Heterogeneous Mediation Analysis for Cox Proportional Hazards Model With Multiple Mediators

This study proposes a heterogeneous mediation analysis for survival data that accommodates multiple mediators and sparsity of the predictors. We introduce a joint modeling approach that links the mediation regression and proportional hazards models through Bayesian additive regression trees with shared typologies. The shared tree component is motivated by the fact that confounders and effect modifiers on the causal pathways linked by different mediators often overlap. A sparsity-inducing prior is incorporated to capture the most relevant confounders and effect modifiers on different causal pathways. The individual-specific interventional direct and indirect effects are derived on the scale of the logarithm of hazards and survival function. A Bayesian approach with an efficient Markov chain Monte Carlo algorithm is developed to estimate the conditional interventional effects through the Monte Carlo implementation of the mediation formula. Simulation studies are conducted to verify the empirical performance of the proposed method. An application to the ACTG175 study further demonstrates the method's utility in causal discovery and heterogeneity quantification.

Longitudinal mediation analysis with multilevel and latent growth models: a separable effects causal approach

BACKGROUND

Causal mediation analysis is widespread in applied medical research, especially in longitudinal settings. However, estimating natural mediational effects in such contexts is often difficult because of the presence of post-treatment confounding. Moreover, many models frequently used in applied research, like multilevel and latent growth models, present an additional difficulty, i.e. the presence of latent variables. In this paper, we propose a causal interpretation of these two classes of models based on a novel type of causal effects called separable, which overcome some of the issues of natural effects.

METHODS

We formally derive conditions for the identifiability of separable mediational effects and their analytical expressions based on the g-formula. We carry out a simulation study to investigate how moderate and severe model misspecification, as well as violation of the identfiability assumptions, affect estimates. We also present an application to real data.

RESULTS

The results show how model misspecification impacts the estimates of mediational effects, particularly in the case of severe misspecification, and that the bias worsens over time. The violation of assumptions affects separable effect estimates in a very different way for the mixed effect and the latent growth models.

CONCLUSION

Our approach allows us to give multilevel and latent growth models an appealing causal interpretation based on separable effects. The simulation study shows that model misspecification can heavily impact effect estimates, highlighting the importance of careful model choice.

Estimands in clinical trials of complex disease processes

Clinical trials with random assignment of treatment provide evidence about causal effects of an experimental treatment compared to standard care. However, when disease processes involve multiple types of possibly semi-competing events, specification of target estimands and causal inferences can be challenging. Intercurrent events such as study withdrawal, the introduction of rescue medication, and death further complicate matters. There has been much discussion about these issues in recent years, but guidance remains ambiguous. Some recommended approaches are formulated in terms of hypothetical settings that have little bearing in the real world. We discuss issues in formulating estimands, beginning with intercurrent events in the context of a linear model and then move on to more complex disease history processes amenable to multistate modeling. We elucidate the meaning of estimands implicit in some recommended approaches for dealing with intercurrent events and highlight the disconnect between estimands formulated in terms of potential outcomes and the real world.

High adherence to the French dietary guidelines decreases type 2 diabetes risk in females through pathways of obesity markers: Evidence from the E3N-EPIC prospective cohort study

OBJECTIVE

Obesity and type 2 diabetes (T2D) have been associated with low adherence to the 2017 French food-based dietary guidelines, as assessed by the Programme National Nutrition Santé - guidelines score 2 (PNNS-GS2). Whether the association between T2D and PNNS-GS2 is direct or mediated by obesity has been little investigated.

RESEARCH METHODS

The study included 71,450 women from the E3N-EPIC cohort, mean age of 52.9 y (SD 6.7). The simplified PNNS-GS2 was derived via food history questionnaire. Multivariable Cox regression models were used to estimate hazard ratios (HRs) and 95% confidence intervals (CIs) of T2D. Causal mediation analyses were used to decompose the total effect of sPNNS-GS2 on T2D into a direct effect and indirect effect mediated by body mass index (BMI) or the waist-hip ratio (WHR).

RESULTS

During a mean follow-up of 19 y, 3679 incident T2D cases were identified and validated. There was a linear association between adherence to sPNNS-GS2 and T2D (P-nonlinearity = 0.92). In the fully adjusted model, each 1-SD increase in the sPNNS-GS2 was associated with a lower T2D risk [HR (95% CI), 0.92 (0.89, 0.95)]. The overall associations were mainly explained by sPNNS-GS2-associated excess weight, with BMI and WHR mediating 52% and 58% of the associations, respectively.

