Semiparametric Estimation of Models for Natural Direct and Indirect Effects

In recent years, researchers in the health and social sciences have become increasingly interested in mediation analysis. Specifically, upon establishing a non-null total effect of an exposure, investigators routinely wish to make inferences about the direct (indirect) pathway of the effect of the exposure not through (through) a mediator variable that occurs subsequently to the exposure and prior to the outcome. Natural direct and indirect effects are of particular interest as they generally combine to produce the total effect of the exposure and therefore provide insight on the mechanism by which it operates to produce the outcome. A semiparametric theory has recently been proposed to make inferences about marginal mean natural direct and indirect effects in observational studies (Tchetgen Tchetgen and Shpitser, 2011), which delivers multiply robust locally efficient estimators of the marginal direct and indirect effects, and thus generalizes previous results for total effects to the mediation setting. In this paper we extend the new theory to handle a setting in which a parametric model for the natural direct (indirect) effect within levels of pre-exposure variables is specified and the model for the observed data likelihood is otherwise unrestricted. We show that estimation is generally not feasible in this model because of the curse of dimensionality associated with the required estimation of auxiliary conditional densities or expectations, given high-dimensional covariates. We thus consider multiply robust estimation and propose a more general model which assumes a subset but not all of several working models holds.

DECOMPOSITION OF REGRESSION ESTIMATORS TO EXPLORE THE INFLUENCE OF "UNMEASURED" TIME-VARYING CONFOUNDERS

In environmental epidemiology, exposure X and health outcome Y vary in space and time. We present a method to diagnose the possible influence of unmeasured confounders U on the estimated effect of X on Y and to propose several approaches to robust estimation. The idea is to use space and time as proxy measures for the unmeasured factors U. We start with the time series case where X and Y are continuous variables at equally-spaced times and assume a linear model. We define matching estimator b(u)s that correspond to pairs of observations with specific lag u. Controlling for a smooth function of time, St, using a kernel estimator is roughly equivalent to estimating the association with a linear combination of the b(u)s with weights that involve two components: the assumptions about the smoothness of St and the normalized variogram of the X process. When an unmeasured confounder U exists, but the model otherwise correctly controls for measured confounders, the excess variation in b(u)s is evidence of confounding by U. We use the plot of b(u)s versus lag u, lagged-estimator-plot (LEP), to diagnose the influence of U on the effect of X on Y. We use appropriate linear combination of b(u)s or extrapolate to b(0) to obtain novel estimators that are more robust to the influence of smooth U. The methods are extended to time series log-linear models and to spatial analyses. The LEP plot gives us a direct view of the magnitude of the estimators for each lag u and provides evidence when models did not adequately describe the data.

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are illustrated with two examples and their validity for cases with practical sample sizes is demonstrated via a simulation study.

USING THE R PACKAGE crlmm FOR GENOTYPING AND COPY NUMBER ESTIMATION

Genotyping platforms such as Affymetrix can be used to assess genotype-phenotype as well as copy number-phenotype associations at millions of markers. While genotyping algorithms are largely concordant when assessed on HapMap samples, tools to assess copy number changes are more variable and often discordant. One explanation for the discordance is that copy number estimates are susceptible to systematic differences between groups of samples that were processed at different times or by different labs. Analysis algorithms that do not adjust for batch effects are prone to spurious measures of association. The R package crlmm implements a multilevel model that adjusts for batch effects and provides allele-specific estimates of copy number. This paper illustrates a workflow for the estimation of allele-specific copy number, develops markerand study-level summaries of batch effects, and demonstrates how the marker-level estimates can be integrated with complimentary Bioconductor software for inferring regions of copy number gain or loss. All analyses are performed in the statistical environment R. A compendium for reproducing the analysis is available from the author’s website (http://www.biostat.jhsph.edu/~rscharpf/crlmmCompendium/index.html).