Cluster-specific nonignorably missing, endogenous, and continuous regressors in multilevel model for binary outcome

In multilevel regression models for observational clustered data, regressors can be correlated with cluster-level error components, namely endogenous, due to omitted cluster-level covariates, measurement error, and simultaneity. When endogeneity is ignored, regression coefficient estimators can be severely biased. To deal with endogeneity, instrument variable methods have been widely used. However, the instrument variable method often requires external instrument variables with certain conditions that cannot be verified empirically. Methods that use the within-cluster variations of the endogenous variable work under the restriction that either the outcome or the endogenous variable has a linear relationship with the cluster-level random effect. We propose a new method for binary outcome when it follows a logistic mixed-effects model and the endogenous variable is normally distributed but not linear in the random effect. The proposed estimator capitalizes on the nested data structure without requiring external instrument variables. We show that the proposed estimator is consistent and asymptotically normal. Furthermore, our method can be applied when the endogenous variable is missing in a cluster-specific nonignorable mechanism, without requiring that the missing mechanism be correctly specified. We evaluate the finite sample performance of the proposed approach via simulation and apply the method to a health care study using a San Diego inpatient dataset. Our study demonstrates that the clustered structure can be exploited to draw valid analysis of multilevel data with correlated effects.

Model-based standardization using an outcome model with random effects

Model-based standardization uses a statistical outcome model or exposure model to estimate a population-average association that is unconfounded by selected covariates. With it, one can compare groups using a distribution of confounders identical in each group to that of a standard population. We develop an approach based on an outcome model, in which the mean of the outcome is modeled conditional on the exposure and the confounders. In our approach, there is a confounder that clusters the observations into a very large number of categories. We treat the parameters for the clusters as random effects. We use a between-within model to account for the association of the random effects not only with the exposure but also with the cluster population sizes. We review alternative approaches presented in the literature, and we compare the outcome-modeling approach to recently proposed exposure-modeling approaches incorporating random effects. To illustrate, we use 2014 to compare proportions of acute respiratory tract infection diagnoses with an antibiotic prescription for emergency department versus outpatient visits, adjusting for confounding by unmeasured patient level variables and measured diagnosis-level variables. We also present results of a simulation study.

Handling ties in continuous outcomes for confounder adjustment with rank-ordered logit and its application to ordinal outcomes

The rank-ordered logit (rologit) model was recently introduced as a robust approach for analysing continuous outcomes, with the linear exposure effect estimated by scaling the rank-based log-odds estimate. Here we extend the application of the rologit model to continuous outcomes with ties and ordinal outcomes treated as imperfectly-observed continuous outcomes. By identifying the functional relationship between survival times and continuous outcomes, we explicitly establish the equivalence between the rologit and Cox models to justify the use of the Breslow, Efron and perturbation methods in the analysis of continuous outcomes with ties. Using simulation, we found all three methods perform well with few ties. Although an increasing extent of ties increased the bias of the log-odds and linear effect estimates and resulted in reduced power, which was somewhat worse when the model was mis-specified, the perturbation method maintained a type I error around 5%, while the Efron method became conservative with heavy ties but outperformed Breslow. In general, the perturbation method had the highest power, followed by the Efron and then the Breslow method. We applied our approach to three real-life datasets, demonstrating a seamless analytical workflow that uses stratification for confounder adjustment in studies of continuous and ordinal outcomes.

Between-within effects in survival models with cross-classified clustering: Application to the evaluation of the effectiveness of medical devices

In many medical applications involving observational survival data there will be a cross-classification of doctors and hospitals, as well as an interest in controlling for potentially confounding doctor and hospital effects when evaluating the effectiveness of a medical intervention. In this paper, we propose the use of a between-within model with cross-classified random effects and show through simulation that it performs better than alternative models. A real data example illustrates the application of the proposed model in a study of the survival of hip implants. The proposed model has broad utility in determining the effectiveness of medical interventions.

Adjusting for unmeasured confounding due to either of two crossed factors with a logistic regression model

Motivated by an investigation of the effect of surface water temperature on the presence of Vibrio cholerae in water samples collected from different fixed surface water monitoring sites in Haiti in different months, we investigated methods to adjust for unmeasured confounding due to either of the two crossed factors site and month. In the process, we extended previous methods that adjust for unmeasured confounding due to one nesting factor (such as site, which nests the water samples from different months) to the case of two crossed factors. First, we developed a conditional pseudolikelihood estimator that eliminates fixed effects for the levels of each of the crossed factors from the estimating equation. Using the theory of U-Statistics for independent but non-identically distributed vectors, we show that our estimator is consistent and asymptotically normal, but that its variance depends on the nuisance parameters and thus cannot be easily estimated. Consequently, we apply our estimator in conjunction with a permutation test, and we investigate use of the pigeonhole bootstrap and the jackknife for constructing confidence intervals. We also incorporate our estimator into a diagnostic test for a logistic mixed model with crossed random effects and no unmeasured confounding. For comparison, we investigate between-within models extended to two crossed factors. These generalized linear mixed models include covariate means for each level of each factor in order to adjust for the unmeasured confounding. We conduct simulation studies, and we apply the methods to the Haitian data. Copyright © 2016 John Wiley & Sons, Ltd.