CONCLUSIONS

Higher adherence to French food-based dietary guidelines was associated with a lower risk of T2D in women, and a significant portion of this effect could be attributed to excess weight measured by BMI or WHR. This finding helps better understand the mechanisms underlying the diet-T2D association.

Separable and controlled direct effects for competing events: Estimation of component specific effects on sickness absence

In many settings, it is reasonable to think of treatment as consisting of a number of components, either because this is the case in practice or because it is conceptually possible to decompose treatment into separate components due to the way in which it exerts effects on the outcome of interest. For competing events, the treatment decomposition idea has recently been suggested to separate effects of treatments on the outcome of interest from effects mediated through competing events using so-called separable effects. Like the idea of separating effects of exposure, it has been pointed out that ideas from mediation analysis generally may help to clarify the interpretation of existing estimands used in competing events settings. One example is the use of the controlled direct effect, to conceptualize the effects of interventions preventing the competing event from occurring. In this article, we identify the controlled direct effect as a component specific effect and discuss the merits of this estimand when the prevented event is non terminal and other methods of effects separation are problematic. Our motivating example is the study of a policy initiative, introduced in 2001, aimed at reducing long term sickness absence (SA) in Norway. The initiative consists of different components, one being to encourage use of graded SA, which is considered a key tool in the Nordic countries to reduce long term SA. The analysis makes use of longitudinal registry data for 113 808 individuals, followed from the time of first SA.

Model-based hypothesis tests for the causal mediation of semi-competing risks

Analyzing the causal mediation of semi-competing risks has become important in medical research. Semi-competing risks refers to a scenario wherein an intermediate event may be censored by a primary event but not vice versa. Causal mediation analyses decompose the effect of an exposure on the primary outcome into an indirect (mediation) effect: an effect mediated through a mediator, and a direct effect: an effect not through the mediator. Here we proposed a model-based testing procedure to examine the indirect effect of the exposure on the primary event through the intermediate event. Under the counterfactual outcome framework, we defined a causal mediation effect using counting process. To assess statistical evidence for the mediation effect, we proposed two tests: an intersection-union test (IUT) and a weighted log-rank test (WLR). The test statistic was developed from a semi-parametric estimator of the mediation effect using a Cox proportional hazards model for the primary event and a series of logistic regression models for the intermediate event. We built a connection between the IUT and WLR. Asymptotic properties of the two tests were derived, and the IUT was determined to be a size [Formula: see text] test and statistically more powerful than the WLR. In numerical simulations, both the model-based IUT and WLR can properly adjust for confounding covariates, and the Type I error rates of the proposed methods are well protected, with the IUT being more powerful than the WLR. Our methods demonstrate the strongly significant effects of hepatitis B or C on the risk of liver cancer mediated through liver cirrhosis incidence in a prospective cohort study. The proposed method is also applicable to surrogate endpoint analyses in clinical trials.

Estimation of separable direct and indirect effects in a continuous-time illness-death model

In this article we study the effect of a baseline exposure on a terminal time-to-event outcome either directly or mediated by the illness state of a continuous-time illness-death process with baseline covariates. We propose a definition of the corresponding direct and indirect effects using the concept of separable (interventionist) effects (Robins and Richardson in Causality and psychopathology: finding the determinants of disorders and their cures, Oxford University Press, 2011; Robins et al. in arXiv:2008.06019 , 2021; Stensrud et al. in J Am Stat Assoc 117:175-183, 2022). Our proposal generalizes Martinussen and Stensrud (Biometrics 79:127-139, 2023) who consider similar causal estimands for disentangling the causal treatment effects on the event of interest and competing events in the standard continuous-time competing risk model. Unlike natural direct and indirect effects (Robins and Greenland in Epidemiology 3:143-155, 1992; Pearl in Proceedings of the seventeenth conference on uncertainty in artificial intelligence, Morgan Kaufmann, 2001) which are usually defined through manipulations of the mediator independently of the exposure (so-called cross-world interventions), separable direct and indirect effects are defined through interventions on different components of the exposure that exert their effects through distinct causal mechanisms. This approach allows us to define meaningful mediation targets even though the mediating event is truncated by the terminal event. We present the conditions for identifiability, which include some arguably restrictive structural assumptions on the treatment mechanism, and discuss when such assumptions are valid. The identifying functionals are used to construct plug-in estimators for the separable direct and indirect effects. We also present multiply robust and asymptotically efficient estimators based on the efficient influence functions. We verify the theoretical properties of the estimators in a simulation study, and we demonstrate the use of the estimators using data from a Danish registry study.

