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.

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.

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.

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.

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.

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.

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.

Genomic Profiles of Diversification and Genotype-Phenotype Association in Island Nematode Lineages.

Understanding how new species form requires investigation of evolutionary forces that cause phenotypic and genotypic changes among populations. However, the mechanisms underlying speciation vary and little is known about whether genomes diversify in the same ways in parallel at the incipient scale. We address this using the nematode, Pristionchus pacificus, which resides at an interesting point on the speciation continuum (distinct evolutionary lineages without reproductive isolation), and inhabits heterogeneous environments subject to divergent environmental pressures. Using whole genome re-sequencing of 264 strains, we estimate FST to identify outlier regions of extraordinary differentiation (∼1.725 Mb of the 172.5 Mb genome). We find evidence for shared divergent genomic regions occurring at a higher frequency than expected by chance among populations of the same evolutionary lineage. We use allele frequency spectra to find that, among lineages, 53% of divergent regions are consistent with adaptive selection, whereas 24% and 23% of such regions suggest background selection and restricted gene flow, respectively. In contrast, among populations from the same lineage, similar proportions (34-48%) of divergent regions correspond to adaptive selection and restricted gene flow, whereas 13-22% suggest background selection. Because speciation often involves phenotypic and genomic divergence, we also evaluate phenotypic variation, focusing on pH tolerance, which we find is diverging in a manner corresponding to environmental differences among populations. Taking a genome-wide association approach, we functionally validate a significant genotype-phenotype association for this trait. Our results are consistent with P. pacificus undergoing heterogeneous genotypic and phenotypic diversification related to both evolutionary and environmental processes.

Choosing appropriate analysis methods for cluster randomised cross-over trials with a binary outcome.

In cluster randomised cross-over (CRXO) trials, clusters receive multiple treatments in a randomised sequence over time. In such trials, there is usual correlation between patients in the same cluster. In addition, within a cluster, patients in the same period may be more similar to each other than to patients in other periods. We demonstrate that it is necessary to account for these correlations in the analysis to obtain correct Type I error rates. We then use simulation to compare different methods of analysing a binary outcome from a two-period CRXO design. Our simulations demonstrated that hierarchical models without random effects for period-within-cluster, which do not account for any extra within-period correlation, performed poorly with greatly inflated Type I errors in many scenarios. In scenarios where extra within-period correlation was present, a hierarchical model with random effects for cluster and period-within-cluster only had correct Type I errors when there were large numbers of clusters; with small numbers of clusters, the error rate was inflated. We also found that generalised estimating equations did not give correct error rates in any scenarios considered. An unweighted cluster-level summary regression performed best overall, maintaining an error rate close to 5% for all scenarios, although it lost power when extra within-period correlation was present, especially for small numbers of clusters. Results from our simulation study show that it is important to model both levels of clustering in CRXO trials, and that any extra within-period correlation should be accounted for. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Multi locus analysis of Pristionchus pacificus on La Réunion Island reveals an evolutionary history shaped by multiple introductions, constrained dispersal events and rare out-crossing.

Pristionchus pacificus, recently established as a model organism in evolutionary biology, is a cosmopolitan nematode that has a necromenic association with scarab beetles. The diverse array of host beetle species and habitat types occupied by P. pacificus make it a good model for investigating local adaptation to novel environments. Presence of P. pacificus on La Réunion Island, a young volcanic island with a dynamic geological history and a wide variety of ecozones, facilitates such investigation in an island biogeographic setting. Microsatellite data from 20 markers and 223 strains and mitochondrial sequence data from 272 strains reveal rich genetic diversity among La Réunion P. pacificus isolates, shaped by differentially timed introductions from diverse sources and in association with different beetle species. Distinctions between volcanic zones and between arid western and wet eastern climatic zones have likely limited westward dispersal of recently colonized lineages and maintained a genetic distinction between eastern and western clades. The highly selfing lifestyle of P. pacificus contributes to the strong fine-scale population structure detected, with each beetle host harbouring strongly differentiated assemblages of strains. Periodic out-crossing generates admixture between genetically diverse lineages, creating a diverse array of allelic combinations likely to increase the evolutionary potential of the species and facilitate adaptation to local environments and beetle hosts.

Comparative phylogeography reveals a shared impact of pleistocene environmental change in shaping genetic diversity within nine Anopheles mosquito species across the Indo-Burma biodiversity hotspot.

