Negative variance components and intercept-slope correlations greater than one in magnitude: How do such "non-regular" random intercept and slope models arise, and what should be done when they do?

Statistical models with random intercepts and slopes (RIAS models) are commonly used to analyze longitudinal data. Fitting such models sometimes results in negative estimates of variance components or estimates on parameter space boundaries. This can be an unlucky chance occurrence, but can also occur because certain marginal distributions are mathematically identical to those from RIAS models with negative intercept and/or slope variance components and/or intercept-slope correlations greater than one in magnitude. We term such parameters "pseudo-variances" and "pseudo-correlations," and the models "non-regular." We use eigenvalue theory to explore how and when such non-regular RIAS models arise, showing: (i) A small number of measurements, short follow-up, and large residual variance increase the parameter space for which data (with a positive semidefinite marginal variance-covariance matrix) are compatible with non-regular RIAS models. (ii) Non-regular RIAS models can arise from model misspecification, when non-linearity in fixed effects is ignored or when random effects are omitted. (iii) A non-regular RIAS model can sometimes be interpreted as a regular linear mixed model with one or more additional random effects, which may not be identifiable from the data. (iv) Particular parameterizations of non-regular RIAS models have no generality for all possible numbers of measurements over time. Because of this lack of generality, we conclude that non-regular RIAS models can only be regarded as plausible data-generating mechanisms in some situations. Nevertheless, fitting a non-regular RIAS model can be acceptable, allowing unbiased inference on fixed effects where commonly recommended alternatives such as dropping the random slope result in bias.

How important is the linearity assumption in a sample size calculation for a randomised controlled trial where treatment is anticipated to affect a rate of change?

BACKGROUND: For certain conditions, treatments aim to lessen deterioration over time. A trial outcome could be change in a continuous measure, analysed using a random slopes model with a different slope in each treatment group. A sample size for a trial with a particular schedule of visits (e.g. annually for three years) can be obtained using a two-stage process. First, relevant (co-) variances are estimated from a pre-existing dataset e.g. an observational study conducted in a similar setting. Second, standard formulae are used to calculate sample size. However, the random slopes model assumes linear trajectories with any difference in group means increasing proportionally to follow-up time. The impact of these assumptions failing is unclear. METHODS: We used simulation to assess the impact of a non-linear trajectory and/or non-proportional treatment effect on the proposed trial's power. We used four trajectories, both linear and non-linear, and simulated observational studies to calculate sample sizes. Trials of this size were then simulated, with treatment effects proportional or non-proportional to time. RESULTS: For a proportional treatment effect and a trial visit schedule matching the observational study, powers are close to nominal even for non-linear trajectories. However, if the schedule does not match the observational study, powers can be above or below nominal levels, with the extent of this depending on parameters such as the residual error variance. For a non-proportional treatment effect, using a random slopes model can lead to powers far from nominal levels. CONCLUSIONS: If trajectories are suspected to be non-linear, observational data used to inform power calculations should have the same visit schedule as the proposed trial where possible. Additionally, if the treatment effect is expected to be non-proportional, the random slopes model should not be used. A model allowing trajectories to vary freely over time could be used instead, either as a second line analysis method (bearing in mind that power will be lost) or when powering the trial.

Power and sample-size calculations for trials that compare slopes over time: Introducing the slopepower command.

Trials of interventions that aim to slow disease progression may analyze a continuous outcome by comparing its change over time-its slope-between the treated and the untreated group using a linear mixed model. To perform a sample-size calculation for such a trial, one must have estimates of the parameters that govern the between- and within-subject variability in the outcome, which are often unknown. The algebra needed for the sample-size calculation can also be complex for such trial designs. We have written a new user-friendly command, slopepower, that performs sample-size or power calculations for trials that compare slope outcomes. The package is based on linear mixed-model methodology, described for this setting by Frost, Kenward, and Fox (2008, Statistics in Medicine 27: 3717-3731). In the first stage of this approach, slopepower obtains estimates of mean slopes together with variances and covariances from a linear mixed model fit to previously collected user-supplied data. In the second stage, these estimates are combined with user input about the target effectiveness of the treatment and design of the future trial to give an estimate of either a sample size or a statistical power. In this article, we present the slopepower command, briefly explain the methodology behind it, and demonstrate how it can be used to help plan a trial and compare the sample sizes needed for different trial designs.

