A generalized estimating equations approach to mixed-effects ordinal probit models

Frequentist Conditional Variance for Nonlinear Mixed-Effects Models

Nonlinear mixed-effects models are commonly used in fisheries and ecological studies to account for complex relationships and dependencies in data. These models involve both fixed parameters to estimate and random-effects (REs) to predict. This paper addresses the inferential setting involving repeated sampling of the data but conditional on the unknown REs. This setting is more appropriate when the focus is on statistical inferences based on the specific values of REs that generated the data. Assuming the Laplace approximation is appropriate to derive the marginal likelihood and following a frequentist framework, this work derives RE-conditional bias approximations of maximum likelihood parameter estimators and empirical Bayes RE predictors, as well as the conditional covariance and mean squared error (MSE) among parameter estimators and RE predictors. It is shown that the RE-conditional MSE can be approximated with the unconditional MSE. Simulation studies demonstrate that the variance and MSE approximations are reasonably accurate for relevant sample sizes. Considering the finite-sample RE-conditional biases in the parameter estimates and RE predictions, the MSE is more appropriate for constructing confidence intervals (CIs), and the CI coverage of REs should be interpreted as the average coverage over a range of REs or over repeated generation of REs.

Does Internet Use Impact the Health Status of Middle-Aged and Older Populations? Evidence from China Health and Retirement Longitudinal Study (CHARLS)

In the context of both rapid technological development and increasing aging, the relationship between technological development and the health of the middle-aged and older population is gradually receiving academic attention. This study empirically examined the health consequences of the Internet for the middle-aged and older population in China using data from the 2018 China Health and Retirement Longitudinal Study. The results indicated that Internet use was effective in improving the self-assessed health and chronic disease status of the middle-aged and older population. However, the effect of Internet use on the improvement of chronic disease conditions in this population was more pronounced than self-assessed health. In the heterogeneity analysis, the effect of Internet use on the health of female and middle-aged adults was more significant than that of male and older adults aged >60 years. This paper also used a propensity score matching model to eliminate the endogeneity problem caused by sample selectivity bias. The results revealed that the propensity score matching model analysis was more robust. Moreover, if sample selectivity bias was not eliminated, the effect of Internet use on the improvement of self-assessed health in the middle-aged and older population would be underestimated, whereas the effect of Internet use on the chronic disease status of the middle-aged and older adults would be overestimated.

The association between statewide vaping prevalence and COVID-19

Existing literature indicated electronic cigarette users (vapers) have impaired immune response that might increase vulnerability to coronavirus disease 2019 (COVID-19) infection and death. However, whether vapers are more susceptible to COVID-19 is unknown. Using integrated data in each US state from the 2018 Behavioral Risk Factor Surveillance System (BRFSS), United States Census Bureau and the 1Point3Acres.com website, generalized estimating equation (GEE) models with negative binomial distribution assumption and log link functions were used to examine the association of statewide e-cigarette use prevalence with number of COVID-19 cases and deaths in the US on a state level from January 21, 2020 to April 25, 2020. The weighted proportion of vapers who used e-cigarettes every day or some days ranged from 2.86% to 6.42% for US states. Statistically significant associations were observed between the weighted proportion of vapers and number of COVID-19 cases as well as COVID-19 deaths in the US after adjusting for the weighted proportion of smokers and other significant covariates in the GEE models. With every one percent increase in weighted proportion of vapers in each state, the number of COVID-19 cases increase by 0.3139 (95% CI: 0.0554-0.5723) and the number of COVID-19 deaths increase by 0.3730 (95% CI: 0.0815-0.6646) in log scale in each US state. The positive associations between the proportion of vapers and the number of COVID-19 cases and deaths in each US state in this ecological study suggest an increased susceptibility of vapers to COVID-19 on a state level and warrants further investigation.

Are Vapers More Susceptible to COVID-19 Infection?

Background COVID-19, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), was declared a global pandemic in March 2020. Electronic cigarette use (vaping) rapidly gained popularity in the US in recent years. Whether electronic cigarette users (vapers) are more susceptible to COVID-19 infection is unknown. Methods Using integrated data in each US state from the 2018 Behavioral Risk Factor Surveillance System (BRFSS), United States Census Bureau and the 1Point3Acres.com website, generalized estimating equation (GEE) models with negative binomial distribution assumption and log link functions were used to examine the association of weighted proportions of vapers with number of COVID-19 infections and deaths in the US. Results The weighted proportion of vapers who used e-cigarettes every day or some days ranged from 2.86% to 6.42% for US states. Statistically significant associations were observed between the weighted proportion of vapers and number of COVID-19 infected cases as well as COVID-19 deaths in the US after adjusting for the weighted proportion of smokers and other significant covariates in the GEE models. With every one percent increase in weighted proportion of vapers in each state, the number of COVID-19 infected cases increase by 0.3139 (95% CI: 0.0554 - 0.5723) and the number of COVID-19 deaths increase by 0.3705 (95% CI: 0.0623 - 0.6786) in log scale in each US state. Conclusions The positive associations between the proportion of vapers and the number of COVID-19 infected cases and deaths in each US state suggest an increased susceptibility of vapers to COVID-19 infections and deaths.

Statistical inference in generalized linear mixed models: a review

We present a review of statistical inference in generalized linear mixed models (GLMMs). GLMMs are an extension of generalized linear models and are suitable for the analysis of non-normal data with a clustered structure. A GLMM contains parameters common to all clusters (fixed regression effects and variance components) and cluster-specific parameters. The latter parameters are assumed to be randomly drawn from a population distribution. The parameters of this population distribution (the variance components) have to be estimated together with the fixed effects. We focus on the case in which the cluster-specific parameters are normally distributed. The cluster-specific effects are integrated out of the likelihood so that the fixed effects and variance components can be estimated. Unfortunately, the integral over the cluster-specific effects is intractable for most GLMMs with a normal mixing distribution. Within a classical statistical framework, we distinguish between two broad classes of methods to handle this intractable integral: methods that rely on a numerical approximation to the integral and methods that use an analytical approximation to the integrand. Finally, we present an overview of available methods for testing hypotheses about the parameters of GLMMs.