A new modified ridge-type estimator for the beta regression model: simulation and application

<abstract> <p>The beta regression model has become a popular tool for assessing the relationships among chemical characteristics. In the BRM, when the explanatory variables are highly correlated, then the maximum likelihood estimator (MLE) does not provide reliable results. So, in this study, we propose a new modified beta ridge-type (MBRT) estimator for the BRM to reduce the effect of multicollinearity and improve the estimation. Initially, we show analytically that the new estimator outperforms the MLE as well as the other two well-known biased estimators i.e., beta ridge regression estimator (BRRE) and beta Liu estimator (BLE) using the matrix mean squared error (MMSE) and mean squared error (MSE) criteria. The performance of the MBRT estimator is assessed using a simulation study and an empirical application. Findings demonstrate that our proposed MBRT estimator outperforms the MLE, BRRE and BLE in fitting the BRM with correlated explanatory variables.</p> </abstract>

Multivariate quasi-beta regression models for continuous bounded data

We propose a multivariate regression model to deal with multiple continuous bounded data. The proposed model is based on second-moment assumptions, only. We adopted the quasi-score and Pearson estimating functions for estimation of the regression and dispersion parameters, respectively. Thus, the proposed approach does not require a multivariate probability distribution for the variable response vector. The multivariate quasi-beta regression model can easily handle multiple continuous bounded outcomes taking into account the correlation between the response variables. Furthermore, the model allows us to analyze continuous bounded data on the interval [0, 1], including zeros and/or ones. Simulation studies were conducted to investigate the behavior of the NORmal To Anything (NORTA) algorithm and to check the properties of the estimating function estimators to deal with multiple correlated response variables generated from marginal beta distributions. The model was motivated by a data set concerning the body fat percentage, which was measured at five regions of the body and represent the response variables. We analyze each response variable separately and compare it with the fit of the multivariate proposed model. The multivariate quasi-beta regression model provides better fit than its univariate counterparts, as well as allows us to measure the correlation between response variables. Finally, we adapted diagnostic tools to the proposed model. In the supplementary material, we provide the data set and R code.

Longitudinal assessment of utilities in patients with migraine: an analysis of erenumab randomized controlled trials

Background Cost-effectiveness analyses in patients with migraine require estimates of patients’ utility values and how these relate to monthly migraine days (MMDs). This analysis examined four different modelling approaches to assess utility values as a function of MMDs. Methods Disease-specific patient-reported outcomes from three erenumab clinical studies (two in episodic migraine [NCT02456740 and NCT02483585] and one in chronic migraine [NCT02066415]) were mapped to the 5-dimension EuroQol questionnaire (EQ-5D) as a function of the Migraine-Specific Quality of Life Questionnaire (MSQ) and the Headache Impact Test (HIT-6™) using published algorithms. The mapped utility values were used to estimate generic, preference-based utility values suitable for use in economic models. Four models were assessed to explain utility values as a function of MMDs: a linear mixed effects model with restricted maximum likelihood (REML), a fractional response model with logit link, a fractional response model with probit link and a beta regression model. Results All models tested showed very similar fittings. Root mean squared errors were similar in the four models assessed (0.115, 0.114, 0.114 and 0.114, for the linear mixed effect model with REML, fractional response model with logit link, fractional response model with probit link and beta regression model respectively), when mapped from MSQ. Mean absolute errors for the four models tested were also similar when mapped from MSQ (0.085, 0.086, 0.085 and 0.085) and HIT-6 and (0.087, 0.088, 0.088 and 0.089) for the linear mixed effect model with REML, fractional response model with logit link, fractional response model with probit link and beta regression model, respectively. Conclusions This analysis describes the assessment of longitudinal approaches in modelling utility values and the four models proposed fitted the observed data well. Mapped utility values for patients treated with erenumab were generally higher than those for individuals treated with placebo with equivalent number of MMDs. Linking patient utility values to MMDs allows utility estimates for different levels of MMD to be predicted, for use in economic evaluations of preventive therapies. Trial registration ClinicalTrials.gov numbers of the trials used in this study: STRIVE, NCT02456740 (registered May 14, 2015), ARISE, NCT02483585 (registered June 12, 2015) and NCT02066415 (registered Feb 17, 2014).

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.