Precipitation and vegetation shape patterns of genomic and craniometric variation in the central African rodent Praomys misonnei.

Predicting species' capacity to respond to climate change is an essential first step in developing effective conservation strategies. However, conservation prioritization schemes rarely take evolutionary potential into account. Ecotones provide important opportunities for diversifying selection and may thus constitute reservoirs of standing variation, increasing the capacity for future adaptation. Here, we map patterns of environmentally associated genomic and craniometric variation in the central African rodent Praomys misonnei to identify areas with the greatest turnover in genomic composition. We also project patterns of environmentally associated genomic variation under future climate change scenarios to determine where populations may be under the greatest pressure to adapt. While precipitation gradients influence both genomic and craniometric variation, vegetation structure is also an important determinant of craniometric variation. Areas of elevated environmentally associated genomic and craniometric variation overlap with zones of rapid ecological transition underlining their importance as reservoirs of evolutionary potential. We also find that populations in the Sanaga river basin, central Cameroon and coastal Gabon are likely to be under the greatest pressure from climate change. Lastly, we make specific conservation recommendations on how to protect zones of high evolutionary potential and identify areas where populations may be the most susceptible to climate change.

The association between anthropometric measures of adiposity and the progression of carotid atherosclerosis.

BACKGROUND: Few reports are available on the contribution of general and abdominal obesity to the progression of carotid atherosclerosis in late adulthood. This study investigated the impact of four simple anthropometric measures of general and abdominal obesity on the progression of carotid atherosclerosis and the extent to which the association between adiposity and the progression of plaque burden is mediated by cardiometabolic markers. METHODS: Four thousand three hundred forty-five adults (median age 60) from the population-based Tromsø Study were followed over 7 years from the first carotid ultrasound screening to the next. The progression of carotid atherosclerosis was measured in three ways: incidence of plaques in previously plaque-free participants; change in the number of plaques; and total plaque area (TPA). We used generalised linear models to investigate the association between each adiposity measure - body mass index (BMI), waist circumference (WC), waist-to-hip ratio (WHR), and waist-to-height ratio (WHtR) - and each outcome. Models were adjusted for potential confounders (age, sex, smoking, education, physical activity). The pathways through which any associations observed might operate were investigated by further adjusting for cardiometabolic mediators (systolic blood pressure, cholesterol, and HbA1c). RESULTS: There was little evidence that adiposity was related to the formation of new plaques during follow-up. However, abdominal adiposity was associated with TPA progression. WHtR showed the largest effect size (mean change in TPA per one standard deviation (SD) increase in WHtR of 0.665 mm2, 95% confidence interval 0.198, 1.133) while BMI showed the smallest. Effect sizes were substantially reduced after the adjustment for potential mediators. CONCLUSIONS: Abdominal obesity indirectly measured with WC seems more strongly associated with the progression of TPA than general obesity. These associations appear to be largely mediated by known cardiometabolic markers.

Disrupted Gene Networks in Subfertile Hybrid House Mice.

The Dobzhansky-Muller (DM) model provides a widely accepted mechanism for the evolution of reproductive isolation: incompatible substitutions disrupt interactions between genes. To date, few candidate incompatibility genes have been identified, leaving the genes driving speciation mostly uncharacterized. The importance of interactions in the DM model suggests that gene coexpression networks provide a powerful framework to understand disrupted pathways associated with postzygotic isolation. Here, we perform weighted gene coexpression network analysis to infer gene interactions in hybrids of two recently diverged European house mouse subspecies, Mus mus domesticus and M. m. musculus, which commonly show hybrid male sterility or subfertility. We use genome-wide testis expression data from 467 hybrid mice from two mapping populations: F2s from a laboratory cross between wild-derived pure subspecies strains and offspring of natural hybrids captured in the Central Europe hybrid zone. This large data set enabled us to build a robust consensus network using hybrid males with fertile phenotypes. We identify several expression modules, or groups of coexpressed genes, that are disrupted in subfertile hybrids, including modules functionally enriched for spermatogenesis, cilium and sperm flagellum organization, chromosome organization, and DNA repair, and including genes expressed in spermatogonia, spermatocytes, and spermatids. Our network-based approach enabled us to hone in on specific hub genes likely to be influencing module-wide gene expression and hence potentially driving large-effect DM incompatibilities. A disproportionate number of hub genes lie within sterility loci identified previously in the hybrid zone mapping population and represent promising candidate barrier genes and targets for future functional analysis.

