Understanding between-cluster variation in prevalence and limits for how much variation is plausible

In clinical trials and observational studies of clustered binary data, understanding between-cluster variation is essential: in sample size and power calculations of cluster randomised trials, for example, the intra-cluster correlation coefficient is often specified. However, quantifications of between-cluster variation can be unintuitive, and an intra-cluster correlation coefficient as low as 0.04 may correspond to surprisingly large between-cluster differences. We suggest that understanding is improved through visualising the implied distribution of true cluster prevalences – possibly by assuming they follow a beta distribution – or by calculating their standard deviation, which is more readily interpretable than the intra-cluster correlation coefficient. Even so, the bounded nature of binary data complicates the interpretation of variances as primary measures of uncertainty, and entropy offers an attractive alternative. Appealing to maximum entropy theory, we propose the following rule of thumb: that plausible intra-cluster correlation coefficients and standard deviations of true cluster prevalences are both bounded above by the overall prevalence, its complement, and one third. We also provide corresponding bounds for the coefficient of variation, and for a different standard deviation and intra-cluster correlation defined on the log odds scale. Using previously published data, we observe the quantities defined on the log odds scale to be more transportable between studies with different outcomes with different prevalences than the intra-cluster correlation and coefficient of variation. The latter increase and decrease, respectively, as prevalence increases from 0% to 50%, and the same is true for our bounds. Our work will help clinical trialists better understand between-cluster variation and avoid specifying implausibly high values for the intra-cluster correlation in sample size and power calculations.

Calibrating the Planck cluster mass scale with CLASH

We determine the mass scale of Planck galaxy clusters using gravitational lensing mass measurements from the Cluster Lensing And Supernova survey with Hubble (CLASH). We have compared the lensing masses to the Planck Sunyaev-Zeldovich (SZ) mass proxy for 21 clusters in common, employing a Bayesian analysis to simultaneously fit an idealized CLASH selection function and the distribution between the measured observables and true cluster mass. We used a tiered analysis strategy to explicitly demonstrate the importance of priors on weak lensing mass accuracy. In the case of an assumed constant bias, bSZ, between true cluster mass, M500, and the Planck mass proxy, MPL, our analysis constrains 1−bSZ = 0.73 ± 0.10 when moderate priors on weak lensing accuracy are used, including a zero-mean Gaussian with standard deviation of 8% to account for possible bias in lensing mass estimations. Our analysis explicitly accounts for possible selection bias effects in this calibration sourced by the CLASH selection function. Our constraint on the cluster mass scale is consistent with recent results from the Weighing the Giants program and the Canadian Cluster Comparison Project. It is also consistent, at 1.34σ, with the value needed to reconcile the Planck SZ cluster counts with Planck’s base ΛCDM model fit to the primary cosmic microwave background anisotropies.

Bayesian meta-analysis: The role of the between-sample heterogeneity

The random effect approach for meta-analysis was motivated by a lack of consistent assessment of homogeneity of treatment effect before pooling. The random effect model assumes that the distribution of the treatment effect is fully heterogenous across the experiments. However, other models arising by grouping some of the experiments are plausible. We illustrate on simulated binary experiments that the fully heterogenous model gives a poor meta-inference when fully heterogeneity is not the true model and that the knowledge of the true cluster model considerably improves the inference. We propose the use of a Bayesian model selection procedure for estimating the true cluster model, and Bayesian model averaging to incorporate into the meta-analysis the clustering estimation. A well-known meta-analysis for six major multicentre trials to assess the efficacy of a given dose of aspirin in post-myocardial infarction patients is reanalysed.

Implementation of a Consensus Set of Hypervariable Mycobacterial Interspersed Repetitive-Unit–Variable-Number Tandem-Repeat Loci in Mycobacterium tuberculosis Molecular Epidemiology

This study shows that the addition of a consensus 4-locus set of hypervariable mycobacterial interspersed repetitive-unit–variable-number tandem repeat (MIRU-VNTR) loci to the spoligotyping-24-locus MIRU-VNTR typing strategy is a well-standardized approach that can contribute to an improvement of the true cluster definition while retaining high typeability in non-Beijing strains.

Gemini/GMOS detection of stellar velocity variations in the ionising cluster of 30 Dor

We have analysed spectra obtained with the Gemini Multi Object Spectrograph (GMOS) for more than 50 stars in the ionising cluster of 30 Doradus during a seven epochs observing campaign at Gemini South. We derive a binary candidate rate of about 50%, which is however consistent with an intrinsic 100% binary rate among massive stars. After decontaminating the sample from the stars that show binary orbital motions, we were able to calculate the “true” cluster velocity dispersion and found it to be about 8 km s−1. This value implies a virial mass of about 4.5 × 105 M⊙ which is consistent with previous photometric mass determinations therefore suggesting that NGC 2070 is a firm candidate for a future globular cluster.