Structural Racism and Quantitative Causal Inference: A Life Course Mediation Framework for Decomposing Racial Health Disparities

Quantitative studies of racial health disparities often use static measures of self-reported race and conventional regression estimators, which critics argue is inconsistent with social-constructivist theories of race, racialization, and racism. We demonstrate an alternative counterfactual approach to explain how multiple racialized systems dynamically shape health over time, examining racial inequities in cardiometabolic risk in the National Longitudinal Study of Adolescent to Adult Health. This framework accounts for the dynamics of time-varying confounding and mediation that is required in operationalizing a “race” variable as part of a social process ( racism) rather than a separable, individual characteristic. We decompose the observed disparity into three types of effects: a controlled direct effect (“unobserved racism”), proportions attributable to interaction (“racial discrimination”), and pure indirect effects (“emergent discrimination”). We discuss the limitations of counterfactual approaches while highlighting how they can be combined with critical theories to quantify how interlocking systems produce racial health inequities.

Some Model Assisted Estimators Using Functional Form Calibration Approach

The Model assisted estimators are approximately design unbiased, consistent and provides robustness in the case of large sample sizes. The model assisted estimators result in reduction of the design variance if underlying model reasonably defines the regression relationship. If the model is misspecified, then model assisted estimators might result in an increase of the design variance but remain approximately design unbiased and show robustness against model-misspecification. The well-known model assisted estimators, generalized regression estimators are members of a larger class of calibration estimators. Calibration method generates calibration weights that meet the calibration constraints and have minimum distance from the sampling design weights. By using different distance measures, classical calibration approach generates different calibration estimators but with asymptotically identical properties. The constraint of distance minimization was reduced for studying the properties of calibration estimators by proposing a simple functional form approach. The approach generates calibration weights that prove helpful to control the changes in calibration weights by using different choices of auxiliary variable’s functions. This paper is an extended work on model assisted approach by using functional form of calibration weights. Some new model assisted estimators are considered to get efficient and stabilized regression weights by introducing a control matrix. The asymptotic un-biasedness of the proposed estimators is verified and the expressions for MSE are derived in three different cases. A simulation study is done to compare and evaluate the efficiency of the proposed estimators with some existing model assisted estimators.

Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise

In this paper, we consider a general nonparametric regression estimation model with the feature of having multiplicative noise. We propose a linear estimator and nonlinear estimator by wavelet method. The convergence rates of those regression estimators under pointwise error over Besov spaces are proved. It turns out that the obtained convergence rates are consistent with the optimal convergence rate of pointwise nonparametric functional estimation.

Robust logistic zero-sum regression for microbiome compositional data

We introduce the Robust Logistic Zero-Sum Regression (RobLZS) estimator, which can be used for a two-class problem with high-dimensional compositional covariates. Since the log-contrast model is employed, the estimator is able to do feature selection among the compositional parts. The proposed method attains robustness by minimizing a trimmed sum of deviances. A comparison of the performance of the RobLZS estimator with a non-robust counterpart and with other sparse logistic regression estimators is conducted via Monte Carlo simulation studies. Two microbiome data applications are considered to investigate the stability of the estimators to the presence of outliers. Robust Logistic Zero-Sum Regression is available as an R package that can be downloaded at https://github.com/giannamonti/RobZS.

Mean Estimators Using Robust Quantile Regression and L-Moments’ Characteristics for Complete and Partial Auxiliary Information

Ratio type regression estimator is a prevalent and readily implemented heuristic under simple random sampling (SRS) and two-stage sampling for the estimation of population. But this existing method is based on the ordinary least square (OLS) regression coefficient which is not an effective approach in the presence outliers in the data. In this article, we proposed a class of estimators firstly for complete auxiliary information and, later on, for partial auxiliary information for the presence of outliers in the data. To address this problem, initially we presented a distinct class of estimators by introducing the characteristics of L-moments in the existing estimators. Later on, quantile regression estimators are defined as more robust in the presence of outliers. These techniques empowered the proposed estimators to handle the problem of outliers. To prove the better performance of the proposed estimators, numerical studies are carried out using R language. To calculate the mean square error (MSE), hypothetical equations are expressed for adapted and proposed estimators. Percentage Relative Efficiencies (PRE) are compared to justify the proposed estimators.

Minimum Covariance Determinant-Based Quantile Robust Regression-Type Estimators for Mean Parameter

Robust regression tools are commonly used to develop regression-type ratio estimators with traditional measures of location whenever data are contaminated with outliers. Recently, the researchers extended this idea and developed regression-type ratio estimators through robust minimum covariance determinant (MCD) estimation. In this study, the quantile regression with MCD-based measures of location is utilized and a class of quantile regression-type mean estimators is proposed. The mean squared errors (MSEs) of the proposed estimators are also obtained. The proposed estimators are compared with the reviewed class of estimators through a simulation study. We also incorporated two real-life applications. To assess the presence of outliers in these real-life applications, the Dixon chi-squared test is used. It is found that the quantile regression estimators are performing better as compared to some existing estimators.