Reflection on modern methods: calculating a sample size for a repeatability sub-study to correct for measurement error in a single continuous exposure.

Using a continuous exposure variable that is measured with random error in a univariable linear regression model leads to regression dilution bias: the observed association between the exposure and outcome is smaller than it would be if the true value of the exposure could be used. A repeatability sub-study, where a sample of study participants have their data measured again, can be used to correct for this bias. It is important to perform a sample size calculation for such a sub-study, to ensure that correction factors can be estimated with sufficient precision. We describe how a previously published method can be used to calculate the sample size from the anticipated size of the correction factor and its desired precision, and demonstrate this approach using the example of the cross-sectional studies conducted as part of the International Project on Cardiovascular Disease in Russia study. We also provide correction factors calculated from repeat data from the UK Biobank study, which can be used to help plan future repeatability studies.

Know Your Heart: Rationale, design and conduct of a cross-sectional study of cardiovascular structure, function and risk factors in 4500 men and women aged 35-69 years from two Russian cities, 2015-18.

Russia has one of the highest rates of cardiovascular disease in the world. The International Project on Cardiovascular Disease in Russia (IPCDR) was set up to understand the reasons for this. A substantial component of this study was the Know Your Heart Study devoted to characterising the nature and causes of cardiovascular disease in Russia by conducting large cross-sectional surveys in two Russian cities Novosibirsk and Arkhangelsk. The study population was 4542 men and women aged 35-69 years recruited from the general population. Fieldwork took place between 2015-18. There were two study components: 1) a baseline interview to collect information on socio-demographic characteristics and cardiovascular risk factors, usually conducted at home, and 2) a comprehensive health check at a primary care clinic which included detailed examination of the cardiovascular system. In this paper we describe in detail the rationale for, design and conduct of these studies.

A pedometer-based walking intervention in 45- to 75-year-olds, with and without practice nurse support: the PACE-UP three-arm cluster RCT.

BACKGROUND: Guidelines recommend walking to increase moderate to vigorous physical activity (MVPA) for health benefits. OBJECTIVES: To assess the effectiveness, cost-effectiveness and acceptability of a pedometer-based walking intervention in inactive adults, delivered postally or through dedicated practice nurse physical activity (PA) consultations. DESIGN: Parallel three-arm trial, cluster randomised by household. SETTING: Seven London-based general practices. PARTICIPANTS: A total of 11,015 people without PA contraindications, aged 45-75 years, randomly selected from practices, were invited. A total of 6399 people were non-responders, and 548 people self-reporting achieving PA guidelines were excluded. A total of 1023 people from 922 households were randomised to usual care (n = 338), postal intervention (n = 339) or nurse support (n = 346). The recruitment rate was 10% (1023/10,467). A total of 956 participants (93%) provided outcome data. INTERVENTIONS: Intervention groups received pedometers, 12-week walking programmes advising participants to gradually add '3000 steps in 30 minutes' most days weekly and PA diaries. The nurse group was offered three dedicated PA consultations. MAIN OUTCOME MEASURES: The primary and main secondary outcomes were changes from baseline to 12 months in average daily step counts and time in MVPA (in ≥ 10-minute bouts), respectively, from 7-day accelerometry. Individual resource-use data informed the within-trial economic evaluation and the Markov model for simulating long-term cost-effectiveness. Qualitative evaluations assessed nurse and participant views. A 3-year follow-up was conducted. RESULTS: Baseline average daily step count was 7479 [standard deviation (SD) 2671], average minutes per week in MVPA bouts was 94 minutes (SD 102 minutes) for those randomised. PA increased significantly at 12 months in both intervention groups compared with the control group, with no difference between interventions; additional steps per day were 642 steps [95% confidence interval (CI) 329 to 955 steps] for the postal group and 677 steps (95% CI 365 to 989 steps) for nurse support, and additional MVPA in bouts (minutes per week) was 33 minutes per week (95% CI 17 to 49 minutes per week) for the postal group and 35 minutes per week (95% CI 19 to 51 minutes per week) for nurse support. Intervention groups showed no increase in adverse events. Incremental cost per step was 19p and £3.61 per minute in a ≥ 10-minute MVPA bout for nurse support, whereas the postal group took more steps and cost less than the control group. The postal group had a 50% chance of being cost-effective at a £20,000 per quality-adjusted life-year (QALY) threshold within 1 year and had both lower costs [-£11M (95% CI -£12M to -£10M) per 100,000 population] and more QALYs [759 QALYs gained (95% CI 400 to 1247 QALYs)] than the nurse support and control groups in the long term. Participants and nurses found the interventions acceptable and enjoyable. Three-year follow-up data showed persistent intervention effects (nurse support plus postal vs. control) on steps per day [648 steps (95% CI 272 to 1024 steps)] and MVPA bouts [26 minutes per week (95% CI 8 to 44 minutes per week)]. LIMITATIONS: The 10% recruitment level, with lower levels in Asian and socioeconomically deprived participants, limits the generalisability of the findings. Assessors were unmasked to the group. CONCLUSIONS: A primary care pedometer-based walking intervention in 45- to 75-year-olds increased 12-month step counts by around one-tenth, and time in MVPA bouts by around one-third, with similar effects for the nurse support and postal groups, and persistent 3-year effects. The postal intervention provides cost-effective, long-term quality-of-life benefits. A primary care pedometer intervention delivered by post could help address the public health physical inactivity challenge. FUTURE WORK: Exploring different recruitment strategies to increase uptake. Integrating the Pedometer And Consultation Evaluation-UP (PACE-UP) trial with evolving PA monitoring technologies. TRIAL REGISTRATION: Current Controlled Trials ISRCTN98538934. FUNDING: This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 22, No. 37. See the NIHR Journals Library website for further project information.