Time-to-event surrogate endpoint validation using mediation analysis and meta-analytic data

With the ongoing development of treatments and the resulting increase in survival in oncology, clinical trials based on endpoints such as overall survival may require long follow-up periods to observe sufficient events and ensure adequate statistical power. This increase in follow-up time may compromise the feasibility of the study. The use of surrogate endpoints instead of final endpoints may be attractive for these studies. However, before a surrogate can be used in a clinical trial, it must be statistically validated. In this article, we propose an approach to validate surrogates when both the surrogate and final endpoints are censored event times. This approach is developed for meta-analytic data and uses a mediation analysis to decompose the total effect of the treatment on the final endpoint as a direct effect and an indirect effect through the surrogate. The meta-analytic nature of the data is accounted for in a joint model with random effects at the trial level. The proportion of the indirect effect over the total effect of the treatment on the final endpoint can be computed from the parameters of the model and used as a measure of surrogacy. We applied this method to investigate time-to-relapse as a surrogate endpoint for overall survival in resectable gastric cancer.

A multistate approach for the study of interventions on an intermediate time-to-event in health disparities research

We propose a novel methodology to quantify the effect of stochastic interventions for a non-terminal intermediate time-to-event on a terminal time-to-event outcome. Investigating these effects is particularly important in health disparities research when we seek to quantify inequities in the timely delivery of treatment and its impact on patients' survival time. Current approaches fail to account for time-to-event intermediates and semi-competing risks arising in this setting. Under the potential outcome framework, we define causal contrasts relevant in health disparities research and provide identifiability conditions when stochastic interventions on an intermediate non-terminal time-to-event are of interest. Causal contrasts are estimated in continuous time within a multistate modeling framework and analytic formulae for the estimators of the causal contrasts are developed. We show via simulations that ignoring censoring in intermediate and/or terminal time-to-event processes or ignoring semi-competing risks may give misleading results. This work demonstrates that a rigorous definition of the causal effects and joint estimation of the terminal outcome and intermediate non-terminal time-to-event distributions are crucial for valid investigation of interventions and mechanisms in continuous time. We employ this novel methodology to investigate the role of delaying treatment uptake in explaining racial disparities in cancer survival in a cohort study of colon cancer patients.

Chronic Exposure to Fine Particulate Matter Increases Mortality Through Pathways of Metabolic and Cardiovascular Disease: Insights From a Large Mediation Analysis

Background Long-term exposure to outdoor fine particulate matter (PM2.5) is the leading environmental risk factor for premature mortality worldwide. Characterizing important pathways through which PM2.5 increases individuals' mortality risk can clarify the PM2.5-mortality relationship and identify possible points of interventions. Recent evidence has linked PM2.5 to the onset of diabetes and cardiovascular disease, but to what extent these associations contribute to the effect of PM2.5 on mortality remains poorly understood. Methods and Results We conducted a population-based cohort study to investigate how the effect of PM2.5 on nonaccidental mortality is mediated by its impacts on incident diabetes, acute myocardial infarction, and stroke. Our study population comprised ≈200 000 individuals aged 20 to 90 years who participated in population-based health surveys in Ontario, Canada, from 1996 to 2014. Follow-up extended until December 2017. Using causal mediation analyses with Aalen additive hazards models, we decomposed the total effect of PM2.5 on mortality into a direct effect and several path-specific indirect effects mediated by diabetes, each cardiovascular event, or both combined. A series of sensitivity analyses were also conducted. After adjusting for various individual- and neighborhood-level covariates, we estimated that for every 1000 adults, each 10 μg/m3 increase in PM2.5 was associated with ≈2 incident cases of diabetes, ≈1 major cardiovascular event (acute myocardial infarction and stroke combined), and ≈2 deaths annually. Among PM2.5-related deaths, 31.7% (95% CI, 17.2%-53.2%) were attributable to diabetes and major cardiovascular events in relation to PM2.5. Specifically, 4.5% were explained by PM2.5-induced diabetes, 22.8% by PM2.5-induced major cardiovascular events, and 4.5% through their interaction. Conclusions This study suggests that a significant portion of the estimated effect of long-term exposure to PM2.5 on deaths can be attributed to its effect on diabetes and cardiovascular diseases, highlighting the significance of PM2.5 on deteriorating cardiovascular health. Our findings should raise awareness among professionals that improving metabolic and cardiovascular health may reduce mortality burden in areas with higher exposure to air pollution.

