Marginal modeling in community randomized trials with rare events: Utilization of the negative binomial regression model

Background/aims This work is motivated by the HEALing Communities Study, which is a post-test only cluster randomized trial in which communities are randomized to two different trial arms. The primary interest is in reducing opioid overdose fatalities, which will be collected as a count outcome at the community level. Communities range in size from thousands to over one million residents, and fatalities are expected to be rare. Traditional marginal modeling approaches in the cluster randomized trial literature include the use of generalized estimating equations with an exchangeable correlation structure when utilizing subject-level data, or analogously quasi-likelihood based on an over-dispersed binomial variance when utilizing community-level data. These approaches account for and estimate the intra-cluster correlation coefficient, which should be provided in the results from a cluster randomized trial. Alternatively, the coefficient of variation or R coefficient could be reported. In this article, we show that negative binomial regression can also be utilized when communities are large and events are rare. The objectives of this article are (1) to show that the negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model and to explain why the estimates may differ; (2) to derive formulas relating the negative binomial overdispersion parameter k with the intra-cluster correlation coefficient, coefficient of variation, and R coefficient; and (3) analyze pre-intervention data from the HEALing Communities Study to demonstrate and contrast models and to show how to report the intra-cluster correlation coefficient, coefficient of variation, and R coefficient when utilizing negative binomial regression. Methods Negative binomial and over-dispersed binomial regression modeling are contrasted in terms of model setup, regression parameter estimation, and formulation of the overdispersion parameter. Three specific models are used to illustrate concepts and address the third objective. Results The negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model, although estimates may differ. Practical differences arise in regard to how overdispersion, and hence the intra-cluster correlation coefficient is modeled. The negative binomial overdispersion parameter is approximately equal to the ratio of the intra-cluster correlation coefficient and marginal probability, the square of the coefficient of variation, and the R coefficient minus 1. As a result, estimates corresponding to all four of these different types of overdispersion parameterizations can be reported when utilizing negative binomial regression. Conclusion Negative binomial regression provides a valid, practical, alternative approach to the analysis of count data, and corresponding reporting of overdispersion parameters, from community randomized trials in which communities are large and events are rare.

Protein microparticles visualize the contact network and rigidity onset in the gelation of model proteins

Protein aggregation into gel networks is of immense importance in diverse areas from food science to medical research; however, it remains a grand challenge as the underlying molecular interactions are complex, difficult to access experimentally, and to model computationally. Early stages of gelation often involve protein aggregation into protein clusters that later on aggregate into a gel network. Recently synthesized protein microparticles allow direct control of these early stages of aggregation, decoupling them from the subsequent gelation stages. Here, by following the gelation of protein microparticles directly at the particle scale, we elucidate in detail the emergence of a percolating structure and the onset of rigidity as measured by microrheology. We find that the largest particle cluster, correlation length, and degree of polymerization all diverge with power laws, while the particles bind irreversibly indicating a nonequilibrium percolation process, in agreement with recent results on weakly attractive colloids. Concomitantly, the elastic modulus increases in a power-law fashion as determined by microrheology. These results give a consistent microscopic picture of the emergence of rigidity in a nonequilibrium percolation process that likely underlies the gelation in many more systems such as proteins, and other strongly interacting structures originating from (bio)molecules.

A new method for evaluating air quality using an ideal grey close function cluster correlation analysis method

To scientifically and reasonably evaluate air quality with a large amount of monitored data, this paper proposes a new evaluation method called ideal grey close function cluster correlation analysis (IGCFCCA). Taking the air quality in Ningxia Province, China, as an example, according to China’s air quality standard, SO2, NO2, PM10, PM2.5 and O3 are selected as evaluation indexes to perform the evaluation. The results show that the air quality in this region in 2018 can be divided into three classifications, among which the relatively poor air quality in March, April and May is the first classification, the better air quality in August and September is the third classification, and the air quality in other months falls under the second classification. Correlation analysis is used to qualitatively determine that these three classifications correspond to first-level air quality in China’s air quality standard, and the correlation degree, which is the distance between the three classifications and the first-level air quality, is quantitatively determined. Specifically, the correlation degrees of the first-classification, second-classification and third-classification of air quality are 0.674, 0.697 and 0.71, respectively. The research results indicate potential directions and objectives for air quality management to achieve scientific management.

Guideline for Selecting Types of Reliability and Suitable Intra-class Correlation Coefficients in Clinical Research

Introduction: Reliability is an integral part of measuring the reproducibility of research information. Intra-cluster correlation coefficient (ICC) is one of the necessary indicators for reliability reporting, which can be misleading in terms of its diversity. The main purpose of this study was to introduce the types of reliability and appropriate ICC indices. Methods: In this tutorial article, useful information about the types of reliability and indicators needed to report the results, as well as the types of ICC and its applications were explained for dummies. Results: Three general types of reliability include inter-rater reliability, test-retest reliability, and intra-rater reliability was presented. 10 different types of ICC were also introduced and explained. Conclusion: The research results may be misleading if any of the reliability types and calculation criteria types are chosen incorrectly. Therefore, to make the results of the study more accurate and valuable. Medical researchers must seek help from relevant guidelines such as this study before conducting reliability analysis.

Sample sizes for cluster-randomised trials with continuous outcomes: Accounting for uncertainty in a single intra-cluster correlation estimate

Sample size calculations for cluster-randomised trials require inclusion of an inflation factor taking into account the intra-cluster correlation coefficient. Often, estimates of the intra-cluster correlation coefficient are taken from pilot trials, which are known to have uncertainty about their estimation. Given that the value of the intra-cluster correlation coefficient has a considerable influence on the calculated sample size for a main trial, the uncertainty in the estimate can have a large impact on the ultimate sample size and consequently, the power of a main trial. As such, it is important to account for the uncertainty in the estimate of the intra-cluster correlation coefficient. While a commonly adopted approach is to utilise the upper confidence limit in the sample size calculation, this is a largely inefficient method which can result in overpowered main trials. In this paper, we present a method of estimating the sample size for a main cluster-randomised trial with a continuous outcome, using numerical methods to account for the uncertainty in the intra-cluster correlation coefficient estimate. Despite limitations with this initial study, the findings and recommendations in this paper can help to improve sample size estimations for cluster randomised controlled trials by accounting for uncertainty in the estimate of the intra-cluster correlation coefficient. We recommend this approach be applied to all trials where there is uncertainty in the intra-cluster correlation coefficient estimate, in conjunction with additional sources of information to guide the estimation of the intra-cluster correlation coefficient.