Increasing the Availability of Psychological Treatments: A Multinational Study of a Scalable Method for Training Therapists.

BACKGROUND: One of the major barriers to the dissemination and implementation of psychological treatments is the scarcity of suitably trained therapists. A highly scalable form of Web-centered therapist training, undertaken without external support, has recently been shown to have promise in promoting therapist competence. OBJECTIVE: The aim of this study was to conduct an evaluation of the acceptability and effectiveness of a scalable independent form of Web-centered training in a multinational sample of therapists and investigate the characteristics of those most likely to benefit. METHODS: A cohort of eligible therapists was recruited internationally and offered access to Web-centered training in enhanced cognitive behavioral therapy, a multicomponent, evidence-based, psychological treatment for any form of eating disorder. No external support was provided during training. Therapist competence was assessed using a validated competence measure before training and after 20 weeks. RESULTS: A total of 806 therapists from 33 different countries expressed interest in the study, and 765 (94.9%) completed a pretraining assessment. The median number of training modules completed was 15 out of a possible 18 (interquartile range, IQR: 4-18), and 87.9% (531/604) reported that they treated at least one patient during training as recommended. Median pretraining competence score was 7 (IQR: 5-10, range: 0-19; N=765), and following training, it was 12 (IQR: 9-15, range: 0-20; N=577). The expected change in competence scores from pretraining to posttraining was 3.5 (95% CI 3.1-3.8; P<.001). After training, 52% (300/574) of therapists with complete competence data met or exceeded the competence threshold, and 45% (95% CI 41-50) of those who had not met this threshold before training did so after training. Compliance with training predicted both an increase in competence scores and meeting or exceeding the competence threshold. Expected change in competence score increased for each extra training module completed (0.19, 95% CI 0.13-0.25), and those who treated a suitable patient during training had an expected change in competence score 1.2 (95% CI 0.4-2.1) points higher than those who did not. Similarly, there was an association between meeting the competence threshold after training and the number of modules completed (odds ratio, OR=1.11, 95% CI 1.07-1.15), and treating at least one patient during training was associated with competence after training (OR=2.2, 95% CI 1.2-4.1). CONCLUSIONS: Independent Web-centered training can successfully train large numbers of therapists dispersed across a wide geographical area. This finding is of importance because the availability of a highly scalable method of training potentially increases the number of people who might receive effective psychological treatments.

The contribution of obesity to carotid atherosclerotic plaque burden in a general population sample in Norway: The Tromsø Study.