Methods of analysis for survival outcomes with time-updated mediators, with application to longitudinal disease registry data

Mediation analysis is a useful tool to illuminate the mechanisms through which an exposure affects an outcome but statistical challenges exist with time-to-event outcomes and longitudinal observational data. Natural direct and indirect effects cannot be identified when there are exposure-induced confounders of the mediator-outcome relationship. Previous measurements of a repeatedly-measured mediator may themselves confound the relationship between the mediator and the outcome. To overcome these obstacles, two recent methods have been proposed, one based on path-specific effects and one based on an additive hazards model and the concept of exposure splitting. We investigate these techniques, focusing on their application to observational datasets. We apply both methods to an analysis of the UK Cystic Fibrosis Registry dataset to identify how much of the relationship between onset of cystic fibrosis-related diabetes and subsequent survival acts through pulmonary function. Statistical properties of the methods are investigated using simulation. Both methods produce unbiased estimates of indirect and direct effects in scenarios consistent with their stated assumptions but, if the data are measured infrequently, estimates may be biased. Findings are used to highlight considerations in the interpretation of the observational data analysis.

Sex-differential non-specific effects of adjuvanted and non-adjuvanted rabies vaccines versus placebo on all-cause mortality in dogs (NERVE-Dog study): a study protocol for a randomized controlled trial with a nested case-control study

BACKGROUND

It has been proposed that childhood vaccines in high-mortality populations may have substantial impacts on mortality rates that are not explained by the prevention of targeted diseases, nor conversely by typical expected adverse reactions to the vaccines, and that these non-specific effects (NSEs) are generally more pronounced in females. The existence of these effects, and any implications for the development of vaccines and the design of vaccination programs to enhance safety, remain controversial. One area of controversy is the reported association of non-live vaccines with increased female mortality. In a previous randomized controlled trial (RCT), we observed that non-live alum-adjuvanted animal rabies vaccine (ARV) was associated with increased female but not male mortality in young, free-roaming dogs. Conversely, non-live non-adjuvanted human rabies vaccine (NRV) has been associated with beneficial non-specific effects in children. Alum adjuvant has been shown to suppress Th1 responses to pathogens, leading us to hypothesize that alum-adjuvanted rabies vaccine in young dogs has a detrimental effect on female survival by modulating the immune response to infectious and/or parasitic diseases. In this paper, we present the protocol of a 3-arm RCT comparing the effect of alum-adjuvanted rabies vaccine, non-adjuvanted rabies vaccine and placebo on all-cause mortality in an owned, free-roaming dog population, with causal mediation analysis of the RCT and a nested case-control study to test this hypothesis.

METHODS

Randomised controlled trial with a nested case-control study.

DISCUSSION

We expect that, among the placebo group, males will have higher mortality caused by higher pathogen loads and more severe disease, as determined by haematological parameters and inflammatory biomarkers. Among females, we expect that there will be no difference in mortality between the NRV and placebo groups, but that the ARV group will have higher mortality, again mediated by higher pathogen loads and more severe disease. We anticipate that these changes are preceded by shifts in key serum cytokine concentrations towards an anti-inflammatory immune response in females. If confirmed, these results will provide a rational basis for mitigation of detrimental NSEs of non-live vaccines in high-mortality populations.

Time-varying intensity of oxygen exposure is associated with mortality in critically ill patients with mechanical ventilation

BACKGROUND

There is no consensus exists regarding the association between oxygen exposure (arterial oxygen tension or fraction of inspired oxygen) and outcomes for patients with mechanical ventilation. Additionally, whether the association remains persistent over time is unknown. We aimed to explore the association between exposure to different intensities of oxygen exposure over time and 28-day mortality in patients with mechanical ventilation.

METHODS

We obtained data from the Medical Information Mart for Intensive Care IV (MIMIC-IV), which included adult (≥ 18 years) patients who received invasive mechanical ventilation for at least 48 h. We excluded patients who received extracorporeal membrane oxygenation (ECMO) or who initiated ventilation more than 24 h after ICU admission. The primary outcome was 28-day mortality. Piece-wise exponential additive mixed models were employed to estimate the strength of associations over time.

