No abstract

Much attention has been paid to estimating the causal effect of adherence to a randomized protocol using instrumental variables to adjust for unmeasured confounding. Researchers tend to use the instrumental variable within one of the three main frameworks: regression with an endogenous variable, principal stratification, or structural-nested modeling. We found in our literature review that even in simple settings, causal interpretations of analyses with endogenous regressors can be ambiguous or rely on a strong assumption that can be difficult to interpret. Principal stratification and structural-nested modeling are alternative frameworks that render unambiguous causal interpretations based on assumptions that are, arguably, easier to interpret. Our interest stems from a wish to estimate the effect of cluster-level adherence on individual-level binary outcomes with a three-armed cluster-randomized trial and polytomous adherence. Principal stratification approaches to this problem are quite challenging because of the sheer number of principal strata involved. Therefore, we developed a structural-nested modeling approach and, in the process, extended the methodology to accommodate cluster-randomized trials with unequal probability of selecting individuals. Furthermore, we developed a method to implement the approach with relatively simple programming. The approach works quite well, but when the structural-nested model does not fit the data, there is no solution to the estimating equation. We investigate the performance of the approach using simulated data, and we also use the approach to estimate the effect on pupil absence of school-level adherence to a randomized water, sanitation, and hygiene intervention in western Kenya.

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.

Recently, we examined methods of adjusting for confounding by neighborhood of an individual exposure effect on a binary outcome, using complex survey data; the methods were found to fail when the neighborhood sample sizes are small and the selection bias is strongly informative. More recently, other authors have adapted an older method from the genetics literature for application to complex survey data; their adaptation achieves a consistent estimator under a broad range of circumstances. The method is based on weighted pseudolikelihoods, in which the contribution from each neighborhood involves all pairs of cases and controls in the neighborhood. The pairs are treated as if they were independent, a pairwise pseudo-conditional likelihood is thus derived, and then the corresponding score equation is weighted with inverse-probabilities of sampling each case-control pair. We have greatly simplified the implementation by translating the pairwise pseudo-conditional likelihood into an equivalent ordinary weighted log-likelihood formulation. We show how to program the method using standard software for ordinary logistic regression with complex survey data (e.g. SAS PROC SURVEYLOGISTIC). We also show that the methodology applies to a broader set of sampling scenarios than the ones considered by the previous authors. We demonstrate the validity of our simplified implementation by applying it to a simulation for which previous methods failed; the new method performs beautifully. We also apply the new method to an analysis of 2009 National Health Interview Survey (NHIS) public-use data, to estimate the effect of education on health insurance coverage, adjusting for confounding by neighborhood.

Estimating the average treatment causal effect in clustered data often involves dealing with unmeasured cluster-specific confounding variables. Such variables may be correlated with the measured unit covariates and outcome. When the correlations are ignored, the causal effect estimation can be biased. By utilizing sufficient statistics, we propose an inverse conditional probability weighting (ICPW) method, which is robust to both (i) the correlation between the unmeasured cluster-specific confounding variable and the covariates and (ii) the correlation between the unmeasured clusterspecific confounding variable and the outcome. Assumptions and conditions for the ICPW method are presented. We establish the asymptotic properties of the proposed estimators. Simulation studies and a case study are presented for illustration.