Recently, it has been shown how to estimate model-adjusted risks, risk differences, and risk ratios from complex survey data based on risk averaging and SUDAAN (Research Triangle Institute, Research Triangle Park, North Carolina). The authors present an alternative approach based on marginal structural models (MSMs) and SAS (SAS Institute, Inc., Cary, North Carolina). The authors estimate the parameters of the MSM using inverse weights that are the product of 2 terms. The first term is a survey weight that adjusts the sample to represent the unstandardized population. The second term is an inverse-probability-of-exposure weight that standardizes the population in order to adjust for confounding; it must be estimated using the survey weights. The authors show how to use the MSM parameter estimates and contrasts to test and estimate effect-measure modification; SAS code is provided. They also explain how to program the previous risk-averaging approach in SAS. The 2 methods are applied and compared using data from the 2007 Florida Behavioral Risk Factor Surveillance System Survey to assess effect modification by age of the difference in risk of cost barriers to health care between persons with disability and persons without disability.

In social epidemiology, an individual's neighborhood is considered to be an important determinant of health behaviors, mediators, and outcomes. Consequently, when investigating health disparities, researchers may wish to adjust for confounding by unmeasured neighborhood factors, such as local availability of health facilities or cultural predispositions. With a simple random sample and a binary outcome, a conditional logistic regression analysis that treats individuals within a neighborhood as a matched set is a natural method to use. The authors present a generalization of this method for ordinal outcomes and complex sampling designs. The method is based on a proportional odds model and is very simple to program using standard software such as SAS PROC SURVEYLOGISTIC (SAS Institute Inc., Cary, North Carolina). The authors applied the method to analyze racial/ethnic differences in dental preventative care, using 2008 Florida Behavioral Risk Factor Surveillance System survey data. The ordinal outcome represented time since last dental cleaning, and the authors adjusted for individual-level confounding by gender, age, education, and health insurance coverage. The authors compared results with and without additional adjustment for confounding by neighborhood, operationalized as zip code. The authors found that adjustment for confounding by neighborhood greatly affected the results in this example.

When investigating health disparities, it can be of interest to explore whether adjustment for socioeconomic factors at the neighborhood level can account for, or even reverse, an unadjusted difference. Recently, we proposed new methods to adjust the effect of an individual-level covariate for confounding by unmeasured neighborhood-level covariates using complex survey data and a generalization of conditional likelihood methods. Generalized linear mixed models (GLMMs) are a popular alternative to conditional likelihood methods in many circumstances. Therefore, in the present article, we propose and investigate a new adaptation of GLMMs for complex survey data that achieves the same goal of adjusting for confounding by unmeasured neighborhood-level covariates. With the new GLMM approach, one must correctly model the expectation of the unmeasured neighborhood-level effect as a function of the individual-level covariates. We demonstrate using simulations that even if that model is correct, census data on the individual-level covariates are sometimes required for consistent estimation of the effect of the individual-level covariate. We apply the new methods to investigate disparities in recency of dental cleaning, treated as an ordinal outcome, using data from the 2008 Florida Behavioral Risk Factor Surveillance System (BRFSS) survey. We operationalize neighborhood as zip code and merge the BRFSS data with census data on ZIP Code Tabulated Areas to incorporate census data on the individual-level covariates. We compare the new results to our previous analysis, which used conditional likelihood methods. We find that the results are qualitatively similar.

Eco-efficiency has been receiving attention worldwide, and the effective implementation of environmental regulations (ERs) has become crucial to regional eco-efficiency. This paper uses a method combining mixed directional distance function and bootstrapping approach to investigate the spatial and temporal distribution characteristics of eco-efficiency under the constraint of land use carbon emission in China from 2004 to 2016. The nonlinear relationship between ER and eco-efficiency is observed with a panel threshold model. Results from empirical tests reveal that eco-efficiency in China during the study period has an upward trend, and the spatial and temporal distribution of eco-efficiency is unbalanced and concentrated. Technical innovation and land marketization (LM) shows double threshold, whereas industrial structure (IS) has a single threshold effect. LM has a promotional effect on eco-efficiency, which differs in the promotion before and after promotion across the threshold value. Reasonable ER can reduce cost by stimulating the innovation of green production technology and achieves a win-win situation between environment and output. This finding further verifies that the ER for eco-efficiency under the constraint of land use carbon emission conforms to the Porter hypothesis. The effect of ER on eco-efficiency changes from negative to positive with the increase of IS level. Adjusting the ownership structure and increasing the proportion of green achievements in the promotion and assessment of officials are important measures in the upgrading of eco-efficiency.

In order to adjust individual-level covariate effects for confounding due to unmeasured neighborhood characteristics, we have recently developed conditional pseudolikelihood methods to estimate the parameters of a proportional odds model for clustered ordinal outcomes with complex survey data. The methods require sampling design joint probabilities for each within-neighborhood pair. In the present article, we develop a similar methodology for a baseline category logit model for clustered multinomial outcomes and for a loglinear model for clustered count outcomes. All of the estimators and asymptotic sampling distributions we present can be conveniently computed using standard logistic regression software for complex survey data, such as sas proc surveylogistic. We demonstrate validity of the methods theoretically and also empirically by using simulations. We apply the new method for clustered multinomial outcomes to data from the 2008 Florida Behavioral Risk Factor Surveillance System survey in order to investigate disparities in frequency of dental cleaning both unadjusted and adjusted for confounding by neighborhood.