RESULTS

A total of 7784 patients were included in the final analysis. Patients had a median duration of invasive mechanical ventilation of 8.1 days (IQR: 3.8-28 days), and the overall 28-day mortality rate was 26.3%. After adjustment for baseline and time-dependent confounders, both daily time-weighted average (TWA) arterial oxygen tension (PaO₂) and fraction of inspired oxygen (FiO₂) were associated with increased 28-day mortality, and the strength of the association manifested predominantly in the early-middle course of illness. A significant increase in the hazard of death was found to be associated with daily exposure to TWA-PaO₂ ≥ 120 mmHg (Hazard ratio 1.166, 95% CI 1.059-1.284) or TWA-FiO₂ ≥ 0.5 (Hazard ratio 1.496, 95% CI 1.363-1.641) during the entire course. A cumulative effect of harmful exposure (TWA-PaO₂ ≥ 120 mmHg or TWA-FiO₂ ≥ 0.5) was also observed.

CONCLUSION

PaO₂ and FiO₂ should be carefully monitored in patients with mechanical ventilation, especially during the early-middle course after ICU admission. Cumulative exposure to higher intensities of oxygen exposure was associated with an increased risk of death.

High-Dimensional Mediation Analysis Based on Additive Hazards Model for Survival Data

Mediation analysis has been extensively used to identify potential pathways between exposure and outcome. However, the analytical methods of high-dimensional mediation analysis for survival data are still yet to be promoted, especially for non-Cox model approaches. We propose a procedure including "two-step" variable selection and indirect effect estimation for the additive hazards model with high-dimensional mediators. We first apply sure independence screening and smoothly clipped absolute deviation regularization to select mediators. Then we use the Sobel test and the BH method for indirect effect hypothesis testing. Simulation results demonstrate its good performance with a higher true-positive rate and accuracy, as well as a lower false-positive rate. We apply the proposed procedure to analyze DNA methylation markers mediating smoking and survival time of lung cancer patients in a TCGA (The Cancer Genome Atlas) cohort study. The real data application identifies four mediate CpGs, three of which are newly found.

Mediating role of multimorbidity in inequality in mortality: a register study on the Danish population

BACKGROUND

The social inequality in mortality is due to differential incidence of several disorders and injury types, as well as differential survival. The resulting clustering and possible interaction in disadvantaged groups of several disorders make multimorbidity a potentially important component in the health divide. This study decomposes the effect of education on mortality into a direct effect, a pure indirect effect mediated by multimorbidity and a mediated interaction between education and multimorbidity.

METHODS

The study uses the Danish population registers on the total Danish population aged 45-69 years. A multimorbidity index based on all somatic and psychiatric hospital contacts as well as prescribed medicines includes 22 diagnostic groups weighted together by their 5 years mortality risk as weight. The Aalen additive hazard model is used to estimate and decompose the 5 years risk difference in absolute numbers of deaths according to educational status.

RESULTS

Most (69%-79%) of the effect is direct not involving multimorbidity, and the mediated effect is for low educated women 155 per 100 000 of which 87 is an effect of mediated interaction. For low educated men, the mediated effect is 250 per 100 000 of which 93 is mediated interaction.

CONCLUSION

Multimorbidity plays an important role in the social inequality in mortality among middle aged in Denmark and mediated interaction represents 5%-17%. As multimorbidity is a growing challenge in specialised health systems, the mediated interaction might be a relevant indicator of inequities in care of multimorbid patients.

A generalized theory of separable effects in competing event settings

In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly contribute to this total effect, complicating its interpretation. We previously proposed the separable effects to define direct and indirect effects of the treatment on the event of interest. This definition was given in a simple setting, where the treatment was decomposed into two components acting along two separate causal pathways. Here we generalize the notion of separable effects, allowing for interpretation, identification and estimation in a wide variety of settings. We propose and discuss a definition of separable effects that is applicable to general time-varying structures, where the separable effects can still be meaningfully interpreted as effects of modified treatments, even when they cannot be regarded as direct and indirect effects. For these settings we derive weaker conditions for identification of separable effects in studies where decomposed, or otherwise modified, treatments are not yet available; in particular, these conditions allow for time-varying common causes of the event of interest, the competing events and loss to follow-up. We also propose semi-parametric weighted estimators that are straightforward to implement. We stress that unlike previous definitions of direct and indirect effects, the separable effects can be subject to empirical scrutiny in future studies.