BACKGROUND AND AIMS: Few studies have investigated the association of different measures of adiposity with carotid plaque. We aimed to investigate and compare the associations of four measures of adiposity: body mass index (BMI), waist circumference (WC), waist-to-hip ratio (WHR), and waist-to-height ratio (WHtR) with the presence of carotid plaque and total plaque area (TPA) in the right carotid artery. METHODS: We included 4906 individuals aged 31-88 years who participated in a population-based study with ultrasonography of the right carotid artery. Adiposity measures were converted to sex-specific SD units to allow comparison of effect sizes. TPA was log transformed due to its skewed distribution. Logistic and linear regression models were used respectively to investigate the association of each adiposity measure with the presence of plaque and with log-transformed TPA. Estimates were adjusted for potential confounders and mediators such as blood pressure and lipids. RESULTS: After adjustment for age, sex, smoking, and education level, there was strong evidence of an association between all adiposity measures and log-transformed TPA, whereas only WHR was weakly associated with presence of plaque. WHR showed the largest adjusted effect size for both log-transformed TPA (beta 0.055, 95%CI 0.028-0.081) and the presence of plaque (OR 1.07, 95%CI 1.01-1.15). Adjustment for mediators led to appreciable attenuation of observed effects. CONCLUSIONS: Adiposity is more consistently associated with extent of plaque burden than with whether an individual does or does not have any plaque. There was evidence that established biomarkers mediate much of this association. Abdominal adiposity appears to show the strongest effect.

Combining optical coherence tomography with visual field data to rapidly detect disease progression in glaucoma: a diagnostic accuracy study.

BACKGROUND: Progressive optic nerve damage in glaucoma results in vision loss, quantifiable with visual field (VF) testing. VF measurements are, however, highly variable, making identification of worsening vision ('progression') challenging. Glaucomatous optic nerve damage can also be measured with imaging techniques such as optical coherence tomography (OCT). OBJECTIVE: To compare statistical methods that combine VF and OCT data with VF-only methods to establish whether or not these allow (1) more rapid identification of glaucoma progression and (2) shorter or smaller clinical trials. DESIGN: Method 'hit rate' (related to sensitivity) was evaluated in subsets of the United Kingdom Glaucoma Treatment Study (UKGTS) and specificity was evaluated in 72 stable glaucoma patients who had 11 VF and OCT tests within 3 months (the RAPID data set). The reference progression detection method was based on Guided Progression Analysis™ (GPA) Software (Carl Zeiss Meditec Inc., Dublin, CA, USA). Index methods were based on previously described approaches [Analysis with Non-Stationary Weibull Error Regression and Spatial enhancement (ANSWERS), Permutation analyses Of Pointwise Linear Regression (PoPLR) and structure-guided ANSWERS (sANSWERS)] or newly developed methods based on Permutation Test (PERM), multivariate hierarchical models with multiple imputation for censored values (MaHMIC) and multivariate generalised estimating equations with multiple imputation for censored values (MaGIC). SETTING: Ten university and general ophthalmology units (UKGTS) and a single university ophthalmology unit (RAPID). PARTICIPANTS: UKGTS participants were newly diagnosed glaucoma patients randomised to intraocular pressure-lowering drops or placebo. RAPID participants had glaucomatous VF loss, were on treatment and were clinically stable. INTERVENTIONS: 24-2 VF tests with the Humphrey Field Analyzer and optic nerve imaging with time-domain (TD) Stratus OCT™ (Carl Zeiss Meditec Inc., Dublin, CA, USA). MAIN OUTCOME MEASURES: Criterion hit rate and specificity, time to progression, future VF prediction error, proportion progressing in UKGTS treatment groups, hazard ratios (HRs) and study sample size. RESULTS: Criterion specificity was 95% for all tests; the hit rate was 22.2% for GPA, 41.6% for PoPLR, 53.8% for ANSWERS and 61.3% for sANSWERS (all comparisons p ≤ 0.042). Mean survival time (weeks) was 93.6 for GPA, 82.5 for PoPLR, 72.0 for ANSWERS and 69.1 for sANSWERS. The median prediction errors (decibels) when the initial trend was used to predict the final VF were 3.8 (5th to 95th percentile 1.7 to 7.6) for PoPLR, 3.0 (5th to 95th percentile 1.5 to 5.7) for ANSWERS and 2.3 (5th to 95th percentile 1.3 to 4.5) for sANSWERS. HRs were 0.57 [95% confidence interval (CI) 0.34 to 0.90; p = 0.016] for GPA, 0.59 (95% CI 0.42 to 0.83; p = 0.002) for PoPLR, 0.76 (95% CI 0.56 to 1.02; p = 0.065) for ANSWERS and 0.70 (95% CI 0.53 to 0.93; p = 0.012) for sANSWERS. Sample size estimates were not reduced using methods including OCT data. PERM hit rates were between 8.3% and 17.4%. Treatment effects were non-significant in MaHMIC and MaGIC analyses; statistical significance was altered little by incorporating imaging. LIMITATIONS: TD OCT is less precise than current imaging technology; current OCT technology would likely perform better. The size of the RAPID data set limited the precision of criterion specificity estimates. CONCLUSIONS: The sANSWERS method combining VF and OCT data had a higher hit rate and identified progression more quickly than the reference and other VF-only methods, and produced more accurate estimates of the progression rate, but did not increase treatment effect statistical significance. Similar studies with current OCT technology need to be undertaken and the statistical methods need refinement. TRIAL REGISTRATION: Current Controlled Trials ISRCTN96423140. FUNDING: This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 22, No. 4. See the NIHR Journals Library website for further project information. Data analysed in the study were from the UKGTS. Funding for the UKGTS was provided through an unrestricted investigator-initiated research grant from Pfizer Inc. (New York, NY, USA), with supplementary funding from the NIHR Biomedical Research Centre at Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology, London, UK. Imaging equipment loans were made by Heidelberg Engineering, Carl Zeiss Meditec and Optovue (Fremont, CA, USA). Pfizer, Heidelberg Engineering, Carl Zeiss Meditec and Optovue had no input into the design, conduct, analysis or reporting of any of the UKGTS findings or this work. The sponsor for both the UKGTS and RAPID data collection was Moorfields Eye Hospital NHS Foundation Trust. David F Garway-Heath, Tuan-Anh Ho and Haogang Zhu are partly funded by the NIHR Biomedical Research Centre based at Moorfields Eye Hospital and UCL Institute of Ophthalmology. David F Garway-Heath's chair at University College London (UCL) is supported by funding from the International Glaucoma Association.