An Integrated Service Delivery Model to Identify Persons Living with HIV and to Provide Linkage to HIV Treatment and Care in Prioritized Neighborhoods: A Geotargeted, Program Outcome Study

BACKGROUND

Recent studies have demonstrated that high human immunodeficiency virus (HIV) prevalence (2.1%) rates exist in "high-risk areas" of US cities that are comparable to rates in developing nations. Community-based interventions (CBIs) have demonstrated potential for improving HIV testing in these areas, thereby facilitating early entry and engagement in the HIV continuum of care. By encouraging neighborhood-based community participation through an organized community coalition, Project LINK sought to demonstrate the potential of the CBI concept to improve widespread HIV testing and referral in an area characterized by high poverty and HIV prevalence with few existing HIV-related services.

OBJECTIVE

This study examines the influence of Project LINK to improve linkage-to-care and HIV engagement among residents of its target neighborhoods.

METHODS

Using a venue-based sampling strategy, survey participants were selected from among all adult participants aged 18 years or more at Project LINK community events (n=547). We explored multilevel factors influencing continuum-of-care outcomes (linkage to HIV testing and CBI network referral) through combined geospatial-survey analyses utilizing hierarchical linear model methodologies and random-intercept models that adjusted for baseline effect differences among zip codes. The study specifically examined participant CBI utilization and engagement in relation to individual and psychosocial factors, as well as neighborhood characteristics including the availability of HIV testing services, and the extent of local prevention, education, and clinical support services.

RESULTS

Study participants indicated strong mean intention to test for HIV using CBI agencies (mean 8.66 on 10-point scale [SD 2.51]) and to facilitate referrals to the program (mean 8.81 on 10-point scale [SD 1.86]). Individual-level effects were consistent across simple multiple regression and random-effects models, as well as multilevel models. Participants with lower income expressed greater intentions to obtain HIV tests through LINK (P<.01 across models). HIV testing and CBI referral intention were associated with neighborhood-level factors, including reduced availability of support services (testing P<.001), greater proportion of black/African Americans (testing and referral P<.001), and reduced socioeconomic capital (testing P=.017 and referral P<.001). Across models, participants expressing positive attitudes toward the CBI exhibited greater likelihood of engaging in routine HIV testing (P<.01) and referring others to HIV care (P<.01). Transgender individuals indicated greater intent to refer others to the CBI (P<.05). These outcomes were broadly influenced by distal community-level factors including availability of neighborhood HIV support organizations, population composition socioeconomic status, and high HIV prevalence.

CONCLUSIONS

Project LINK demonstrated its potential as a geotargeted CBI by evidencing greater individual intention to engage in HIV testing, care, and personal referrals to its coalition partner organizations. This study highlights important socioecological effects of US-based CBIs to improve HIV testing and initiate acceptable mechanisms for prompt referral to care among a vulnerable population.

Model-based standardization to adjust for unmeasured cluster-level confounders with complex survey data

Model-based standardization uses a statistical model to estimate a standardized, or unconfounded, population-averaged effect. With it, one can compare groups had the distribution of confounders been identical in both groups to that of the standard population. We develop two methods for model-based standardization with complex survey data that accommodate a categorical confounder that clusters the individual observations into a very large number of subgroups. The first method combines a random-intercept generalized linear mixed model with a conditional pseudo-likelihood estimator of the fixed effects. The second method combines a between-within generalized linear mixed model with census data on the cluster-level means of the individual-level covariates. We conduct simulation studies to compare the two approaches. We apply the two methods to the 2008 Florida Behavioral Risk Factor Surveillance System survey data to estimate standardized proportions of people who drink alcohol, within age groups, adjusting for measured individual-level and unmeasured cluster-level confounders.