Simulating longitudinal data from marginal structural models using the additive hazard model

Observational longitudinal data on treatments and covariates are increasingly used to investigate treatment effects, but are often subject to time-dependent confounding. Marginal structural models (MSMs), estimated using inverse probability of treatment weighting or the g-formula, are popular for handling this problem. With increasing development of advanced causal inference methods, it is important to be able to assess their performance in different scenarios to guide their application. Simulation studies are a key tool for this, but their use to evaluate causal inference methods has been limited. This paper focuses on the use of simulations for evaluations involving MSMs in studies with a time-to-event outcome. In a simulation, it is important to be able to generate the data in such a way that the correct forms of any models to be fitted to those data are known. However, this is not straightforward in the longitudinal setting because it is natural for data to be generated in a sequential conditional manner, whereas MSMs involve fitting marginal rather than conditional hazard models. We provide general results that enable the form of the correctly specified MSM to be derived based on a conditional data generating procedure, and show how the results can be applied when the conditional hazard model is an Aalen additive hazard or Cox model. Using conditional additive hazard models is advantageous because they imply additive MSMs that can be fitted using standard software. We describe and illustrate a simulation algorithm. Our results will help researchers to effectively evaluate causal inference methods via simulation.

Discussion on "Causal mediation of semicompeting risks" by Yen-Tsung Huang

Huang proposes a method for assessing the impact of a point treatment on mortality either directly or mediated by occurrence of a nonterminal health event, based on data from a prospective cohort study in which the occurrence of the nonterminal health event may be preemptied by death but not vice versa. The author uses a causal mediation framework to formally define causal quantities known as natural (in)direct effects. The novelty consists of adapting these concepts to a continuous-time modeling framework based on counting processes. In an effort to posit "scientifically interpretable estimands," statistical and causal assumptions are introduced for identification. In this commentary, we argue that these assumptions are not only difficult to interpret and justify, but are also likely violated in the hepatitis B motivating example and other survival/time to event settings as well.

Insights into the Cross-world Independence Assumption of Causal Mediation Analysis

Causal mediation analysis is a useful tool for epidemiologic research, but it has been criticized for relying on a "cross-world" independence assumption that counterfactual outcome and mediator values are independent even in causal worlds where the exposure assignments for the outcome and mediator differ. This assumption is empirically difficult to verify and problematic to justify based on background knowledge. In the present article, we aim to assist the applied researcher in understanding this assumption. Synthesizing what is known about the cross-world independence assumption, we discuss the relationship between assumptions for causal mediation analyses, causal models, and nonparametric identification of natural direct and indirect effects. In particular, we give a practical example of an applied setting where the cross-world independence assumption is violated even without any post-treatment confounding. Further, we review possible alternatives to the cross-world independence assumption, including the use of bounds that avoid the assumption altogether. Finally, we carry out a numeric study in which the cross-world independence assumption is violated to assess the ensuing bias in estimating natural direct and indirect effects. We conclude with recommendations for carrying out causal mediation analyses.

Reducing socio-economic inequalities in all-cause mortality: a counterfactual mediation approach

Background

Socio-economic inequalities in mortality are well established, yet the contribution of intermediate risk factors that may underlie these relationships remains unclear. We evaluated the role of multiple modifiable intermediate risk factors underlying socio-economic-associated mortality and quantified the potential impact of reducing early all-cause mortality by hypothetically altering socio-economic risk factors.

Methods

Data were from seven cohort studies participating in the LIFEPATH Consortium (total n = 179 090). Using both socio-economic position (SEP) (based on occupation) and education, we estimated the natural direct effect on all-cause mortality and the natural indirect effect via the joint mediating role of smoking, alcohol intake, dietary patterns, physical activity, body mass index, hypertension, diabetes and coronary artery disease. Hazard ratios (HRs) were estimated, using counterfactual natural effect models under different hypothetical actions of either lower or higher SEP or education.

Results

Lower SEP and education were associated with an increase in all-cause mortality within an average follow-up time of 17.5 years. Mortality was reduced via modelled hypothetical actions of increasing SEP or education. Through higher education, the HR was 0.85 [95% confidence interval (CI) 0.84, 0.86] for women and 0.71 (95% CI 0.70, 0.74) for men, compared with lower education. In addition, 34% and 38% of the effect was jointly mediated for women and men, respectively. The benefits from altering SEP were slightly more modest.

