As with other instrumental variable (IV) analyses, Mendelian randomization (MR) studies rest on strong assumptions. These assumptions are not routinely systematically evaluated in MR applications, although such evaluation could add to the credibility of MR analyses. In this article, the authors present several methods that are useful for evaluating the validity of an MR study. They apply these methods to a recent MR study that used fat mass and obesity-associated (FTO) genotype as an IV to estimate the effect of obesity on mental disorder. These approaches to evaluating assumptions for valid IV analyses are not fail-safe, in that there are situations where the approaches might either fail to identify a biased IV or inappropriately suggest that a valid IV is biased. Therefore, the authors describe the assumptions upon which the IV assessments rely. The methods they describe are relevant to any IV analysis, regardless of whether it is based on a genetic IV or other possible sources of exogenous variation. Methods that assess the IV assumptions are generally not conclusive, but routinely applying such methods is nonetheless likely to improve the scientific contributions of MR studies.

The question of which statistical approach is the most effective for investigating gene-environment (G-E) interactions in the context of genome-wide association studies (GWAS) remains unresolved. By using 2 case-control GWAS (the Nurses’ Health Study, 1976–2006, and the Health Professionals Follow-up Study, 1986–2006) of type 2 diabetes, the authors compared 5 tests for interactions: standard logistic regression-based case-control; case-only; semiparametric maximum-likelihood estimation of an empirical-Bayes shrinkage estimator; and 2-stage tests. The authors also compared 2 joint tests of genetic main effects and G-E interaction. Elevated body mass index was the exposure of interest and was modeled as a binary trait to avoid an inflated type I error rate that the authors observed when the main effect of continuous body mass index was misspecified. Although both the case-only and the semiparametric maximum-likelihood estimation approaches assume that the tested markers are independent of exposure in the general population, the authors did not observe any evidence of inflated type I error for these tests in their studies with 2,199 cases and 3,044 controls. Both joint tests detected markers with known marginal effects. Loci with the most significant G-E interactions using the standard, empirical-Bayes, and 2-stage tests were strongly correlated with the exposure among controls. Study findings suggest that methods exploiting G-E independence can be efficient and valid options for investigating G-E interactions in GWAS.

Background

Selective attrition may introduce bias into analyses of the determinants of cognitive decline. This is a concern especially for risk factors, such as smoking, that strongly influence mortality and drop-out. Using inverse-probability-of-attrition weights (IPAWs), we examined the influence of selective attrition on the estimated association of current smoking (versus never smoking) with cognitive decline.

Methods

Chicago Health and Aging Project participants (n=3,713), aged 65–109, who were current smokers or never-smokers underwent cognitive assessments up to 5 times at 3-year intervals. We used pooled logistic regression to fit predictive models of attrition due to death or study drop-out across the follow-up waves. With these models, we computed inverse-probability-of-attrition weights for each observation. We fit unweighted and weighted, multivariable-adjusted generalized-estimating-equation models, contrasting rates of change in cognitive scores in current versus never-smokers. Estimates are expressed as rates of change in z-score per decade.

Results

Over the 12 years of follow-up, smokers had higher mortality than never-smokers (hazard ratio= 1.93 [95% confidence interval= 1.67 to 2.23]). Higher previous cognitive score was associated with increased likelihood of survival and continued participation. In unweighted analyses, current smokers’ cognitive scores declined 0.11 standard units per decade more rapidly than never-smokers’ (95% CI= −0.20 to −0.02). Weighting to account for attrition yielded estimates that were 56%–86% larger, with smokers’ estimated 10-year rate of decline up to 0.20 units faster than never smokers’ (95% CI= −0.36 to −0.04).

Conclusions

Estimates of smoking’s effects on cognitive decline may be underestimated due to differential attrition. Analyses that weight for the inverse probability of attrition help - for this attrition.

