Generalized causal mediation analysis

The goal of mediation analysis is to assess direct and indirect effects of a treatment or exposure on an outcome. More generally, we may be interested in the context of a causal model as characterized by a directed acyclic graph (DAG), where mediation via a specific path from exposure to outcome may involve an arbitrary number of links (or "stages"). Methods for estimating mediation (or pathway) effects are available for a continuous outcome and a continuous mediator related via a linear model, while for a categorical outcome or categorical mediator, methods are usually limited to two-stage mediation. We present a method applicable to multiple stages of mediation and mixed variable types using generalized linear models. We define pathway effects using a potential outcomes framework and present a general formula that provides the effect of exposure through any specified pathway. Some pathway effects are nonidentifiable and their estimation requires an assumption regarding the correlation between counterfactuals. We provide a sensitivity analysis to assess the impact of this assumption. Confidence intervals for pathway effect estimates are obtained via a bootstrap method. The method is applied to a cohort study of dental caries in very low birth weight adolescents. A simulation study demonstrates low bias of pathway effect estimators and close-to-nominal coverage rates of confidence intervals. We also find low sensitivity to the counterfactual correlation in most scenarios.     

Causal mediation analysis with a latent mediator

Health researchers are often interested in assessing the direct effect of a treatment or exposure on an outcome variable, as well as its indirect (or mediation) effect through an intermediate variable (or mediator). For an outcome following a nonlinear model, the mediation formula may be used to estimate causally interpretable mediation effects. This method, like others, assumes that the mediator is observed. However, as is common in structural equations modeling, we may wish to consider a latent (unobserved) mediator. We follow a potential outcomes framework and assume a generalized structural equations model (GSEM). We provide maximum‐likelihood estimation of GSEM parameters using an approximate Monte Carlo EM algorithm, coupled with a mediation formula approach to estimate natural direct and indirect effects. The method relies on an untestable sequential ignorability assumption; we assess robustness to this assumption by adapting a recently proposed method for sensitivity analysis. Simulation studies show good properties of the proposed estimators in plausible scenarios. Our method is applied to a study of the effect of mother education on occurrence of adolescent dental caries, in which we examine possible mediation through latent oral health behavior.     

Posttreatment confounding in causal mediation studies: A cutting-edge problem and a novel solution via sensitivity analysis

In causal mediation studies that decompose an average treatment effect into indirect and direct effects, examples of posttreatment confounding are abundant. In the presence of treatment-by-mediator interactions, past research has generally considered it infeasible to adjust for a posttreatment confounder of the mediator–outcome relationship due to incomplete information: for any given individual, a posttreatment confounder is observed under the actual treatment condition while missing under the counterfactual treatment condition. This paper proposes a new sensitivity analysis strategy for handling posttreatment confounding and incorporates it into weighting-based causal mediation analysis. The key is to obtain the conditional distribution of the posttreatment confounder under the counterfactual treatment as a function of not only pretreatment covariates but also its counterpart under the actual treatment. The sensitivity analysis then generates a bound for the natural indirect effect and that for the natural direct effect over a plausible range of the conditional correlation between the posttreatment confounder under the actual and that under the counterfactual conditions. Implemented through either imputation or integration, the strategy is suitable for binary as well as continuous measures of posttreatment confounders. Simulation results demonstrate major strengths and potential limitations of this new solution. A reanalysis of the National Evaluation of Welfare-to-Work Strategies (NEWWS) Riverside data reveals that the initial analytic results are sensitive to omitted posttreatment confounding.     

