Efforts to adjust for confounding by neighborhood using complex survey data

In social epidemiology, one often considers neighborhood or contextual effects on health outcomes, in addition to effects of individual exposures. This paper is concerned with the estimation of an individual exposure effect in the presence of confounding by neighborhood effects, motivated by an analysis of National Health Interview Survey (NHIS) data. In the analysis, we operationalize neighborhood as the secondary sampling unit of the survey, which consists of small groups of neighboring census blocks. Thus the neighborhoods are sampled with unequal probabilities, as are individuals within neighborhoods. We develop and compare several approaches for the analysis of the effect of dichotomized individual-level education on the receipt of adequate mammography screening. In the analysis, neighborhood effects are likely to confound the individual effects, due to such factors as differential availability of health services and differential neighborhood culture. The approaches can be grouped into three broad classes: ordinary logistic regression for survey data, with either no effect or a fixed effect for each cluster; conditional logistic regression extended for survey data; and generalized linear mixed model (GLMM) regression for survey data. Standard use of GLMMs with small clusters fails to adjust for confounding by cluster (e.g. neighborhood); this motivated us to develop an adaptation. We use theory, simulation, and analyses of the NHIS data to compare and contrast all of these methods. One conclusion is that all of the methods perform poorly when the sampling bias is strong; more research and new methods are clearly needed.