A generalized theory of separable effects in competing event settings

Towards a Clearer Causal Question Underlying the Association Between Cancer and Dementia

BACKGROUND

Several observational studies have described an inverse association between cancer diagnosis and subsequent dementia risk. Multiple biologic mechanisms and potential biases have been proposed in attempts to explain this association. One proposed explanation is the opposite expression of Pin1 in cancer and dementia, and we use this explanation and potential drug target to illustrate the required assumptions and potential sources of bias for inferring an effect of Pin1 on dementia risk from analyses measuring cancer diagnosis as a proxy for Pin1 expression.

METHODS

We used data from the Rotterdam Study, a population-based cohort. We estimate the association between cancer diagnosis (as a proxy for Pin1) and subsequent dementia diagnosis using two different proxy methods and with confounding and censoring for death addressed with inverse probability weights. We estimate and compare the complements of a weighted Kaplan-Meier survival estimator at 20 years of follow-up.

RESULTS

Out of 3634 participants, 899 (25%) were diagnosed with cancer, of whom 53 (6%) had dementia, and 567 (63%) died. Among those without cancer, 15% (411) were diagnosed with dementia, and 667 (24%) died over follow-up. Depending on the confounding and selection bias control, and the way in which cancer was used as a time-varying proxy exposure, the risk ratio for dementia diagnosis ranged from 0.71 (95% confidence interval [CI] = 0.49, 0.95) to 1.1 (95% CI = 0.79, 1.3).

CONCLUSION

Being explicit about the underlying mechanism of interest is key to maximizing what we can learn from this cancer-dementia association given available or readily collected data, and to defining, detecting, and preventing potential biases.

Direct and indirect treatment effects in the presence of semicompeting risks

Semicompeting risks refer to the phenomenon that the terminal event (such as death) can censor the nonterminal event (such as disease progression) but not vice versa. The treatment effect on the terminal event can be delivered either directly following the treatment or indirectly through the nonterminal event. We consider 2 strategies to decompose the total effect into a direct effect and an indirect effect under the framework of mediation analysis in completely randomized experiments by adjusting the prevalence and hazard of nonterminal events, respectively. They require slightly different assumptions on cross-world quantities to achieve identifiability. We establish asymptotic properties for the estimated counterfactual cumulative incidences and decomposed treatment effects. We illustrate the subtle difference between these 2 decompositions through simulation studies and two real-data applications in the Supplementary Materials.

Selection Bias in Health Research: Quantifying, Eliminating, or Exacerbating Health Disparities?

Purpose of review

To summarize recent literature on selection bias in disparities research addressing either descriptive or causal questions, with examples from dementia research.

Recent findings

Defining a clear estimand, including the target population, is essential to assess whether generalizability bias or collider-stratification bias are threats to inferences. Selection bias in disparities research can result from sampling strategies, differential inclusion pipelines, loss to follow-up, and competing events. If competing events occur, several potentially relevant estimands can be estimated under different assumptions, with different interpretations. The apparent magnitude of a disparity can differ substantially based on the chosen estimand. Both randomized and observational studies may misrepresent health disparities or heterogeneity in treatment effects if they are not based on a known sampling scheme.

Conclusion

Researchers have recently made substantial progress in conceptualization and methods related to selection bias. This progress will improve the relevance of both descriptive and causal health disparities research.

Distinguishing Immunologic and Behavioral Effects of Vaccination

The interpretation of vaccine efficacy estimands is subtle, even in randomized trials designed to quantify the immunologic effects of vaccination. In this article, we introduce terminology to distinguish between different vaccine efficacy estimands and clarify their interpretations. This allows us to explicitly consider the immunologic and behavioral effects of vaccination, and establish that policy-relevant estimands can differ substantially from those commonly reported in vaccine trials. We further show that a conventional vaccine trial allows the identification and estimation of different vaccine estimands under plausible conditions if one additional post-treatment variable is measured. Specifically, we utilize a "belief variable" that indicates the treatment an individual believed they had received. The belief variable is similar to "blinding assessment" variables that are occasionally collected in placebo-controlled trials in other fields. We illustrate the relations between the different estimands, and their practical relevance, in numerical examples based on an influenza vaccine trial.

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.