Multiple mediation analysis of racial disparity in breast cancer survival

BackgroundRacial (Black vs. White) disparities in breast cancer survival have proven difficult to mitigate. Targeted strategies aimed at the primary factors driving the disparity offer the greatest potential for success. The purpose of this study was to use multiple mediation analysis to identify the most important mediators of the racial disparity in breast cancer survival.MethodsThis was a retrospective cohort study of non-Hispanic Black and non-Hispanic White women diagnosed with invasive breast cancer in Florida between 2004 and 2015. Cox regression was used to obtain unadjusted and adjusted hazard ratios (HR) with 95% confidence intervals (CI) for the association of race with 5- and 10-year breast cancer death. Multiple mediation analysis of tumor (advanced disease stage, tumor grade, hormone receptor status) and treatment-related factors (receipt of surgery, chemotherapy, radiotherapy, and hormone therapy) was used to determine the most important mediators of the survival disparity.ResultsThe study population consisted of 101,872 women of whom 87.0% (n = 88,617) were White and 13.0% were Black (n = 13,255). Black women experienced 2.3 times (HR, 2.27; 95% CI, 2.16–2.38) the rate of 5-year breast cancer death over the follow-up period, which decreased to a 38% increased rate (HR, 1.38; 95% CI, 1.31–1.45) after adjustment for age and the mediators of interest. Combined, all examined mediators explained 73% of the racial disparity in 5-year breast cancer survival. The most important mediators were: (1) advanced disease stage (44.8%), (2) nonreceipt of surgery (34.2%), and (3) tumor grade (18.2%) and hormone receptor status (17.6%). Similar results were obtained for 10-year breast cancer death.ConclusionThese results suggest that additional efforts to increase uptake of screening mammography in hard-to-reach women, and, following diagnosis, access to and receipt of surgery may offer the greatest potential to reduce racial disparities in breast cancer survival for women in Florida.     

High dimensional mediation analysis with latent variables

We propose a model for high dimensional mediation analysis that includes latent variables. We describe our model in the context of an epidemiologic study for incident breast cancer with one exposure and a large number of biomarkers (i.e., potential mediators). We assume that the exposure directly influences a group of latent, or unmeasured, factors which are associated with both the outcome and a subset of the biomarkers. The biomarkers associated with the latent factors linking the exposure to the outcome are considered “mediators.” We derive the likelihood for this model and develop an expectation‐maximization algorithm to maximize an L1‐penalized version of this likelihood to limit the number of factors and associated biomarkers. We show that the resulting estimates are consistent and that the estimates of the nonzero parameters have an asymptotically normal distribution. In simulations, procedures based on this new model can have significantly higher power for detecting the mediating biomarkers compared with the simpler approaches. We apply our method to a study that evaluates the relationship between body mass index, 481 metabolic measurements, and estrogen‐receptor positive breast cancer.     

Bayesian shrinkage estimation of high dimensional causal mediation effects in omics studies

Causal mediation analysis aims to examine the role of a mediator or a group of mediators that lie in the pathway between an exposure and an outcome. Recent biomedical studies often involve a large number of potential mediators based on high-throughput technologies. Most of the current analytic methods focus on settings with one or a moderate number of potential mediators. With the expanding growth of -omics data, joint analysis of molecular-level genomics data with epidemiological data through mediation analysis is becoming more common. However, such joint analysis requires methods that can simultaneously accommodate high-dimensional mediators and that are currently lacking. To address this problem, we develop a Bayesian inference method using continuous shrinkage priors to extend previous causal mediation analysis techniques to a high-dimensional setting. Simulations demonstrate that our method improves the power of global mediation analysis compared to simpler alternatives and has decent performance to identify true nonnull contributions to the mediation effects of the pathway. The Bayesian method also helps us to understand the structure of the composite null cases for inactive mediators in the pathway. We applied our method to Multi-Ethnic Study of Atherosclerosis and identified DNA methylation regions that may actively mediate the effect of socioeconomic status on cardiometabolic outcomes.     

On null hypotheses in survival analysis

The conventional nonparametric tests in survival analysis, such as the log‐rank test, assess the null hypothesis that the hazards are equal at all times. However, hazards are hard to interpret causally, and other null hypotheses are more relevant in many scenarios with survival outcomes. To allow for a wider range of null hypotheses, we present a generic approach to define test statistics. This approach utilizes the fact that a wide range of common parameters in survival analysis can be expressed as solutions of differential equations. Thereby, we can test hypotheses based on survival parameters that solve differential equations driven by cumulative hazards, and it is easy to implement the tests on a computer. We present simulations, suggesting that our tests perform well for several hypotheses in a range of scenarios. As an illustration, we apply our tests to evaluate the effect of adjuvant chemotherapies in patients with colon cancer, using data from a randomized controlled trial.     

