varying versus constant cluster sizes. Simple, but nearly cost-optimal, correction factors are derived for the numbers of clusters to repair this efficiency loss. In an extensive Monte Carlo simulation, the accuracy of the asymptotic relative efficiency and its Taylor approximation are examined for small sample sizes. Practical guidelines are derived to correct the numbers of clusters calculated under constant cluster sizes (within each treatment) when planning a study. Because of the variety of simulation conditions, these guidelines can be considered conservative but safe in many realistic situations. Copyright © 2016 John Wiley & Sons, Ltd.

Efficient treatment allocation in 2 × 2 cluster randomized trials, when costs and variances are heterogeneous.

Typically, clusters and individuals in cluster randomized trials are allocated across treatment conditions in a balanced fashion. This is optimal under homogeneous costs and outcome variances. However, both the costs and the variances may be heterogeneous. Then, an unbalanced allocation is more efficient but impractical as the outcome variance is unknown in the design stage of a study. A practical alternative to the balanced design could be a design optimal for known and possibly heterogeneous costs and homogeneous variances. However, when costs and variances are heterogeneous, both designs suffer from loss of efficiency, compared with the optimal design. Focusing on cluster randomized trials with a 2 × 2 design, the relative efficiency of the balanced design and of the design optimal for heterogeneous costs and homogeneous variances is evaluated, relative to the optimal design. We consider two heterogeneous scenarios (two treatment arms with small, and two with large, costs or variances, or one small, two intermediate, and one large costs or variances) at each design level (cluster, individual, and both). Within these scenarios, we compute the relative efficiency of the two designs as a function of the extents of heterogeneity of the costs and variances, and the congruence (the cheapest treatment has the smallest variance) and incongruence (the cheapest treatment has the largest variance) between costs and variances. We find that the design optimal for heterogeneous costs and homogeneous variances is generally more efficient than the balanced design and we illustrate this theory on a trial that examines methods to reduce radiological referrals from general practices. Copyright © 2016 John Wiley & Sons, Ltd.

On the Strength and Validity of Hazard Banding.

Hazard Banding (HB) is a process of allocating chemical substances in bands of increasing health hazard based on their hazard classifications. Recent Control Banding (CB) tools use the classifications of the United Nations Global Harmonized System (UN GHS) or the European Union Classifications, Labelling and Packaging (EU CLP) which are grouped over 5 HBs. The use of CB is growing worldwide for the risk control of substances without an Occupational Exposure Limit Value (OELV). Well-known CB-tools like HSE-COSHH Essentials, BAuA-Einfaches Maßnahmenkonzept Gefahrstoffe (EMKG), and DGUV-IFA-Spaltenmodell (IFA) use however different GHS/CLP groupings which may lead to dissimilar HBs and control regimes for individual substances. And as the choice for a CB tool seems to be determined by geography and/or local status these differences may hamper a global, aligned HSE approach. Therefore, the HB-engines of the three public CBs and an in-company (Solvay) CB called 'Occupational Exposure Banding' (S-OEB) were compared mutually and ranked in their relation with the OELV as the 'de facto' standard. This was investigated graphically and using a 5 strength indicator, statistical method. A data set of 229 substances with high-quality GHS/CLP classifications and OELVs was used. HB concentration ranges, as linked to S-OEB and COSHH, were validated against the corresponding OELV distributions. The four HB-engines allocate between 23 and 64% of the 229 substances in the same bands. The remaining substances differ at least one band, with IFA placing more substances in a higher hazard band, EMKG doing the opposite and COSHH and S-OEB in between. The overall strength scores of S-OEB, IFA, and EMGK HB-engines are higher than COSHH, with S-OEB having the highest overall strength score. The lower ends of the concentration ranges defined for the 3 'highest' hazard bands of S-OEB were in good agreement with the 10th percentiles of the corresponding OELV distributions obtained from the substance data set. The lower ends of the COSHH concentration ranges comply with the 10th percentiles of the COSHH OELV distributions for dust/aerosol but not for vapour/gas substances. Both the S-OEB and COSHH concentration ranges underestimate the overall width of the OELV distributions that can span 2-3 orders of magnitude. As the performance of the S-OEB HB-engine meets our criteria of being at least as good as the public engines, it will be used as a standard within Solvay's global operations. In addition, the method described here to evaluate the strength of HB-engines and the validity of their corresponding concentration ranges is a useful tool enabling further developments and worldwide alignment of HB.