Causal inference with recurrent and competing events

Many research questions concern treatment effects on outcomes that can recur several times in the same individual. For example, medical researchers are interested in treatment effects on hospitalizations in heart failure patients and sports injuries in athletes. Competing events, such as death, complicate causal inference in studies of recurrent events because once a competing event occurs, an individual cannot have more recurrent events. Several statistical estimands have been studied in recurrent event settings, with and without competing events. However, the causal interpretations of these estimands, and the conditions that are required to identify these estimands from observed data, have yet to be formalized. Here we use a formal framework for causal inference to formulate several causal estimands in recurrent event settings, with and without competing events. When competing events exist, we clarify when commonly used classical statistical estimands can be interpreted as causal quantities from the causal mediation literature, such as (controlled) direct effects and total effects. Furthermore, we show that recent results on interventionist mediation estimands allow us to define new causal estimands with recurrent and competing events that may be of particular clinical relevance in many subject matter settings. We use causal directed acyclic graphs and single world intervention graphs to illustrate how to reason about identification conditions for the various causal estimands based on subject matter knowledge. Furthermore, using results on counting processes, we show that our causal estimands and their identification conditions, which are articulated in discrete time, converge to classical continuous time counterparts in the limit of fine discretizations of time. We propose estimators and establish their consistency for the various identifying functionals. Finally, we use the proposed estimators to compute the effect of blood pressure lowering treatment on the recurrence of acute kidney injury using data from the Systolic Blood Pressure Intervention Trial.

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.

Effect Measure Modification by Covariates in Mediation: Extending Regression-based Causal Mediation Analysis

Existing methods for regression-based mediation analysis assume that the exposure-mediator effect, exposure-outcome effect, and mediator-outcome effect are constant across levels of the baseline characteristics of patients. However, investigators often have insight into how these underlying effects may be modified by baseline characteristics and are interested in how the resulting mediation effects, such as the natural direct effect (NDE), the natural indirect effect. (NIE), and the proportion mediated, are modified by these baseline characteristics. Motivated by an empirical example of anti-interleukin-1 therapy's benefit on incident anemia reduction and its mediation by an early change in an inflammatory biomarker, we extended the closed-form regression-based causal mediation analysis with effect measure modification (EMM). Using a simulated numerical example, we demonstrated that naive analysis without considering EMM can give biased estimates of NDE and NIE and visually illustrated how baseline characteristics affect the presence and magnitude of EMM of NDE and NIE. We then applied the extended method to the empirical example informed by pathophysiologic insights into potential EMM by age, diabetes, and baseline inflammation. We found that the proportion modified through the early post-treatment inflammatory biomarker was greater for younger, nondiabetic patients with lower baseline level of inflammation, suggesting differential usefulness of the early post-treatment inflammatory biomarker in monitoring patients depending on baseline characteristics. To facilitate the adoption of EMM considerations in causal mediation analysis by the wider clinical and epidemiologic research communities, we developed a free- and open-source R package, regmedint.

Considering Questions Before Methods in Dementia Research With Competing Events and Causal Goals

Studying causal exposure effects on dementia is challenging when death is a competing event. Researchers often interpret death as a potential source of bias, although bias cannot be defined or assessed if the causal question is not explicitly specified. Here we discuss 2 possible notions of a causal effect on dementia risk: the "controlled direct effect" and the "total effect." We provide definitions and discuss the "censoring" assumptions needed for identification in either case and their link to familiar statistical methods. We illustrate concepts in a hypothetical randomized trial on smoking cessation in late midlife, and emulate such a trial using observational data from the Rotterdam Study, the Netherlands, 1990-2015. We estimated a total effect of smoking cessation (compared with continued smoking) on 20-year dementia risk of 2.1 (95% confidence interval: -0.1, 4.2) percentage points and a controlled direct effect of smoking cessation on 20-year dementia risk had death been prevented of -2.7 (95% confidence interval: -6.1, 0.8) percentage points. Our study highlights how analyses corresponding to different causal questions can have different results, here with point estimates on opposite sides of the null. Having a clear causal question in view of the competing event and transparent and explicit assumptions are essential to interpreting results and potential bias.

Emulating Target Trials to Avoid Immortal Time Bias - An Application to Antibiotic Initiation and Preterm Delivery

BACKGROUND

Randomized trials in pregnancy are extremely challenging, and observational studies are often the only option to evaluate medication safety during pregnancy. However, such studies are often susceptible to immortal time bias if treatment initiation occurs after time zero of follow-up. We describe how emulating a sequence of target trials avoids immortal time bias and apply the approach to estimate the safety of antibiotic initiation between 24 and 37 weeks gestation on preterm delivery.

METHODS

The Tsepamo Study captured birth outcomes at hospitals throughout Botswana from 2014 to 2021. We emulated 13 sequential target trials of antibiotic initiation versus no initiation among individuals presenting to care <24 weeks, one for each week from 24 to 37 weeks. For each trial, eligible individuals had not previously initiated antibiotics. We also conducted an analysis susceptible to immortal time bias by defining time zero as 24 weeks and exposure as antibiotic initiation between 24 and 37 weeks. We calculated adjusted risk ratios (RR) and 95% confidence intervals (CI) for preterm delivery.