Interpreting population reach of a large, successful physical activity trial delivered through primary care.

BACKGROUND: Failure to include socio-economically deprived or ethnic minority groups in physical activity (PA) trials may limit representativeness and could lead to implementation of interventions that then increase health inequalities. Randomised intervention trials often have low recruitment rates and rarely assess recruitment bias. A previous trial by the same team using similar methods recruited 30% of the eligible population but was in an affluent setting with few non-white residents and was limited to those over 60 years of age. METHODS: PACE-UP is a large, effective, population-based walking trial in inactive 45-75 year-olds that recruited through seven London general practices. Anonymised practice demographic data were available for all those invited, enabling investigation of inequalities in trial recruitment. Non-participants were invited to complete a questionnaire. RESULTS: From 10,927 postal invitations, 1150 (10.5%) completed baseline assessment. Participation rate ratios (95% CI), adjusted for age and gender as appropriate, were lower in men 0.59 (0.52, 0.67) than women, in those under 55 compared with those ≥65, 0.60 (0.51, 0.71), in the most deprived quintile compared with the least deprived 0.52 (0.39, 0.70) and in Asian individuals compared with whites 0.62 (0.50, 0.76). Black individuals were equally likely to participate as white individuals. Participation was also associated with having a co-morbidity or some degree of health limitation. The most common reasons for non-participation were considering themselves as being too active or lack of time. CONCLUSIONS: Conducting the trial in this diverse setting reduced overall response, with lower response in socio-economically deprived and Asian sub-groups. Trials with greater reach are likely to be more expensive in terms of recruitment and gains in generalizability need to be balanced with greater costs. Differential uptake of successful trial interventions may increase inequalities in PA levels and should be monitored. TRIAL REGISTRATION: ISRCTN.com ISRCTN98538934 . Registered 2nd March 2012.

Climate warming causes declines in crop yields and lowers school attendance rates in Central Africa.