Suppose that having established a marginal total effect of a point exposure on a time-to-event outcome, an investigator wishes to decompose this effect into its direct and indirect pathways, also known as natural direct and indirect effects, mediated by a variable known to occur after the exposure and prior to the outcome. This paper proposes a theory of estimation of natural direct and indirect effects in two important semiparametric models for a failure time outcome. The underlying survival model for the marginal total effect and thus for the direct and indirect effects, can either be a marginal structural Cox proportional hazards model, or a marginal structural additive hazards model. The proposed theory delivers new estimators for mediation analysis in each of these models, with appealing robustness properties. Specifically, in order to guarantee ignorability with respect to the exposure and mediator variables, the approach, which is multiply robust, allows the investigator to use several flexible working models to adjust for confounding by a large number of pre-exposure variables. Multiple robustness is appealing because it only requires a subset of working models to be correct for consistency; furthermore, the analyst need not know which subset of working models is in fact correct to report valid inferences. Finally, a novel semiparametric sensitivity analysis technique is developed for each of these models, to assess the impact on inference, of a violation of the assumption of ignorability of the mediator.

In the presence of interference, the exposure of one individual may affect the outcomes of others. We provide new effect partitioning results under interferences that express the overall effect as a sum of (i) the indirect (or spillover) effect and (ii) a contrast between two direct effects.

Modern epidemiologic studies often aim to evaluate the causal effect of a point exposure on the risk of a disease from cohort or case-control observational data. Because confounding bias is of serious concern in such non-experimental studies, investigators routinely adjust for a large number of potential confounders in a logistic regression analysis of the effect of exposure on disease outcome. Unfortunately, when confounders are not correctly modeled, standard logistic regression is likely biased in its estimate of the effect of exposure, potentially leading to erroneous conclusions. We partially resolve this serious limitation of standard logistic regression analysis with a new iterative approach that we call ProRetroSpective estimation, which carefully combines standard logistic regression with a logistic regression analysis in which exposure is the dependent variable and the outcome and confounders are the independent variables. As a result, we obtain a correct estimate of the exposure-outcome odds ratio, if either the standard logistic regression of the outcome given exposure and confounding factors is correct, or the regression model of exposure given the outcome and confounding factors is correct but not necessarily both, that is, it is double-robust. In fact, it also has certain advantadgeous efficiency properties. The approach is general in that it applies to both cohort and case-control studies whether the design of the study is matched or unmatched on a subset of covariates. Finally, an application illustrates the methods using data from the National Cancer Institute's Black/White Cancer Survival Study.

We propose a semi-parametric case-only estimator of multiplicative gene-environment or gene-gene interactions, under the assumption of conditional independence of the two factors given a vector of potential confounding variables. Our estimator yields valid inferences on the interaction function if either but not necessarily both of two unknown baseline functions of the confounders is correctly modeled. Furthermore, when both models are correct, our estimator has the smallest possible asymptotic variance for estimating the interaction parameter in a semi-parametric model that assumes that at least one but not necessarily both baseline models are correct.

Purpose

Using a longitudinal cohort, we assessed the association between neighborhood disadvantage and incidence of poor health and function in three domains.

Methods

Over 4,000 enrollees aged 55–65 in the national Health and Retirement Study were assessed biennially from 1998 through 2006 for incidence of: fair/poor self-rated health (SRH), elevated depressive symptoms, and limitations in five basic Activities of Daily Living (disability). Each analysis was restricted to subjects without that condition in 1994 or 1996. Neighborhoods (census tracts, time-updated for moves), were considered disadvantaged if they fell below the 25th percentile in an index comprising 6 socioeconomic status indicators. Repeated measures logistic regressions, inverse probability weighted to account for individual confounders, selective survival, and loss to follow-up, were used to estimate odds ratios (ORs) for incidence of each outcome in the wave following exposure to disadvantaged neighborhood.

Results

After covariate adjustment, neighborhood disadvantage predicted onset of fair/poor SRH (OR=1.32; 95% confidence interval 1.11, 1.57), but not disability (OR=0.98; 0.82, 1.16) or elevated depressive symptoms (OR=0.98; 0.83, 1.16).

Conclusions

Results confirmed prior findings that neighborhood disadvantage predicts SRH in a longitudinal context, but did not support an association between neighborhood disadvantage and onset of disability or elevated depressive symptoms.

We consider the doubly robust estimation of the parameters in a semiparametric conditional odds ratio model. Our estimators are consistent and asymptotically normal in a union model that assumes either of two variation independent baseline functions is correctly modelled but not necessarily both. Furthermore, when either outcome has finite support, our estimators are semiparametric efficient in the union model at the intersection submodel where both nuisance functions models are correct. For general outcomes, we obtain doubly robust estimators that are nearly efficient at the intersection submodel. Our methods are easy to implement as they do not require the use of the alternating conditional expectations algorithm of Chen (2007).