RESULTS

Of 111,403 eligible individuals, 17,009 (15.3%) initiated antibiotics between 24 and 37 weeks. In the sequence of target trials, RRs (95% CIs) ranged from 1.04 (0.90, 1.19) to 1.24 (1.11, 1.39) (pooled RR: 1.11 [1.06, 1.15]). In the analysis susceptible to immortal time bias, the RR was 0.90 (0.86, 0.94).

CONCLUSIONS

Defining exposure as antibiotic initiation at any time during follow-up after time zero resulted in substantial immortal time bias, making antibiotics appear protective against preterm delivery. Conducting a sequence of target trials can avoid immortal time bias in pregnancy studies.

Initiation of Antihypertensive Medication from Midlife on Incident Dementia: The Health and Retirement Study

BACKGROUND

Hypertension has been identified as a risk factor of dementia, but most randomized trials did not show efficacy in reducing the risk of dementia. Midlife hypertension may be a target for intervention, but it is infeasible to conduct a trial initiating antihypertensive medication from midlife till dementia occurs late life.

OBJECTIVE

We aimed to emulate a target trial to estimate the effectiveness of initiating antihypertensive medication from midlife on reducing incident dementia using observational data.

METHODS

The Health and Retirement Study from 1996 to 2018 was used to emulate a target trial among non-institutional dementia-free subjects aged 45 to 65 years. Dementia status was determined using algorithm based on cognitive tests. Individuals were assigned to initiating antihypertensive medication or not, based on the self-reported use of antihypertensive medication at baseline in 1996. Observational analog of intention-to-treat and per-protocol effects were conducted. Pooled logistic regression models with inverse-probability of treatment and censoring weighting using logistic regression models were applied, and risk ratios (RRs) were calculated, with 200 bootstrapping conducted for the 95% confidence intervals (CIs).

RESULTS

A total of 2,375 subjects were included in the analysis. After 22 years of follow-up, initiating antihypertensive medication reduced incident dementia by 22% (RR = 0.78, 95% CI: 0.63, 0.99). No significant reduction of incident dementia was observed with sustained use of antihypertensive medication.

CONCLUSION

Initiating antihypertensive medication from midlife may be beneficial for reducing incident dementia in late life. Future studies are warranted to estimate the effectiveness using large samples with improved clinical measurements.

Estimating causal effects in the presence of competing events using regression standardisation with the Stata command standsurv

BACKGROUND

When interested in a time-to-event outcome, competing events that prevent the occurrence of the event of interest may be present. In the presence of competing events, various estimands have been suggested for defining the causal effect of treatment on the event of interest. Depending on the estimand, the competing events are either accommodated or eliminated, resulting in causal effects with different interpretations. The former approach captures the total effect of treatment on the event of interest while the latter approach captures the direct effect of treatment on the event of interest that is not mediated by the competing event. Separable effects have also been defined for settings where the treatment can be partitioned into two components that affect the event of interest and the competing event through different causal pathways.

METHODS

We outline various causal effects that may be of interest in the presence of competing events, including total, direct and separable effects, and describe how to obtain estimates using regression standardisation with the Stata command standsurv. Regression standardisation is applied by obtaining the average of individual estimates across all individuals in a study population after fitting a survival model.

RESULTS

With standsurv several contrasts of interest can be calculated including differences, ratios and other user-defined functions. Confidence intervals can also be obtained using the delta method. Throughout we use an example analysing a publicly available dataset on prostate cancer to allow the reader to replicate the analysis and further explore the different effects of interest.

CONCLUSIONS

Several causal effects can be defined in the presence of competing events and, under assumptions, estimates of those can be obtained using regression standardisation with the Stata command standsurv. The choice of which causal effect to define should be given careful consideration based on the research question and the audience to which the findings will be communicated.

Translating questions to estimands in randomized clinical trials with intercurrent events

Intercurrent (post‐treatment) events occur frequently in randomized trials, and investigators often express interest in treatment effects that suitably take account of these events. Contrasts that naively condition on intercurrent events do not have a straight‐forward causal interpretation, and the practical relevance of other commonly used approaches is debated. In this work, we discuss how to formulate and choose an estimand, beyond the marginal intention‐to‐treat effect, from the point of view of a decision maker and drug developer. In particular, we argue that careful articulation of a practically useful research question should either reflect decision making at this point in time or future drug development. Indeed, a substantially interesting estimand is simply a formalization of the (plain English) description of a research question. A common feature of estimands that are practically useful is that they correspond to possibly hypothetical but well‐defined interventions in identifiable (sub)populations. To illustrate our points, we consider five examples that were recently used to motivate consideration of principal stratum estimands in clinical trials. In all of these examples, we propose alternative causal estimands, such as conditional effects, sequential regime effects, and separable effects, that correspond to explicit research questions of substantial interest.

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.