A targeted maximum likelihood estimator of a causal effect on a bounded continuous outcome

Targeted maximum likelihood estimation of a parameter of a data generating distribution, known to be an element of a semi-parametric model, involves constructing a parametric model through an initial density estimator with parameter ? representing an amount of fluctuation of the initial density estimator, where the score of this fluctuation model at ? = 0 equals the efficient influence curve/canonical gradient. The latter constraint can be satisfied by many parametric fluctuation models since it represents only a local constraint of its behavior at zero fluctuation. However, it is very important that the fluctuations stay within the semi-parametric model for the observed data distribution, even if the parameter can be defined on fluctuations that fall outside the assumed observed data model. In particular, in the context of sparse data, by which we mean situations where the Fisher information is low, a violation of this property can heavily affect the performance of the estimator. This paper presents a fluctuation approach that guarantees the fluctuated density estimator remains inside the bounds of the data model. We demonstrate this in the context of estimation of a causal effect of a binary treatment on a continuous outcome that is bounded. It results in a targeted maximum likelihood estimator that inherently respects known bounds, and consequently is more robust in sparse data situations than the targeted MLE using a naive fluctuation model. When an estimation procedure incorporates weights, observations having large weights relative to the rest heavily influence the point estimate and inflate the variance. Truncating these weights is a common approach to reducing the variance, but it can also introduce bias into the estimate. We present an alternative targeted maximum likelihood estimation (TMLE) approach that dampens the effect of these heavily weighted observations. As a substitution estimator, TMLE respects the global constraints of the observed data model. For example, when outcomes are binary, a fluctuation of an initial density estimate on the logit scale constrains predicted probabilities to be between 0 and 1. This inherent enforcement of bounds has been extended to continuous outcomes. Simulation study results indicate that this approach is on a par with, and many times superior to, fluctuating on the linear scale, and in particular is more robust when there is sparsity in the data.     

Quantitative genetic analysis suggests causal association between cuticular hydrocarbon composition and desiccation survival in Drosophila melanogaster

Survival to low relative humidity is a complex adaptation, and many repeated instances of evolution to desiccation have been observed among Drosophila populations and species. One general mechanism for desiccation resistance is Cuticular Hydrocarbon (CHC) melting point. We performed the first Quantitative Trait Locus (QTL) map of population level genetic variation in desiccation resistance in D. melanogaster. Using a panel of Recombinant Inbred Lines (RILs) derived from a single natural population, we mapped QTL in both sexes throughout the genome. We found that in both sexes, CHCs correlated strongly with desiccation resistance. At most desiccation resistance loci there was a significant association between CHCs and desiccation resistance of the sort predicted from clinal patterns of CHC variation and biochemical properties of lipids. This association was much stronger in females than males, perhaps because of greater overall abundance of CHCs in females, or due to correlations between CHCs used for waterproofing and sexual signalling in males. CHC evolution may be a common mechanism for desiccation resistance in D. melanogaster. It will be interesting to compare patterns of CHC variation and desiccation resistance in species which adapt to desiccation, and rainforest restricted species which cannot.     

Estimation and inference for the causal effect of receiving treatment on a multinomial outcome

Summary .  This article considers the analysis of two-arm randomized trials with noncompliance, which have a multinomial outcome. We first define the causal effect in these trials as some function of outcome distributions of compliers with and without treatment (e.g., the complier average causal effect, the measure of stochastic superiority of treatment over control for compliers), then estimate the causal effect with the likelihood method. Next, based on the likelihood-ratio (LR) statistic, we test those functions of or the equality of the outcome distributions of compliers with and without treatment. Although the corresponding LR statistic follows a chi-squared  (χ²)  distribution asymptotically when the true values of parameters are in the interior of the parameter space under the null, its asymptotic distribution is not  χ²  when the true values of parameters are on the boundary of the parameter space under the null. Therefore, we propose a bootstrap/double bootstrap version of a LR test for the causal effect in these trials. The methods are illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices.     