Although a number of recent studies suggest that climate associated shifts in agriculture are affecting social and economic systems, there have been relatively few studies of these effects in Africa. Such studies would be particularly useful in Central Africa, where the impacts of climate warming are predicted to be high but coincide with an area with low adaptive capacity. Focusing on plantain (Musa paradisiaca), we assess whether recent climate change has led to reduced yields. Analysis of annual temperature between 1950 and 2013 indicated a 0.8°C temperature increase over this 63-year period - a trend that is also observed in monthly temperatures in the last twenty years. From 1991 to 2011, there was a 43% decrease in plantain productivity in Central Africa, which was explained by shifts in temperature (R2=0.68). This decline may have reduced rural household wealth and decreased parental investment in education. Over the past two decades, there was a six month decrease in the duration of school attendance, and the decline was tightly linked to plantain yield (R2=0.82). By 2080, mean annual temperature is expected to increase at least 2°C in Central Africa, and our models predict a concomitant decrease of 39% in plantain yields and 51% in education outcomes, relative to the 1991 baseline. These predictions should be seen as a call-to-action for policy interventions such as farmer training programs to enhance the adaptive capacity of food production systems to mitigate impacts on rural income and education.

Cluster randomized trials with a small number of clusters: which analyses should be used?

Background: Cluster randomized trials (CRTs) are increasingly used to assess the effectiveness of health interventions. Three main analysis approaches are: cluster-level analyses, mixed-models and generalized estimating equations (GEEs). Mixed models and GEEs can lead to inflated type I error rates with a small number of clusters, and numerous small-sample corrections have been proposed to circumvent this problem. However, the impact of these methods on power is still unclear. Methods: We performed a simulation study to assess the performance of 12 analysis approaches for CRTs with a continuous outcome and 40 or fewer clusters. These included weighted and unweighted cluster-level analyses, mixed-effects models with different degree-of-freedom corrections, and GEEs with and without a small-sample correction. We assessed these approaches across different values of the intraclass correlation coefficient (ICC), numbers of clusters and variability in cluster sizes. Results: Unweighted and variance-weighted cluster-level analysis, mixed models with degree-of-freedom corrections, and GEE with a small-sample correction all maintained the type I error rate at or below 5% across most scenarios, whereas uncorrected approaches lead to inflated type I error rates. However, these analyses had low power (below 50% in some scenarios) when fewer than 20 clusters were randomized, with none reaching the expected 80% power. Conclusions: Small-sample corrections or variance-weighted cluster-level analyses are recommended for the analysis of continuous outcomes in CRTs with a small number of clusters. The use of these corrections should be incorporated into the sample size calculation to prevent studies from being underpowered.

Using the Internet to Train Therapists: Randomized Comparison of Two Scalable Methods.

BACKGROUND: One of the major barriers to the dissemination and implementation of psychological treatments is the scarcity of suitably trained therapists. The currently accepted method of training is not scalable. Recently, a scalable form of training, Web-centered training, has been shown to have promise. OBJECTIVE: The goal of our research was to conduct a randomized comparison of the relative effects of independent and supported Web-centered training on therapist competence and investigate the persistence of the effects. METHODS: Eligible therapists were recruited from across the United States and Canada. They were randomly assigned to 1 of 2 forms of training in enhanced cognitive behavior therapy (CBT-E), a multicomponent evidence-based psychological treatment for any form of eating disorder. Independent training was undertaken autonomously, while supported training was accompanied by support from a nonspecialist worker. Therapist competence was assessed using a validated competence measure before training, after 20 weeks of training, and 6 months after the completion of training. RESULTS: A total of 160 therapists expressed interest in the study, and 156 (97.5%) were randomized to the 2 forms of training (81 to supported training and 75 to independent training). Mixed effects analysis showed an increase in competence scores in both groups. There was no difference between the 2 forms of training, with mean difference for the supported versus independent group being -0.06 (95% Cl -1.29 to 1.16, P=.92). A total of 58 participants (58/114, 50.9%) scored above the competence threshold; three-quarters (43/58, 74%) had not met this threshold before training. There was no difference between the 2 groups in the odds of scoring over the competence threshold (odds ratio [OR] 1.02, 95% CI 0.52 to 1.99; P=.96). At follow-up, there was no significant difference between the 2 training groups (mean difference 0.19, 95% Cl -1.27 to 1.66, P=.80). Overall, change in competence score from end of training to follow-up was not significant (mean difference -0.70, 95% CI -1.52 to 0.11, P=.09). There was also no difference at follow-up between the training groups in the odds of scoring over the competence threshold (OR 0.95, 95% Cl 0.34 to 2.62; P=.92). CONCLUSIONS: Web-centered training was equally effective whether undertaken independently or accompanied by support, and its effects were sustained. The independent form of Web-centered training is particularly attractive as it provides a means of training large numbers of geographically dispersed therapists at low cost, thereby overcoming several obstacles to the widespread dissemination of psychological treatments.