Random-effects, fixed-effects and the within-between specification for clustered data in observational health studies: a simulation study

Background

When unaccounted-for group-level characteristics affect an outcome variable, traditional linear regression is inefficient and can be biased. The random- and fixed-effects estimators (RE and FE, respectively) are two competing methods that address these problems. While each estimator controls for otherwise unaccounted-for effects, the two estimators require different assumptions. Health researchers tend to favor RE estimation, while researchers from some other disciplines tend to favor FE estimation. In addition to RE and FE, an alternative method called within-between (WB) was suggested by Mundlak in 1978, although is utilized infrequently.

Methods

We conduct a simulation study to compare RE, FE, and WB estimation across 16,200 scenarios. The scenarios vary in the number of groups, the size of the groups, within-group variation, goodness-of-fit of the model, and the degree to which the model is correctly specified. Estimator preference is determined by lowest mean squared error of the estimated marginal effect and root mean squared error of fitted values.

Results

Although there are scenarios when each estimator is most appropriate, the cases in which traditional RE estimation is preferred are less common. In finite samples, the WB approach outperforms both traditional estimators. The Hausman test guides the practitioner to the estimator with the smallest absolute error only 61% of the time, and in many sample sizes simply applying the WB approach produces smaller absolute errors than following the suggestion of the test.

Conclusions

Specification and estimation should be carefully considered and ultimately guided by the objective of the analysis and characteristics of the data. The WB approach has been underutilized, particularly for inference on marginal effects in small samples. Blindly applying any estimator can lead to bias, inefficiency, and flawed inference.

Review of methods for handling confounding by cluster and informative cluster size in clustered data

Clustered data are common in medical research. Typically, one is interested in a regression model for the association between an outcome and covariates. Two complications that can arise when analysing clustered data are informative cluster size (ICS) and confounding by cluster (CBC). ICS and CBC mean that the outcome of a member given its covariates is associated with, respectively, the number of members in the cluster and the covariate values of other members in the cluster. Standard generalised linear mixed models for cluster-specific inference and standard generalised estimating equations for population-average inference assume, in general, the absence of ICS and CBC. Modifications of these approaches have been proposed to account for CBC or ICS. This article is a review of these methods. We express their assumptions in a common format, thus providing greater clarity about the assumptions that methods proposed for handling CBC make about ICS and vice versa, and about when different methods can be used in practice. We report relative efficiencies of methods where available, describe how methods are related, identify a previously unreported equivalence between two key methods, and propose some simple additional methods. Unnecessarily using a method that allows for ICS/CBC has an efficiency cost when ICS and CBC are absent. We review tools for identifying ICS/CBC. A strategy for analysis when CBC and ICS are suspected is demonstrated by examining the association between socio-economic deprivation and preterm neonatal death in Scotland.

Methods of estimating or accounting for neighborhood associations with health using complex survey data

Reasons for health disparities may include neighborhood-level factors, such as availability of health services, social norms, and environmental determinants, as well as individual-level factors. Investigating health inequalities using nationally or locally representative data often requires an approach that can accommodate a complex sampling design, in which individuals have unequal probabilities of selection into the study. The goal of the present article is to review and compare methods of estimating or accounting for neighborhood influences with complex survey data. We considered 3 types of methods, each generalized for use with complex survey data: ordinary regression, conditional likelihood regression, and generalized linear mixed-model regression. The relative strengths and weaknesses of each method differ from one study to another; we provide an overview of the advantages and disadvantages of each method theoretically, in terms of the nature of the estimable associations and the plausibility of the assumptions required for validity, and also practically, via a simulation study and 2 epidemiologic data analyses. The first analysis addresses determinants of repeat mammography screening use using data from the 2005 National Health Interview Survey. The second analysis addresses disparities in preventive oral health care using data from the 2008 Florida Behavioral Risk Factor Surveillance System Survey.

Between-within models for survival analysis

A popular way to control for confounding in observational studies is to identify clusters of individuals (e.g., twin pairs), such that a large set of potential confounders are constant (shared) within each cluster. By studying the exposure-outcome association within clusters, we are in effect controlling for the whole set of shared confounders. An increasingly popular analysis tool is the between-within (BW) model, which decomposes the exposure-outcome association into a 'within-cluster effect' and a 'between-cluster effect'. BW models are relatively common for nonsurvival outcomes and have been studied in the theoretical literature. Although it is straightforward to use BW models for survival outcomes, this has rarely been carried out in practice, and such models have not been studied in the theoretical literature. In this paper, we propose a gamma BW model for survival outcomes. We compare the properties of this model with the more standard stratified Cox regression model and use the proposed model to analyze data from a twin study of obesity and mortality. We find the following: (i) the gamma BW model often produces a more powerful test of the 'within-cluster effect' than stratified Cox regression; and (ii) the gamma BW model is robust against model misspecification, although there are situations where it could give biased estimates.