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.

Fisher consistent estimation of regression parameter in the proportional mean residual life model with frailty

In the article, we consider the Fisher consistent estimation of the regression parameters in the proportional mean residual life model with arbitrary frailty. It is discussed that conventional estimation procedures, such as the maximum likelihood estimation or Cox’s approach, which are employed in common regression models, may also yield consistent inference in the extended models.

A New Ridge-Type Estimator for the Gamma Regression Model

The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.

PEMODELAN ANGKA HARAPAN HIDUP PROVINSI JAWA TENGAH MENGGUNAKAN ROBUST SPATIAL DURBIN MODEL

Spatial regression is a model used to determine relationship between response variables and predictor variables that gets spatial influence. If there are spatial influences on both variables, the model that will be formed is Spatial Durbin Model. One reason for the inaccuracy of the spatial regression model in predicting is the existence of outlier observations. Removing outliers in spatial analysis can change the composition of spatial effects on data. One way to overcome of outliers in the spatial regression model is by using robust spatial regression. The application of M-estimator is carried out in estimating the spatial regression parameter coefficients that are robust against outliers. The aim of this research is obtaining model of number of life expectancy in Central Java Province in 2017 that contain outliers. The results by applying M-estimator to estimating robust spatial durbin model regression parameters can accommodate the existence of outliers in the spatial regression model. This is indicated by the change in the estimating coefficient value of the robust spatial durbin model regression parameter which can increase adjusted R2 value becomes 93,69% and decrease MSE value becomes 0,12551.Keywords: Outliers, M-estimator, Spatial Durbin Model, Number of Life Expectancy.

Scaling relations of seismic moment and rupture area for outer-rise earthquakes

A new piece-wise scaling relation for rupture area ( S ) and seismic moment ( M 0 ) was obtained for outer-rise earthquakes using data compiled from previous seismological studies. The compiled source parameters were examined carefully to ensure that rupture area dimensions represent the "actual" rupture area. Twenty sets of S and M 0 pairs for ten earthquakes from independent studies were used for regression analysis. To estimate rupture areas of outer-rise earthquakes whose fault down dip tips, respectively, do and do not reach the oceanic lithosphere base, regression parameter b in S=(M 0 /a) 1/b is 2 with the corresponding regression parameter log 10 a 2 being 1.402 (±0.250), and b is 1.5 with the corresponding regression parameter log 10 a 1 being 6.401 (±0.187). The piece-wise scaling relation developed here can fit outer-rise earthquake data from Mw 7.2 to Mw 8.4 and can be used to estimate rupture areas of earthquakes greater than Mw 8.4.

Ensemble estimation and variable selection with semiparametric regression models

Summary We consider scenarios in which the likelihood function for a semiparametric regression model factors into separate components, with an efficient estimator of the regression parameter available for each component. An optimal weighted combination of the component estimators, named an ensemble estimator, may be employed as an overall estimate of the regression parameter, and may be fully efficient under uncorrelatedness conditions. This approach is useful when the full likelihood function may be difficult to maximize, but the components are easy to maximize. It covers settings where the nuisance parameter may be estimated at different rates in the component likelihoods. As a motivating example we consider proportional hazards regression with prospective doubly censored data, in which the likelihood factors into a current status data likelihood and a left-truncated right-censored data likelihood. Variable selection is important in such regression modelling, but the applicability of existing techniques is unclear in the ensemble approach. We propose ensemble variable selection using the least squares approximation technique on the unpenalized ensemble estimator, followed by ensemble re-estimation under the selected model. The resulting estimator has the oracle property such that the set of nonzero parameters is successfully recovered and the semiparametric efficiency bound is achieved for this parameter set. Simulations show that the proposed method performs well relative to alternative approaches. Analysis of an AIDS cohort study illustrates the practical utility of the method.