Human eosinophils: Apoptosis versus survival in the mediation of inflammation

Eosinophil-derived mediators are thought to make a major contribution to the inflammation underlying a number of allergic diseases, most notably asthma. The toxic potential of eosinophils at tissue sites of inflammation might be limited if they were cleared by the process of programmed cell death or apoptosis. In this review we have examined the relationship between the signal transduction pathways important in controlling cytokine-induced prolonged survival and the mechanisms responsible for the induction and control of apoptosis in the eosinophil. A greater understanding of these processes might result in the development of novel therapeutic agents which would promote the safe and rapid removal by apoptosis of this important pro-inflammatory cell.     

Long non-coding RNAs correlate with genomic stability in prostate cancer: A clinical outcome and survival analysis

BackgroundLong non-coding RNAs (lncRNAs) participate in the regulation of genomic stability. Understanding their biological functions can help us identify the mechanisms of the occurrence and progression of cancers and can provide theoretical guidance and the basis for treatment.ResultsBased on the mutation hypothesis, we proposed a computational framework to identify genomic instability-related lncRNAs. Based on the differentially-expressed lncRNAs (DElncRNAs), we constructed a genomic instability-derived lncRNA signature (GILncSig) to calculate and stratify outcomes in patients with prostate cancer. It is an independent predictor of overall survival. The area under the curve = 0.805. This value may be more significant than the classic prognostic markers TP53 and Speckle-type POZ protein (SPOP) in terms of outcome prediction.ConclusionsIn summary, we conducted a computation approach and resource for mining genome instability-related lncRNAs. It may turn out to be highly significant for genomic instability and customized decision-making for patients with prostate cancer. It also may lead to effective methods and resources to study the molecular mechanism of genomic instability-related lncRNAs.     

Incorporating short-term outcome information to predict long-term survival with discrete markers

In disease screening and prognosis studies, an important task is to determine useful markers for identifying high-risk subgroups. Once such markers are established, they can be incorporated into public health practice to provide appropriate strategies for treatment or disease monitoring based on each individual's predicted risk. In the recent years, genetic and biological markers have been examined extensively for their potential to signal progression or risk of disease. In addition to these markers, it has often been argued that short-term outcomes may be helpful in making a better prediction of disease outcomes in clinical practice. In this paper we propose model-free non-parametric procedures to incorporate short-term event information to improve the prediction of a long-term terminal event. We include the optional availability of a single discrete marker measurement and assess the additional information gained by including the short-term outcome. We focus on the semi-competing risk setting where the short-term event is an intermediate event that may be censored by the terminal event while the terminal event is only subject to administrative censoring. Simulation studies suggest that the proposed procedures perform well in finite samples. Our procedures are illustrated using a data set of post-dialysis patients with end-stage renal disease.     

Risk prediction with imperfect survival outcome information from electronic health records

Readily available proxies for the time of disease onset such as the time of the first diagnostic code can lead to substantial risk prediction error if performing analyses based on poor proxies. Due to the lack of detailed documentation and labor intensiveness of manual annotation, it is often only feasible to ascertain for a small subset the current status of the disease by a follow-up time rather than the exact time. In this paper, we aim to develop risk prediction models for the onset time efficiently leveraging both a small number of labels on the current status and a large number of unlabeled observations on imperfect proxies. Under a semiparametric transformation model for onset and a highly flexible measurement error model for proxy onset time, we propose the semisupervised risk prediction method by combining information from proxies and limited labels efficiently. From an initially estimator solely based on the labeled subset, we perform a one-step correction with the full data augmenting against a mean zero rank correlation score derived from the proxies. We establish the consistency and asymptotic normality of the proposed semisupervised estimator and provide a resampling procedure for interval estimation. Simulation studies demonstrate that the proposed estimator performs well in a finite sample. We illustrate the proposed estimator by developing a genetic risk prediction model for obesity using data from Mass General Brigham Healthcare Biobank.