Conclusions

These observational findings support policies to reduce mortality both through improving socio-economic circumstances and increasing education, and by altering intermediaries, such as lifestyle behaviours and morbidities.

Mediation effects that emulate a target randomised trial: Simulation-based evaluation of ill-defined interventions on multiple mediators

Many epidemiological questions concern potential interventions to alter the pathways presumed to mediate an association. For example, we consider a study that investigates the benefit of interventions in young adulthood for ameliorating the poorer mid-life psychosocial outcomes of adolescent self-harmers relative to their healthy peers. Two methodological challenges arise. First, mediation methods have hitherto mostly focused on the elusive task of discovering pathways, rather than on the evaluation of mediator interventions. Second, the complexity of such questions is invariably such that there are no well-defined mediator interventions (i.e. actual treatments, programs, etc.) for which data exist on the relevant populations, outcomes and time-spans of interest. Instead, researchers must rely on exposure (non-intervention) data, that is, on mediator measures such as depression symptoms for which the actual interventions that one might implement to alter them are not well defined. We propose a novel framework that addresses these challenges by defining mediation effects that map to a target trial of hypothetical interventions targeting multiple mediators for which we simulate the effects. Specifically, we specify a target trial addressing three policy-relevant questions, regarding the impacts of hypothetical interventions that would shift the mediators' distributions (separately under various interdependence assumptions, jointly or sequentially) to user-specified distributions that can be emulated with the observed data. We then define novel interventional effects that map to this trial, simulating shifts by setting mediators to random draws from those distributions. We show that estimation using a g-computation method is possible under an expanded set of causal assumptions relative to inference with well-defined interventions, which reflects the lower level of evidence that is expected with ill-defined interventions. Application to the self-harm example in the Victorian Adolescent Health Cohort Study illustrates the value of our proposal for informing the design and evaluation of actual interventions in the future.

Identification of causal intervention effects under contagion

Defining and identifying causal intervention effects for transmissible infectious disease outcomes is challenging because a treatment - such as a vaccine - given to one individual may affect the infection outcomes of others. Epidemiologists have proposed causal estimands to quantify effects of interventions under contagion using a two-person partnership model. These simple conceptual models have helped researchers develop causal estimands relevant to clinical evaluation of vaccine effects. However, many of these partnership models are formulated under structural assumptions that preclude realistic infectious disease transmission dynamics, limiting their conceptual usefulness in defining and identifying causal treatment effects in empirical intervention trials. In this paper, we propose causal intervention effects in two-person partnerships under arbitrary infectious disease transmission dynamics, and give nonparametric identification results showing how effects can be estimated in empirical trials using time-to-infection or binary outcome data. The key insight is that contagion is a causal phenomenon that induces conditional independencies on infection outcomes that can be exploited for the identification of clinically meaningful causal estimands. These new estimands are compared to existing quantities, and results are illustrated using a realistic simulation of an HIV vaccine trial.

Explained variation under the additive hazards model

We study explained variation under the additive hazards regression model for right-censored data. We consider different approaches for developing such a measure, and focus on one that estimates the proportion of variation in the failure time explained by the covariates. We study the properties of the measure both analytically, and through extensive simulations. We apply the measure to a well-known survival dataset as well as the linked surveillance, epidemiology, and end results-Medicare database for prediction of mortality in early stage prostate cancer patients using high-dimensional claims codes.

Defining causal mediation with a longitudinal mediator and a survival outcome

In the context of causal mediation analysis, prevailing notions of direct and indirect effects are based on nested counterfactuals. These can be problematic regarding interpretation and identifiability especially when the mediator is a time-dependent process and the outcome is survival or, more generally, a time-to-event outcome. We propose and discuss an alternative definition of mediated effects that does not suffer from these problems, and is more transparent than the current alternatives. Our proposal is based on the extended graphical approach of Robins and Richardson (in: Shrout (ed) Causality and psychopathology: finding the determinants of disorders and their cures, Oxford University Press, Oxford, 2011), where treatment is decomposed into different components, or aspects, along different causal paths corresponding to real world mechanisms. This is an interesting alternative motivation for any causal mediation setting, but especially for survival outcomes. We give assumptions allowing identifiability of such alternative mediated effects leading to the familiar mediation g-formula (Robins in Math Model 7:1393, 1986); this implies that a number of available methods of estimation can be applied.