Evaluating the role of Pleistocene refugia, rivers and environmental variation in the diversification of central African duikers (genera Cephalophus and Philantomba).

BACKGROUND: This study aims to assess the role that Pleistocene refugia, rivers and local habitat conditions may have played in the evolutionary diversification of three central African duiker species (Cephalophus dorsalis, C. callipygus and Philantomba monticola). Genetic data from geo-referenced feces were collected from a wide range of sites across Central Africa. Historical patterns of population genetic structure were assessed using a ~ 650 bp fragment of the mitochondrial control region and contemporary patterns of genetic differentiation were evaluated using 12 polymorphic microsatellite loci. RESULTS: Mitochondrial analyses revealed that populations of C. callipygus and P. monticola in the Gulf of Guinea refugium are distinct from other populations in west central Africa. All three species exhibit signatures of past population expansion across much of the study area consistent with a history of postglacial expansion. There was no strong evidence for a riverine barrier effect in any of the three species, suggesting that duikers can readily cross major rivers. Generalized dissimilarity models (GDM) showed that environmental variation explains most of the nuclear genetic differentiation in both C. callipygus and P. monticola. The forest-savanna transition across central Cameroon and the Plateaux Batéké region in southeastern Gabon show the highest environmentally-associated turnover in genetic variability. A pattern of genetic differentiation was also evident between the coast and forest interior that may reflect differences in precipitation and/or vegetation. CONCLUSIONS: Findings from this study highlight the historical impact of Pleistocene fragmentation and current influence of environmental variation on genetic structure in duikers. Conservation efforts should therefore target areas that harbor as much environmentally-associated genetic variation as possible in order to maximize species' capacity to adapt to environmental change.

Variation in rates of spontaneous male production within the nematode species Pristionchus pacificus supports an adaptive role for males and outcrossing.

BACKGROUND: The nematode species Pristionchus pacificus has an androdioecious mating system in which populations consist of self-fertilizing hermaphrodites and relatively few males. The prevalence of males in such a system is likely to depend on the relative pros and cons of outcrossing. While outcrossing generates novel allelic combinations and can therefore increase adaptive potential, it may also disrupt the potentially beneficial consequences of repeated generations of selfing. These include purging of deleterious alleles, inheritance of co-adapted allele complexes, improved hermaphrodite fitness and increased population growth. Here we use experimental and population genetic approaches to test hypotheses relating to male production and outcrossing in laboratory and natural populations of P. pacificus sampled from the volcanic island of La Réunion. RESULTS: We find a significant interaction between sampling locality and temperature treatment influencing rates of spontaneous male production in the laboratory. While strains isolated at higher altitude, cooler localities produce a higher proportion of male offspring at 25 °C relative to 20 or 15 °C, the reverse pattern is seen in strains isolated from warmer, low altitude localities. Linkage disequilibrium extends across long physical distances, but fails to approach levels reported for the partially selfing nematode species Caenorhabditis elegans. Finally, we find evidence for admixture between divergent genetic lineages. CONCLUSIONS: Elevated rates of laboratory male generation appear to occur under environmental conditions which differ from those experienced by populations in nature. Such elevated male generation may result in higher outcrossing rates, hence driving increased effective recombination and the creation of potentially adaptive novel allelic combinations. Patterns of linkage disequilibrium decay support selfing as the predominant reproductive strategy in P. pacificus. Finally, despite the potential for outcrossing depression, our results suggest admixture has occurred between distinct genetic lineages since their independent colonization of the island, suggesting outcrossing depression may not be uniform in this species.