South-East Asia is one of the world's richest regions in terms of biodiversity. An understanding of the distribution of diversity and the factors shaping it is lacking, yet essential for identifying conservation priorities for the region's highly threatened biodiversity. Here, we take a large-scale comparative approach, combining data from nine forest-associated Anopheles mosquito species and using statistical phylogeographical methods to disentangle the effects of environmental history, species-specific ecology and random coalescent effects. Spatially explicit modelling of Pleistocene demographic history supports a common influence of environmental events in shaping the genetic diversity of all species examined, despite differences in species' mtDNA gene trees. Populations were periodically restricted to allopatric northeastern and northwestern refugia, most likely due to Pleistocene forest fragmentation. Subsequent southwards post-glacial recolonization is supported by a north-south gradient of decreasing genetic diversity. Repeated allopatric fragmentation and recolonization have led to the formation of deeply divergent geographical lineages within four species and a suture zone where these intraspecific lineages meet along the Thai-Myanmar border. A common environmental influence for this divergence was further indicated by strong support for simultaneous divergence within the same four species, dating to approximately 900 thousand years ago (kya). Differences in the geographical structuring of genetic diversity between species are probably the result of varying species' biology. The findings have important implications for conservation planning; if the refugial regions and suture zone identified here are shared by other forest taxa, the unique and high levels of genetic diversity they house will make these areas conservation priorities.

Inter-specific gene flow dynamics during the Pleistocene-dated speciation of forest-dependent mosquitoes in Southeast Asia.

Tropical forests have undergone repeated fragmentation and expansion during Pleistocene glacial and interglacial periods, respectively. The effects of this repeated forest fragmentation in driving vicariance in tropical taxa have been well studied. However, relatively little is known about how often this process results in allopatric speciation, since it may be inhibited by recurrent gene flow during repeated secondary contact, or to what extent Pleistocene-dated speciation results from ecological specialization in the face of gene flow. Here, divergence times and gene flow between three closely-related mosquito species of the Anopheles dirus species complex endemic to the forests of Southeast Asia, are inferred using coalescent based Bayesian analysis. An Isolation with Migration model is applied to sequences of two mitochondrial and three nuclear genes, and 11 microsatellites. The divergence of An. scanloni has occurred despite unidirectional nuclear gene flow from this species into An. dirus. The inferred asymmetric gene flow may result from the unique evolutionary adaptation of An. scanloni to limestone karst habitat, and therefore the fitness advantage of this species over An. dirus in regions of sympatry. Mitochondrial introgression has led to the complete replacement of An. dirus haplotypes with those of An. baimaii through a recent (approximately 62 kya) selective sweep. Speciation of An. baimaii and An. dirus is inferred to have involved allopatric divergence throughout much of the Pleistocene. Secondary contact and bidirectional gene flow has occurred only within the last 100 000 years, by which time the process of allopatric speciation seems to have been largely completed.

Molecular phylogenetics and biogeography of the Neocellia Series of Anopheles mosquitoes in the Oriental Region.

Molecular studies of population divergence and speciation across the Oriental Region are sparse, despite the region's high biodiversity and extensive Pliocene and Pleistocene environmental change. A molecular phylogenetic study of the Neocellia Series of Anopheles mosquitoes was undertaken to identify patterns of diversification across the Oriental Region and to infer the role of Pleistocene and Pliocene climatic change. A robust phylogeny was constructed using CO2 and ND5 mitochondrial genes and ITS2 and D3 nuclear ribosomal markers. Bayesian analysis of mitochondrial genes was used to date divergence events. The repeated contraction and expansion of forest habitat resulting from Pleistocene climatic fluctuations appears to have had a substantial impact on intraspecific diversification, but has not driven speciation within this group. Primarily early to mid Pliocene speciation was detected within the Annularis Group, whereas speciation within the Maculatus and Jamesii Groups occurred during the mid and late Pliocene. Both allopatric divergence driven by late Pliocene environmental changes and ecological adaptation, involving altitudinal replacement and seasonality, are likely to have influenced speciation in the Maculatus Group.

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.

Crossing experiments supporting the specific status of Anopheles maculatus chromosomal form K.

There are 3 recognized chromosomal forms (B, E, K) in the taxon of Anopheles maculatus, 1 of the 8 members of the Anopheles maculatus group. Previous studies suggested that forms B and E are cytotypes of the species, but genetic characteristics of form K are unknown. The present study used crossing experiments, and polytene chromosomes of the ovarian nurse cell in F1 hybrids to show that form K is genetically distinct from forms B and E. In addition, postzygotic genetic incompatibility between form K and An. sawadwongporni, An. dravidicus, and An. pseudowillmori are demonstrated. In all crosses, hybrid males were sterile, with atrophied testes and accessory glands, or partially sterile with abnormal spermatozoa. The hybrid females showed varying degrees of atrophied ovaries. The ovarian nurse cell polytene chromosomes of the F1 hybrid females displayed approximately 70% to almost complete asynapsis. The results provide clear evidence that form K should no longer be regarded as a cytotype of An. maculatus. The present study supports previous suggestions that form K represents another species of the Maculatus group.

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.